Math
Advanced Math Operations
Adjacency Matrix Calculator - Convert between adjacency matrix, edge list, and adjacency list. Auto-detects directed/undirected graphs, computes degree sequence, density, connected components, and matrix powers — with an interactive SVG graph visualization. New
Antilog Calculator - Calculate the antilogarithm (antilog) of any number with any base. Features step-by-step calculation, interactive visualization, base comparison chart, and comprehensive explanations of logarithmic functions.
Beta Function Calculator - Calculate the beta function B(x, y) with step-by-step calculations, gamma function relationship, interactive visualization, and detailed mathematical explanations.
Binomial Coefficient Calculator - Calculate binomial coefficients C(n, k) with step-by-step solutions, Pascal's triangle visualization, and real-world probability applications.
Binomial Probability Distribution Calculator - Calculate binomial probabilities P(X=k), cumulative probabilities P(X≤k), P(X≥k), with interactive PMF/CDF charts, step-by-step solutions, and complete distribution tables.
Bitwise Calculator - Perform bitwise operations (AND, OR, XOR, NOT) and bit shift operations on integers with interactive visual bit diagrams showing each bit position. Featured
Boolean Algebra Simplifier - Simplify Boolean expressions using algebraic laws, Quine-McCluskey, and Karnaugh map minimization. Enter any logic expression (AND, OR, NOT, XOR, NAND, NOR) and instantly get the minimal SOP/POS form, full truth table, K-map visualization, gate diagram, step-by-step law applications, and NAND/NOR-only equivalents. New
Central Limit Theorem Calculator - Calculate probabilities using the Central Limit Theorem (CLT) with interactive visualizations, step-by-step solutions, and Z-score calculations for sample means.
Chinese Remainder Theorem Calculator - Solve systems of simultaneous congruences using the Chinese Remainder Theorem (CRT). Find the smallest x satisfying multiple modular equations with step-by-step Extended Euclidean Algorithm breakdown, interactive number line visualization, and verification.
Combination Calculator - Calculate combinations C(n,k) with step-by-step solutions, Pascal's Triangle visualization, interactive diagrams, and detailed formula breakdowns for combinatorics problems.
Complementary Error Function Calculator - Calculate the complementary error function erfc(x) with interactive visualization, step-by-step solution, and comprehensive erfc table for values from -3 to 3.
Complex Number Calculator - Perform operations with complex numbers: add, subtract, multiply, divide, convert forms, calculate modulus, argument, conjugate, powers and roots with detailed step-by-step solutions and interactive complex plane visualization.
Continued Fraction Calculator - Convert any decimal, fraction, or square root to its continued fraction representation with convergents, step-by-step Euclidean algorithm, and interactive visualization.
Derangement (Subfactorial) Calculator - Calculate the number of derangements (subfactorial !n) for n elements where no element appears in its original position. Features step-by-step inclusion-exclusion formula, interactive visualization, derangement table, and probability analysis.
Dijkstra's Shortest Path Calculator - Find the shortest path between nodes in a weighted graph using Dijkstra's algorithm. Features interactive graph visualization, step-by-step priority queue trace, and shortest path tree display.
Entropy Calculator - Calculate Shannon entropy of probability distributions with step-by-step formulas, interactive visualizations, entropy classification, and educational insights for information theory analysis.
Error Function Calculator - Calculate the error function erf(x), complementary error function erfc(x), and inverse error function with interactive Gaussian curve visualization, step-by-step explanations, and comprehensive analysis for statistics and probability.
Euler's Totient Function Calculator - Calculate Euler's totient function φ(n) with step-by-step prime factorization, interactive coprime number grid, and detailed analysis. Essential for RSA cryptography, modular arithmetic, and number theory.
Exponential Decay Calculator - Calculate exponential decay with interactive visualizations, half-life computation, decay constant, and step-by-step solutions. Solve for initial amount, final amount, decay rate, or time.
Exponential Growth Calculator - Calculate exponential growth and decay with step-by-step solutions, interactive growth curve visualization, and high-precision results for population, investment, and scientific modeling.
Exponential Integral Calculator - Calculate the exponential integral Ei(x) with high precision, interactive visualization, and detailed step-by-step mathematical derivation.
Exponents Calculator - Calculate exponents (powers) with high precision. Supports fractional exponents, negative exponents, and provides detailed step-by-step solutions with visual explanations and exponent rule demonstrations.
Extended Euclidean Algorithm Calculator - Calculate the GCD of two integers and find Bézout coefficients using the Extended Euclidean Algorithm, with step-by-step table, back-substitution, and modular inverse.
Factorial Calculator - Calculate the factorial of any non-negative integer (n!) with step-by-step expansion, scientific notation for large numbers, digit count analysis, and factorial growth visualization. Supports values up to 1 million.
Gamma Function Calculator - Calculate the Gamma function with step-by-step solutions, interactive graphs, and factorial comparison tables. Supports both positive and negative real numbers.
Golden Ratio Calculator - Calculate golden ratio proportions from any number. Generate phi-based sequences, find complementary segments, golden rectangle dimensions, and explore the divine proportion with step-by-step calculations and visualizations.
Graph Coloring Calculator - Find the chromatic number and a valid vertex coloring for any undirected graph. Enter edges or an adjacency list, and get the minimum number of colors, a color assignment, animated DSATUR step-by-step solution, and an interactive SVG graph visualization. New
Graph Degree Sequence Validator - Use the Havel-Hakimi algorithm to determine if a given sequence of numbers can form a simple, undirected graph. Features animated step-by-step visualization, adjacency matrix, and a sample graph rendering.
Group Theory Order Calculator - Compute the order of every element in a finite group, check whether the group is abelian or cyclic, render the Cayley table as a color-coded heatmap, and visualize the subgroup lattice as a Hasse diagram. Supports cyclic Z_n, direct products Z_m x Z_n, dihedral D_n, and symmetric S_n. New
Half Life Calculator - Calculate half-life, initial quantity, remaining quantity, or elapsed time in exponential decay with interactive decay curve visualization, step-by-step formulas, and preset isotope values.
Hamiltonian Path Checker - Check whether a graph contains a Hamiltonian path or Hamiltonian cycle. Runs backtracking with Warnsdorff pruning, verifies connectivity and degree prerequisites, tests Dirac and Ore sufficient conditions, and shows the witness path on an animated SVG visualization. New
Inclusion-Exclusion Calculator - Compute the size of a union of up to 5 sets using the inclusion–exclusion principle. Enter raw elements or cardinalities of every intersection — get the signed expansion, a live Venn-diagram visualization, and the size of every disjoint region. New
Karnaugh Map (K-Map) Solver - Minimize Boolean logic functions using Karnaugh maps. Enter minterms, maxterms, or toggle a truth table — get the simplified Sum-of-Products (SOP) or Product-of-Sums (POS) expression with color-coded grouping visualization, prime implicants, essential prime implicants, and step-by-step Quine-McCluskey solution. New
Linear Programming Solver - Solve linear programming problems online using the simplex method. Supports maximize or minimize objectives, mixed ≤/≥/= constraints, up to 8 decision variables, and for 2-variable LPs shows an interactive feasible-region plot with every vertex and the optimum highlighted. New
Markov Chain Steady State Calculator - Calculate the steady-state (stationary) distribution of a Markov chain from its transition matrix. Includes interactive state diagram, convergence visualization, step-by-step solution, and power iteration analysis.
Minimum Spanning Tree Calculator - Calculate the Minimum Spanning Tree (MST) of a weighted graph using Kruskal's or Prim's algorithm. Features interactive graph visualization, step-by-step algorithm trace, and edge selection animation.
Modular Exponentiation Calculator - Calculate modular exponentiation a^b mod n efficiently using the binary exponentiation (fast power) algorithm. Enter the base, exponent, and modulus to get instant results with a step-by-step breakdown of the squaring-and-multiply method, binary decomposition visualization, and cryptographic context. New
Modular Multiplicative Inverse Calculator - Calculate the modular multiplicative inverse of an integer a under modulo m using the Extended Euclidean Algorithm, with step-by-step table, verification, and clock visualization.
Negative Binomial Distribution Calculator - Calculate negative binomial distribution probabilities for modeling the number of trials or failures needed to achieve a target number of successes. Get exact PMF, CDF, step-by-step solutions, interactive charts, and trial sequence visualizations. New
Network Flow Calculator (Max Flow) - Compute the maximum flow from source to sink in a capacitated directed network using the Ford-Fulkerson method (Edmonds-Karp). Animates every augmenting path, shows residual capacities, saturated edges, and the min-cut partition that proves optimality. New
Percent Growth Rate Calculator - Calculate percent growth rate with multiple methods: simple growth, compound annual growth rate (CAGR), and average growth rate. Features interactive visualizations, year-by-year analysis, and detailed step-by-step calculations. Featured
Permutation Calculator - Calculate permutations P(n,r) with step-by-step solutions, visual explanations, formula breakdown, and practical examples. Find how many ways to arrange r items from n total items where order matters.
Permutations with Repetition Calculator - Calculate the number of permutations with repetition (ordered arrangements with replacement) using the formula n^r. Enter the number of items and positions to get instant results with step-by-step solutions, slot-machine visualizations, comparisons to other counting methods, and real-world examples like passwords, PIN codes, and license plates. New
Pigeonhole Principle Calculator - Calculate the minimum number of items guaranteed to share a container using the pigeonhole principle. Includes interactive visualization, step-by-step proof, generalized analysis, and real-world examples.
Planar Graph Checker - Check whether a graph is planar (drawable without edge crossings) using Kuratowski's theorem. Detects K5 and K3,3 subdivisions, verifies Euler's inequality m ≤ 3n − 6, and highlights the forbidden minor visually when the graph is non-planar. New
Poisson Distribution Calculator - Calculate Poisson probabilities P(X=k), cumulative probabilities, and visualize PMF/CDF distributions with detailed step-by-step solutions.
Polynomial Roots Calculator - Calculate the roots of polynomial equations up to degree 4 with detailed step-by-step solutions, interactive graph visualization, and root analysis. Supports linear, quadratic, cubic, and quartic equations.
Primitive Root Calculator - Find all primitive roots of a given modulus n — generators of the multiplicative group (Z/nZ)*. Enter any positive integer to get primitive roots, Euler's totient, cyclic group visualization, and a step-by-step verification with power tables.
Probability Calculator - Calculate probabilities of events using addition rule, conditional probability, and Bayes' theorem with interactive Venn diagrams and step-by-step solutions.
Probability Distribution Calculator - Calculate probabilities, cumulative distributions (CDF), and quantiles for Normal, Binomial, Poisson, Exponential, Uniform, Chi-Square, and Student's t distributions with step-by-step solutions and interactive visualizations.
Proportion Calculator - Solve proportion problems and find missing values with detailed step-by-step solutions, interactive visual diagrams, and comprehensive explanations of proportion relationships. Featured
Quadratic Formula Calculator - Solve quadratic equations using the quadratic formula with step-by-step solutions, discriminant analysis, vertex form conversion, and interactive parabola visualization.
Ring and Field Calculator - Compute addition, subtraction, multiplication, division, inverses, and powers in modular rings Z_n and Galois finite fields GF(p^k). Visualise Cayley tables, classify units, zero divisors, nilpotents, and idempotents, and inspect the multiplicative group structure. New
Rounding Calculator - Round numbers to decimal places, significant figures, or nearest value. Compare 6 rounding methods side by side with visual number line and step-by-step explanations. New
Scientific Calculator - A full-featured online scientific calculator with trigonometric, logarithmic, exponential, factorial, and other advanced mathematical functions. Supports degree and radian modes, memory functions, calculation history, and keyboard input.
Scientific Notation Calculator - Convert numbers to scientific notation, perform arithmetic operations (+, -, ×, ÷), compare values, and visualize results with step-by-step explanations and interactive diagrams.
Set Theory Calculator - Perform set operations including Union (A ∪ B), Intersection (A ∩ B), Difference (A − B), Symmetric Difference (A ∆ B), Cartesian Product (A × B), Power Set, and Complement. Visualize with interactive Venn diagrams.
Significant Figures Calculator - Round numbers to significant figures, count sig figs with digit-by-digit analysis, and perform arithmetic with proper significant figure rules. New
Stable Marriage Problem Solver - Solve the stable marriage / stable matching problem using the Gale-Shapley algorithm. Paste ranked preference lists for two equally-sized groups and get the guaranteed-stable pairing, with an animated proposal-by-proposal trace, satisfaction statistics, blocking-pair verification, and an interactive bipartite visualization. New
Stirling Numbers Calculator - Calculate Stirling numbers of the First Kind (unsigned, permutations into cycles) and Second Kind (set partitions into non-empty subsets). Features interactive triangle visualization, step-by-step recurrence derivation, full triangle tables, and combinatorial interpretations.
Sum of Cubes Calculator - Calculate the sum of consecutive cubes from n₁³ to n₂³ with step-by-step formula breakdown, visual cube representation, and mathematical analysis. Perfect for algebra, calculus, and number theory studies.
Sum of Positive Integers Calculator - Calculate the sum of consecutive positive integers using the elegant Gauss summation formula. Features step-by-step calculation breakdown, visual pairing diagrams, and educational insights into arithmetic sequences. Featured
Sum of Squares Calculator - Calculate the sum of consecutive square numbers (1² + 2² + ... + n²) with step-by-step formulas, interactive charts, and visual geometric representations.
Topological Sort Calculator - Compute a topological ordering of a directed acyclic graph (DAG) using Kahn's algorithm or DFS. Detects cycles, reports the cycle path, builds a parallel-execution layer view, supports lexicographically smallest ordering, and animates each step on an interactive graph. New
Traveling Salesman Solver (TSP) - Find the shortest tour that visits every city exactly once and returns to the start. Exact dynamic programming (Held-Karp) for small instances and nearest-neighbor + 2-opt heuristics for larger ones. Accepts coordinates or a distance matrix and renders an animated SVG tour. New
Truth Table Generator - Generate truth tables for any boolean logic expression. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, and conditional operators. Visualize logic gates with animated evaluation.
Venn Diagram Generator (3 Sets) - Generate interactive Venn diagrams for three sets. Enter set elements or region values, customize colors, and download as PNG or SVG. Visualize unions, intersections, and differences instantly.
Algebra Calculators
Absolute Value Equation Solver - Solve equations involving absolute values step by step. Shows both positive and negative cases with detailed explanations and verification.
Absolute Value Inequality Solver - Solve inequalities involving absolute values (e.g., |x+a| < b, |x-2| > 3). Understand 'and' vs 'or' conditions with detailed step-by-step solutions.
Age Word Problem Solver - Solve classic age word problems step by step — "X is N years older than Y", "in Y years X will be K times Y", three-person age ratios, and father-son past-vs-present puzzles. Sets up the algebra, solves the linear system, verifies the answer, and animates an age timeline for past, present, and future ages. New
Algebraic Expression Simplifier - Simplify complex algebraic expressions by combining like terms, applying the distributive property, and reducing fractions. Features step-by-step solutions, multiple simplification modes, and detailed explanations.
Binomial Theorem Expansion Calculator - Expand (a+b)^n using the binomial theorem. Get step-by-step expansion with each term, binomial coefficients, Pascal's triangle visualization, and detailed coefficient analysis. New
Coin Word Problem Solver - Solve classic coin word problems step by step — "I have N coins totaling $V in nickels and dimes", "twice as many quarters as dimes", three-coin mixtures with count relationships, and "fewest coins to make $V". Sets up the algebra, solves the linear system, animates coin stacks, and verifies the answer. New
Completing the Square Calculator - Solve quadratic equations by completing the square. Get detailed step-by-step algebraic work, vertex form, geometric visualization, and interactive parabola graph. New
Cubic Equation Solver - Solve any cubic equation ax³+bx²+cx+d=0 using Cardano's formula. Get all three roots (real and complex), step-by-step solution, discriminant analysis, and interactive graph. New
Descartes' Rule of Signs Calculator - Use Descartes' Rule of Signs to determine the possible number of positive and negative real roots of any polynomial. Enter coefficients and see step-by-step sign change analysis with visual diagrams. New
Distance-Speed-Time Triangle Calculator - Solve any one of distance, speed, or time given the other two. Use the interactive D-S-T triangle to pick the unknown, mix units freely (km, mi, m, ft, km/h, mph, m/s, ft/s, knots, sec/min/hr/day), enter time as 1h 30m or 5400 sec, and see an animated journey, full step-by-step solution, plus bonus modes for multi-leg average speed and round-trip harmonic-mean speed. New
Domain and Range Calculator - Determine the domain (possible inputs) and range (possible outputs) of algebraic functions with step-by-step analysis and interval notation.
Expand Polynomials Calculator - Multiply and expand polynomials (binomials, trinomials, and higher-degree expressions) using FOIL method and Binomial Theorem. Get step-by-step solutions with detailed explanations.
Exponential Equation Solver - Solve exponential equations step by step. Supports simple, linear exponent, coefficient, two-base, and quadratic-in-exponential forms. Get detailed solutions with domain analysis and interactive graphs. New
Function Composition Calculator - Calculate the composition of two functions (f ∘ g)(x) and (g ∘ f)(x) with detailed step-by-step instructions showing how to compose functions algebraically.
Function Grapher - Visualize algebraic functions on an interactive coordinate system. Plot multiple equations, identify key features like intercepts, asymptotes, and analyze function behavior.
Function Odd Even Neither Checker - Determine whether a function f(x) is even, odd, or neither with step-by-step algebraic proof, symmetry graph, numerical verification table, and even-odd decomposition. Supports polynomials, trigonometric, exponential, logarithmic, and absolute value functions.
Inequality Solver - Solve linear, quadratic, polynomial, and rational inequalities with step-by-step solutions. Display results graphically on a number line and in interval notation.
Inverse Function Calculator - Calculate the inverse function f^(-1)(x) of a given function f(x) with detailed step-by-step instructions showing how to find the inverse algebraically.
Linear Equation Solver - Solve single-variable linear equations (e.g., ax + b = c) with detailed step-by-step solutions. Shows all algebraic manipulations and verifies the answer.
Literal Equation Solver - Solve literal equations and rearrange multi-variable formulas. Enter any equation like A = πr², choose a variable, and get the isolated solution with step-by-step algebraic manipulation. New
Logarithmic Equation Solver - Solve logarithmic equations step by step. Supports log, ln, and custom bases. Enter any log equation and get the solution with detailed steps, domain analysis, and interactive graph. New
Mixture Problem Solver - Solve concentration and mixture word problems step by step. Blend two solutions of any strength, find how much of a stock solution to add to reach a target concentration, dilute with pure water, strengthen with pure solute, or drain-and-replace part of a mixture — with an animated two-beaker pour visualization, conservation-of-mass equations, and full LaTeX explanations. New
Polar Equation Plotter - Plot polar equations interactively — graph r = sin(3θ), r = θ (Archimedean spiral), cardioids, limaçons, lemniscates and butterfly curves with adjustable θ range, sampling resolution, color palettes and polar grid. Overlay up to three equations on the same canvas and export the chart as crisp SVG or PNG. New
Polynomial Factoring Calculator - Factor polynomials using various methods including GCF, difference of squares, perfect square trinomials, sum/difference of cubes, and quadratic trinomials. Features step-by-step solutions, automatic pattern recognition, and verification.
Polynomial Long Division Calculator - Divide one polynomial by another using long division. Shows the complete step-by-step process, quotient, and remainder with detailed explanations.
Quartic Equation Solver - Solve any quartic equation ax⁴+bx³+cx²+dx+e=0 using Ferrari's method. Get all four roots (real and complex), step-by-step solution, discriminant analysis, factored form, and interactive graph. New
Radical Equation Solver - Solve equations containing radicals (square roots, cube roots, etc.) with step-by-step solutions. Automatically checks for extraneous solutions to ensure accuracy.
Radical Simplifier - Simplify square roots and higher-order radicals into their simplest radical form (e.g., sqrt(50) becomes 5*sqrt(2)), including rationalizing the denominator. Features step-by-step solutions with prime factorization and detailed explanations.
Rational Equation Solver - Solve rational equations containing fractions with variables in the denominator. Get step-by-step solutions showing LCD calculation, fraction clearing, polynomial solving, and extraneous solution checks with interactive graphs. New
Rational Expression Calculator - Simplify, add, subtract, multiply, or divide rational expressions (fractions involving polynomials). Features step-by-step solutions, factoring visualization, domain analysis, and detailed explanations.
Rational Root Theorem Calculator - Use the Rational Root Theorem to find all possible rational roots of a polynomial with integer coefficients. Enter coefficients and get the complete list of candidates, actual roots verification, step-by-step factoring, and interactive visualization. New
Standard Form to Slope-Intercept Converter - Convert linear equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Enter the equation or coefficients to get instant results with step-by-step solution, graph, and key line properties. New
Synthetic Division Calculator - Divide polynomials by linear binomials (x - a) using the streamlined synthetic division method. Shows step-by-step process with coefficients and remainder.
System of Inequalities Grapher - Visualize the feasible region (solution set) for a system of two or more linear inequalities. Graph each inequality on a coordinate plane and identify the intersection region.
System of Linear Equations Solver - Solve systems of linear equations (2x2, 3x3, or larger) using Gaussian elimination, Cramer's Rule, or matrix methods. Features detailed step-by-step solutions and multiple solution approaches.
System of Nonlinear Equations Solver - Solve systems of two or more nonlinear equations using the Newton-Raphson method. Find all solutions with step-by-step iterations, Jacobian matrix, convergence analysis, and interactive contour graph. New
Train Meeting Problem Solver - Solve classic two-train word problems step by step. Handles trains meeting head-on, overtaking in the same direction, two trains crossing each other (with lengths), a train passing a pole, and a train crossing a platform or bridge — with animated track visualization, relative-speed math, and full LaTeX explanations. New
Trigonometric Equation Solver - Solve trigonometric equations step by step. Enter any trig equation like sin(x)=0.5 or 2cos(x)+1=0 and get all solutions in any interval, with unit circle visualization and interactive graph. New
Vertex and Axis of Symmetry Calculator - Calculate the vertex (maximum or minimum point) and the axis of symmetry for any quadratic function (parabola) with detailed step-by-step solutions.
Work Rate Problem Solver - Solve "A and B working together" rate problems in five flavors: combined time when both work simultaneously, the missing solo time of one worker, fill-vs-drain pipe problems, alternating-shift problems, and partial completion where one worker joins midway. Animated dual-pie progress visualization, full LaTeX step-by-step explanation, and unit-friendly hour/day/minute support. New
X and Y Intercept Calculator - Calculate the x-intercept (where the graph crosses the x-axis) and y-intercept (where the graph crosses the y-axis) of any equation with detailed step-by-step solutions.
Area Calculators
Area of a Circle Calculator - Calculate the area of a circle from radius, diameter, or circumference. Get instant results with step-by-step calculations, interactive diagrams, and comprehensive circle metrics.
Area of a Parallelogram Calculator - Calculate the area of a parallelogram using three methods: base and height, two sides with included angle, or diagonals with intersection angle. Get step-by-step calculations with formulas.
Area of A Sector Calculator - Calculate the area of a sector of a circle with interactive SVG diagram, step-by-step calculation, arc length, and comprehensive sector formulas using radius and central angle.
Area of a Trapezoid Calculator - Calculate the area of a trapezoid instantly with our interactive calculator. Features a dynamic visual diagram, step-by-step formula breakdown, and support for various unit systems.
Area of An Ellipse Calculator - Calculate ellipse area instantly with our free tool. Get area, perimeter (Ramanujan formula), eccentricity, and interactive visualization. Perfect for geometry, engineering, and design calculations.
Area of Equilateral Triangle Calculator - Calculate the area of an equilateral triangle from side length, height, or perimeter. Includes step-by-step formulas, interactive triangle diagram, and complete property calculations.
Surface Area Calculator - Calculate the surface area of 8 geometric shapes including sphere, cylinder, cone, cuboid, rectangular prism, triangular prism, square pyramid, and tetrahedron with detailed step-by-step solutions and interactive diagrams.
Surface Area of a Cone Calculator - Calculate the surface area of a cone instantly with our free calculator. Get lateral surface area, base area, and total surface area with step-by-step formulas and interactive visual diagram.
Surface Area of a Cube Calculator - Calculate the total surface area of a cube with step-by-step solutions. Find surface area from edge length, space diagonal, face diagonal, or volume with interactive 3D visualization and comprehensive measurements.
Surface Area of a Cylinder Calculator - Calculate the total, lateral, and base surface area of a cylinder with high precision, interactive 3D visualization, step-by-step formula breakdown, and area distribution analysis.
Surface Area of a Rectangular Prism Calculator - Calculate the surface area of a rectangular prism (cuboid/box) with interactive 3D visualization, step-by-step formulas, face-by-face breakdown, and high-precision results.
Surface Area of Sphere Calculator - Calculate the surface area of a sphere from radius or diameter with step-by-step formula breakdown, interactive visualization, and unit conversions. Perfect for geometry, engineering, and science.
Basic Math Operations
Absolute Value Calculator - Calculate the absolute value (modulus) of any real or complex number. See step-by-step solutions, number line visualization, and distance-from-zero animation. New
Amicable Number Checker - Check whether two positive integers form an amicable pair, or enter just one number and let the tool discover its partner automatically. Features animated divisor "handshake" visualizations, step-by-step sigma function breakdowns, aliquot-chain previews, and historical context dating back to Pythagoras. New
Carry and Borrow Visualizer - See carrying and borrowing happen column by column. This animated visualizer walks through every step of long addition and subtraction, including cascading borrows across zeros, so kids and learners can finally see why the trick works. New
Ceiling and Floor Function Calculator - Compute the ceiling ⌈x⌉ and floor ⌊x⌋ of any real number. See step-by-step solutions, interactive number line, staircase graph, and fractional part analysis. New
Common Factor Calculator - Find common factors of two or more numbers with interactive Venn diagram, step-by-step explanations, GCF calculation, and multiple solving methods including prime factorization.
Cross Multiplication Calculator - Solve proportions using cross multiplication. Find the unknown value in a/b = c/d equations with step-by-step solutions and visual diagrams. New
Cube and Cube Root Calculator - Calculate the cube (n³) and cube root (∛n) of any number with step-by-step solutions, perfect cube detection, and interactive visualizations.
Cube Root Calculator - Calculate the cube root of any number with precision up to 1000 decimal places. Features interactive 3D cube visualization, root comparison chart, perfect cube finder, step-by-step solution, and practical volume-to-side converter.
Digital Root Calculator - Calculate the digital root of any number by repeatedly summing its digits until a single digit remains. Supports additive and multiplicative modes, bases 2/8/10/16, animated step-by-step breakdown, O(1) formula verification, and persistence counter. New
Divide Into Two Parts - Divide any number into two parts based on ratios or fractions. Interactive visual balance shows proportional splits with step-by-step calculations and downloadable results.
Divisibility Test Calculator - Test if a number is divisible by another number. Check multiple divisors at once, learn divisibility rules for 2-12, see step-by-step calculations, and explore prime factorization.
Egyptian Multiplication Calculator - Multiply two whole numbers the ancient Egyptian way: by repeated doubling and selective adding. Watch the doubling table build row by row, see which powers of two are picked, and discover why this 4,000-year-old trick is really binary arithmetic in disguise. New
Estimation Calculator - Round and estimate results of arithmetic expressions. See side-by-side comparisons of rounding strategies, visual number lines, error analysis, and step-by-step estimation breakdowns. New
Even or Odd Number Checker - Quickly check if numbers are even or odd. Supports batch input with visual grouping, divisibility explanations, number line visualization, and detailed parity analysis. New
Factor Calculator - Calculate all factors of a number step by step with factor pairs visualization, interactive factor tree diagram, prime factorization, and comprehensive number analysis including perfect square detection.
Fibonacci Number Checker - Instantly check whether any positive integer belongs to the Fibonacci sequence. Uses Gessel's perfect-square theorem for an O(1) mathematical test, reveals the exact index F_n, shows the unique Zeckendorf representation, visualizes the golden spiral, and plots the golden ratio convergence — a complete Fibonacci x-ray in one click. New
Find Minimum and Maximum - Find the minimum and maximum values in any number set with visual data distribution, sorted rankings, statistical analysis, and position indicators for comprehensive data exploration.
First n Digits of e - Generate and analyze the first n digits (up to 1000) of e (Euler's number) with comprehensive digit frequency analysis, pattern exploration, and interactive visualizations.
First n Digits of Pi - Generate and analyze the first n digits (up to 10,000) of Pi (π) with comprehensive digit frequency analysis, pattern exploration, interactive visualizations, and unique Pi-themed insights. Featured
Goldbach Conjecture Verifier - Verify the Goldbach conjecture for any even integer greater than 2. Decompose your number into every possible pair of prime numbers that sum to it, explore the Goldbach partition function g(n), and visualize the famous Goldbach comet interactively. New
Greatest Common Factor Calculator - Calculate the greatest common factor (GCF) of two or more numbers with step-by-step solutions using multiple methods.
Is it a Prime Number? - Check if a number is prime with detailed analysis, factorization, and visual number line representation.
Least Common Multiple Calculator - Calculate the least common multiple (LCM) of two or more numbers with interactive prime factorization visualization, step-by-step solutions, and multiple calculation methods explained.
Long Addition and Subtraction Calculator - Visualize addition and subtraction step by step with column-by-column carrying and borrowing. Color-coded animations show each digit computation for easy learning. New
Long Division Calculator - Solve long division problems step by step. See the full working process with quotient, remainder, and decimal expansion. Perfect for learning and verifying division. New
Long Multiplication Calculator - Solve multiplication problems step-by-step using the long multiplication method. See each partial product, carry digits, and column alignment for clear understanding. New
Möbius Function Calculator - Calculate the Möbius function μ(n) for any positive integer. Instantly returns −1, 0, or +1 with full prime factorization, squarefree analysis, step-by-step explanation, Mertens function M(n), and a color-coded μ-value heatmap showing nearby integers. New
Mental Math Trainer - Sharpen mental arithmetic with daily drills graded across five difficulty levels — from first-grade single-digit addition all the way to two-digit multiplication and percentage estimation. Every problem is paired with a named mental-math strategy (Doubling, Compensating, Place-Value Split, Round-and-Adjust, Nines Trick, Halve-Then-Double, Front-End Estimation, and Distributive Split) and an animated step-by-step coach card, so each drill teaches a technique you can carry to the next problem. The Daily Workout serves a fixed, date-seeded set everyone in the world gets at the same time so you can compare your time and score with friends. Mobile-friendly, print-ready, and built for Common Core mental-math standards, UK Y3-Y6 reasoning, and adult GED, ASVAB, GMAT, and civil-service numeracy prep. New
Mersenne Prime Checker - Test whether 2^p − 1 is a Mersenne prime for a given exponent p. Uses the Lucas–Lehmer primality test with an animated iteration trace, binary bit-pattern visualization, Euclid-Euler perfect-number pairing, and historical context on the 52 known Mersenne primes. New
Modulo Calculator - Calculate modulo (remainder) with step-by-step division process, interactive visual diagrams, and support for integers, decimals, negative numbers, and scientific notation. Featured
Multiplication Calculator - Free online multiplication calculator that multiplies any numbers instantly with detailed step-by-step solutions, visual factor breakdown, and comprehensive result analysis including sign rules and magnitude insights.
Multiplication Table Generator - Generate printable multiplication tables for any range. Customize rows and columns, highlight specific multiples, and export as PDF for classroom or study use. New
n-th Root Calculator - Calculate the n-th root of any number with high precision up to 1000 decimal places. Features step-by-step solutions, visual diagrams, and mathematical notation in both radical and exponential forms.
Number Bonds Generator - Generate animated number bond practice problems for early arithmetic. Pick a total from 5 to 100 (or any custom number), choose Practice Quiz, Bond Chart, or Fact Family mode, and the generator builds a worksheet that pairs each problem with three matching visual models: a cherry part-part-whole diagram, a ten-frame, and a two-color bar model. Built-in self-check, live score tracker, fact-family reveal, and print-ready output make this the friendliest number bonds tool for Kindergarten through Grade 2, Singapore Math classrooms, and homeschool parents. New
Number of Digits Calculator - Calculate the number of digits in any integer, analyze digit distribution, and visualize the breakdown of each position value (ones, tens, hundreds, etc.). Featured
Number Pattern Finder - Identify the pattern in a number sequence and predict the next values. Detects arithmetic, geometric, Fibonacci-like, quadratic, cubic, power, factorial, triangular, and prime patterns with step-by-step explanations. New
Order of Operations Calculator (PEMDAS) - Solve math expressions step by step following PEMDAS/BODMAS order of operations. See each step with highlighted operations, perfect for learning operator precedence. New
Perfect Number Checker - Check if a number is perfect, abundant, or deficient by comparing it to the sum of its proper divisors. View divisor pairs, sigma function values, and an interactive visual breakdown with animated charts. New
Place Value Chart Generator - Visualize place values from billions to thousandths with an interactive chart. Enter any number to see each digit's place value, expanded form, and word representation. New
Prime Factor Calculator - Calculate the prime factors of any number with step-by-step factorization, interactive factor tree visualization, prime factorization in exponential form, and detailed mathematical analysis.
Prime Factorization Calculator - Calculate the prime factorization of any positive integer instantly. Get step-by-step breakdown, factor tree visualization, and complete analysis of prime factors.
Quotient and Remainder Calculator - Calculate quotient and remainder with interactive visual representations, step-by-step explanations, and comprehensive division insights. Featured
Random Math Problem Generator - Generate fresh random math practice problems by grade level (K-8) and topic. Pick from addition, subtraction, multiplication, division, fractions, decimals, percentages, word problems, order of operations, and pre-algebra equations. Each problem ships with an animated visual aid, a hidden step-by-step solution you can reveal on demand, and a built-in self-check answer field — perfect for teachers building worksheets, parents drilling kids, and students self-quizzing for tests. New
Ratio Calculator - Solve proportions, simplify ratios to lowest terms, scale ratios up or down, and generate equivalent ratios. Free online ratio calculator with step-by-step solutions and visual ratio bars. New
Roman Numeral Math Solver - Compute directly with Roman numerals (I, V, X, L, C, D, M). Watch each step: subtractive expansion (IV → IIII), regrouping (5 I → V, 2 V → X, 5 X → L, 2 L → C, 5 C → D, 2 D → M), borrowing for subtraction, the Roman doubling method for multiplication and division, and final canonicalization. Built for students, teachers, history fans, and anyone curious how the ancients actually did arithmetic without a place-value system. New
Russian Peasant Multiplication - Multiply two whole numbers the Russian peasant way: halve the left, double the right, and keep only the odd-left rows. Watch the halving stair build downward step by step, see the parities reveal the binary form of your multiplier, and add up the kept rows to reach the product. New
Skip Counting Generator - Generate skip counting sequences by any number. Visualize patterns on an interactive number line with hop animations, a hundreds chart, and printable sequence lists for classroom use. New
Soroban Abacus Simulator - Practice on a virtual Japanese soroban with realistic bead movement. Click beads to set any value, or feed in an addition, subtraction, multiplication, or division problem and watch the abacus solve it step by step using the traditional 5-complement and 10-complement rules. New
Sort Numbers - Sort numbers in ascending or descending order with comprehensive statistics, visual distribution charts, and detailed analysis. Handles decimals, negatives, and thousands separators. Featured
Square Root (√) Calculator - Calculate the square root of any number with high precision up to 1000 decimals. Features step-by-step explanations, geometric visualizations, and Newton's method demonstration. Featured
Sum Calculator - High-Precision Number Adder Online Featured
Times Tables Quiz - Practice multiplication tables with a live timer, streak counter, and a colour-coded 12×12 heatmap that pinpoints your weakest facts. Pick any combination of tables from 2 to 12, choose Sprint (60-second race), Marathon (fixed length), or Boss Battle (drills only the facts you most often miss), and switch between three question formats — standard, missing factor, and reversed. Every right answer feeds an animated streak bar; every wrong one shakes the card and flags the fact for review. Mobile-friendly, print-ready, and a teacher-loved alternative to flashcards for Years 2–6, Common Core Grade 3, and homeschool drill sessions. New
Unit Rate Calculator - Calculate unit rate from any ratio. Compare prices per unit, find speed per hour, cost per item, and determine the better deal between two options. New
Vedic Math Tricks Calculator - Apply classical Vedic math sutras — Urdhva-Tiryagbhyam (vertically and crosswise), Nikhilam Navatashcaramam Dashatah (all from 9 and the last from 10), Ekadhikena Purvena (by one more than the previous one), and Nikhilam division — to multiply, square, and divide numbers far faster than long multiplication. Each step is animated with cross-lines, base-deficit pills, and a running explanation panel. New
Calculus
Average Rate of Change Calculator - Calculate the average rate of change of a function over an interval [a, b] using the difference quotient. Enter any function f(x), get the secant line slope, step-by-step solution with MathJax formulas, and an interactive graph showing the secant line and curve. New
Bernoulli ODE Solver - Solve Bernoulli differential equations y' + P(x)y = Q(x)yⁿ step by step. Applies the v = y^(1-n) substitution to linearize, builds the integrating factor, finds the closed-form solution, and plots the particular solution curve against the slope field. New
Convolution Calculator - Calculate linear, circular, and continuous convolution of signals and functions with interactive visualizations, detailed step-by-step solutions, and comprehensive mathematical analysis. Featured
Curl Calculator - Calculate the curl ∇×F of any 2D or 3D vector field with step-by-step cross product determinant expansion. Enter component functions P, Q (and R for 3D), get symbolic curl, evaluate at a point, identify irrotational fields, and view an interactive vector field visualization with vorticity overlay. New
Curvature Calculator - Calculate the curvature (κ) of a function y=f(x) or a parametric curve at a specific point, with step-by-step derivatives, osculating circle visualization, and radius of curvature.
Derivative Calculator - Calculate derivatives instantly with step-by-step solutions. Supports single-variable, partial, implicit, and directional derivatives with interactive visualizations.
Direction Field / Slope Field Plotter - Plot the slope field of any first-order ODE y' = f(x, y) over a custom x-y region. Click the canvas to spawn new solution curves, watch particles flow along the field, and see equilibrium nullclines — rendered as a pure SVG you can save or share. New
Directional Derivative Calculator - Calculate directional derivatives of multivariable functions with step-by-step solutions, gradient computation, unit vector normalization, and interactive 3D surface visualization.
Divergence Calculator - Calculate the divergence ∇·F of any 2D or 3D vector field with step-by-step partial derivative computation. Enter component functions P, Q (and R for 3D), get symbolic divergence, evaluate at a point, identify sources and sinks, and view an interactive vector field visualization with divergence heat map. New
Double Integral Calculator - Compute double integrals with detailed step-by-step solutions and 3D surface visualization. Supports definite and indefinite integrals with polynomial, trigonometric, exponential, and hyperbolic functions.
Euler's Method Calculator - Solve any first-order ODE y' = f(x, y) numerically with Euler's method. See the iteration table, the Euler polygon superimposed on the slope field, and a live convergence comparison at h, h/2, and h/4 — with optional error analysis against a closed-form solution. New
Fast Fourier Transform (FFT) Calculator - Compute the discrete FFT of a real or complex signal sequence. Apply common window functions, choose FFT length and zero padding, inspect magnitude, phase, frequency bins, dominant peaks, and copy the full complex spectrum. New
First-Order ODE Solver - Solve first-order ordinary differential equations symbolically and numerically. Auto-detects separable, linear, exact, and autonomous forms, applies the right technique, and renders an interactive slope field with the solution curve overlaid. New
Fourier Series Coefficients Calculator - Calculate the Fourier series coefficients a₀, aₙ, and bₙ for any periodic function. See the full integral computations, coefficient table, partial sum formula, and an interactive graph comparing the original function with its Fourier approximation.
Gradient Calculator (Multivariable) - Calculate the gradient vector ∇f of multivariable functions. Enter any function f(x, y) or f(x, y, z), get all partial derivatives, evaluate the gradient at a specific point, see the magnitude and direction, step-by-step solution with MathJax formulas, and an interactive 2D gradient field visualization. New
Implicit Derivative Calculator - Compute derivatives of implicit functions F(x,y)=0 with detailed step-by-step solutions. Supports polynomials, trigonometric, exponential, and logarithmic functions up to 5th order derivatives.
Improper Integral Calculator - Evaluate improper integrals with infinite limits or discontinuities. Supports Type I (infinite bounds) and Type II (unbounded integrand) with step-by-step solutions, convergence analysis, animated visualizations, and comparison of truncation limits. New
Infinite Series Sum Calculator - Calculate the exact sum of convergent infinite series including geometric, telescoping, p-series, and well-known special series. Get step-by-step convergence proofs with animated partial sum visualizations. New
Instantaneous Rate of Change Calculator - Calculate the instantaneous rate of change (derivative) of any function f(x) at a specific point using the limit definition. Get step-by-step solutions with MathJax formulas, an interactive tangent line graph, and a convergence table showing how h→0 approaches the derivative. New
Integral Calculator - Calculate definite and indefinite integrals with detailed step-by-step solutions, interactive function visualization, and comprehensive explanations for calculus students and professionals.
Inverse Laplace Transform Calculator - Compute the inverse Laplace transform of F(s) to find f(t). Get step-by-step solutions, visualizations, and understand the transformation from frequency domain to time domain.
L'Hôpital's Rule Calculator - Evaluate limits of indeterminate forms (0/0, ∞/∞) using L'Hôpital's rule with step-by-step differentiation, interactive graph visualization, and detailed explanations. New
Laplace Transform Calculator - Compute Laplace transforms instantly with detailed step-by-step solutions, interactive function presets, and dual visualization of time-domain and frequency-domain functions.
Limit Calculator - Calculate limits of mathematical functions with detailed step-by-step solutions. Supports one-sided limits, indeterminate forms, and L'Hospital's Rule.
Line Integral Calculator - Calculate line integrals of scalar fields (∫f ds) and vector fields (∫F·dr) along parametric curves in 2D and 3D. Enter the field, parametric equations, and bounds to get symbolic results with step-by-step solutions, arc length, and an interactive curve visualization. New
Maclaurin Series Calculator - Compute the Maclaurin series expansion of common functions at x=0. Get nth-order polynomial terms, Lagrange remainder estimate, radius of convergence, and an interactive animated graph showing how partial sums converge to the original function. New
Newton's Method Calculator - Find roots of equations using the Newton-Raphson method. Enter any function f(x), set an initial guess, and see step-by-step iterations with tangent line approximations, convergence analysis, and an interactive graph showing the iteration path to the root. New
Numerical Integration Calculator - Approximate definite integrals with Gauss-Legendre quadrature, Romberg extrapolation, and adaptive Simpson quadrature. Compare estimates, error signals, function evaluations, convergence behavior, and adaptive interval placement in one visual workspace. New
Optimization Calculator (Calculus) - Find the maximum and minimum values of any function using the first and second derivative tests. Get critical points, intervals of increase and decrease, concavity analysis, inflection points, and interactive graph visualization with step-by-step solutions. New
Partial Derivative Calculator - Compute partial derivatives of multivariable functions with detailed step-by-step solutions, interactive examples, and geometric visualization of tangent planes.
Power Series Calculator - Find the power series representation of functions centered at any point. Compute Taylor/Maclaurin coefficients, determine the radius and interval of convergence with endpoint analysis, and visualize how partial sums converge with an interactive animated graph. New
Radius of Convergence Calculator - Determine the radius and interval of convergence for power series using the Ratio Test or Root Test, with step-by-step solutions, convergence visualization, and endpoint analysis.
Related Rates Solver - Set up and solve related rates problems step-by-step with implicit differentiation and chain rule. Supports expanding sphere, sliding ladder, filling cone, ripple in water, shadow length, approaching cars, inflating balloon, and rectangular box scenarios with animated diagrams. New
Riemann Sum Calculator - Approximate definite integrals using Riemann sums with left endpoint, right endpoint, midpoint, trapezoidal, and Simpson's rule. View animated rectangle visualizations, step-by-step solutions, and convergence analysis. New
Runge-Kutta (RK4) Method Calculator - Solve ordinary differential equations numerically using the classic 4th-order Runge-Kutta method. Enter dy/dx = f(x,y) with initial conditions and step size to see step-by-step iterations with k1, k2, k3, k4 computations, solution table, and interactive solution curve plot.
Second-Order ODE Solver - Solve second-order linear ordinary differential equations with constant coefficients (homogeneous and non-homogeneous). Auto-derives the characteristic equation, classifies the damping regime (over/critical/under-damped), gives the closed-form y(x), and shows an interactive solution curve plus phase-plane (y, y') trajectory. New
Series Convergence Test Calculator - Test the convergence or divergence of infinite series using the Ratio Test, Root Test, Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, and p-Series Test. Get step-by-step solutions with MathJax-rendered formulas and animated partial sum graphs. New
Simpson's Rule Calculator - Approximate definite integrals using Simpson's 1/3 rule, 3/8 rule, and composite Simpson's rule. Features interactive parabolic visualization, error estimation, convergence analysis, method comparison, and detailed MathJax step-by-step solutions. New
Single Variable Derivative Calculator - Compute derivatives of any single-variable function with step-by-step solutions, differentiation rule identification, interactive graph, and critical point analysis.
Surface Integral Calculator - Evaluate surface integrals of scalar fields (∬f dS) and vector fields / flux integrals (∬F·dS) over parametric surfaces. Choose from preset surfaces (sphere, cylinder, cone, paraboloid, torus) or enter custom parametrizations. Get step-by-step solutions with normal vector computation, surface area element, and interactive 3D visualization. New
Surface of Revolution Calculator - Calculate the surface area of a solid of revolution. Enter any function f(x), set integration bounds and axis of rotation, and get step-by-step solutions with interactive 3D visualizations using the disk and shell surface area formulas. New
System of ODEs Solver - Solve systems of ordinary differential equations x' = Ax symbolically and numerically. Auto-classifies the equilibrium (saddle, node, spiral, center), derives eigenvalues and eigenvectors step by step, writes the closed-form general and particular solution, and draws an interactive phase portrait with animated trajectory — for 2×2, 3×3 linear and nonlinear 2D systems. New
Taylor Series Calculator - Calculate the Taylor series expansion of any function around a point with step-by-step derivative calculations, interactive comparison graph, and educational explanations.
Trapezoidal Rule Calculator - Approximate definite integrals using the trapezoidal rule with interactive trapezoid visualization, error estimation, Richardson extrapolation, convergence analysis, and per-trapezoid area breakdown. Supports both function input and data point mode. New
Triple Integral Calculator - Compute triple integrals with detailed step-by-step solutions and 3D visualization. Supports definite and indefinite integrals with symbolic computation.
Volume of Revolution Calculator - Calculate the volume of a solid of revolution using the disk, washer, and shell methods. Enter your function, bounds, and axis of rotation to get step-by-step solutions with interactive 3D visualizations. New
Wronskian Calculator - Calculate the Wronskian determinant of a set of functions to test linear independence. See the full Wronskian matrix with derivatives, step-by-step determinant expansion, and a clear verdict on whether your functions form a fundamental set of solutions for differential equations.
Z-Transform Calculator - Compute one-sided Z-transforms and causal inverse Z-transforms. Enter a sequence formula, finite sample list, or rational X(z) to get the transform, ROC, poles and zeros, sample table, and visual z-plane analysis. New
Fraction Calculators
Comparing Fractions Calculator - Compare two fractions with step-by-step explanations, visual pie charts, and interactive diagrams to see which fraction is larger or smaller.
Decimal to Fraction Calculator - Convert any decimal number to a fraction with step-by-step visual explanation, multiple output formats, and interactive fraction visualization.
Egyptian Fraction Calculator - Express any proper fraction as a sum of distinct unit fractions — the ancient Egyptian way. Run the Greedy (Fibonacci-Sylvester), Binary, and Practical algorithms side-by-side, watch an animated pie visualization converge slice by slice, and explore historical expansions from the Rhind Papyrus (c. 1650 BC). Step-by-step breakdown included. New
Equivalent Fractions Calculator - Generate equivalent fractions with visual fraction bars, number line diagrams, and pattern highlighting. Check if two fractions are equivalent or find up to 100 equivalent fractions instantly.
Fraction Calculator - Perform fraction arithmetic with our interactive calculator. Get step-by-step solutions, visual diagrams, and results in multiple formats including mixed numbers and decimals. Featured
Fraction Simplifier - Simplify any fraction to lowest terms with interactive bar diagrams, step-by-step prime factorization, and animated GCF visualization. Perfect for students learning fraction reduction.
Fraction to Decimal Calculator - Convert any fraction to its decimal equivalent with interactive long division visualization, repeating decimal detection, and step-by-step explanations. Perfect for students and educators.
Fraction to Mixed Number Converter - Convert any improper fraction to a mixed number instantly with animated visual diagrams, step-by-step division breakdown, and educational explanations. Perfect for students, teachers, and anyone learning fractions.
Fraction to Percent Converter - Convert fractions to percentages instantly with visual pie charts, animated progress bars, step-by-step solutions, and support for mixed numbers. Perfect for students, teachers, and professionals.
Mixed Number to Fraction Converter - Convert any mixed number to an improper fraction instantly with animated visual diagrams, step-by-step breakdown, and educational explanations. Perfect for students learning fractions.
Multiple Fraction Calculator - Calculate expressions with 3 or more fractions or mixed numbers. See multiplication/division precedence, common denominator steps, simplification, mixed-number answers, and visual fraction strips. Featured
Number to Fraction Converter - Convert any decimal, repeating decimal, or mixed number to a simplified fraction. See step-by-step GCD reduction, visual fraction bar, and verification with long division. New
Reduce Fractions Calculator - Simplify any fraction to its lowest terms with interactive visual diagrams, step-by-step prime factorization, and animated GCF calculation. Perfect for students and educators.
Geometry Calculators
3D Distance Calculator - Calculate the Euclidean distance between two points in three-dimensional space. Enter coordinates (x₁, y₁, z₁) and (x₂, y₂, z₂) to get the distance, midpoint, displacement vector, and direction angles with step-by-step formulas and an interactive 3D diagram. New
3D Surface Plotter - Plot interactive 3D surfaces z = f(x, y) with mouse-driven rotation, zoom and pan. Adjust x/y domain, mesh resolution, six color maps, wireframe overlay and lighting. Explore saddle points, Gaussian bumps, ripples, monkey saddles, hyperbolic paraboloids and the famous Mexican-hat sinc surface — all in your browser, no plugin required. New
Angle Bisector Calculator - Calculate the angle bisectors of a triangle. Enter three sides or three vertex coordinates to find bisector lengths, division points on opposite sides, incenter, inradius, and see an interactive diagram with step-by-step formulas. New
Arc Length Calculator - Calculate arc length, radius, or central angle of a circle sector with interactive diagram, step-by-step solution, and support for degrees and radians. Featured
Cartesian to Polar Coordinates Converter - Convert Cartesian coordinates (x, y) to polar coordinates (r, θ) with adjustable precision from 1 to 1000 decimal places. Features step-by-step solutions, interactive coordinate plane visualization, quadrant analysis, and verification.
Circle Calculator - Calculate radius, diameter, circumference, and area of a circle from any single value. Includes arc length, sector area, chord length, and segment area calculations with step-by-step solutions and interactive diagram.
Circumscribed Circle (Circumcircle) Calculator - Calculate the circumscribed circle (circumcircle) of a triangle. Enter three sides or three vertex coordinates to find the circumradius, circumcenter, area, angles, and see an interactive diagram with step-by-step formulas. New
Cone Flat Pattern (Template) Generator - Generate the 2D flat pattern (developed surface) of a cone or truncated cone (frustum). Calculate the outer radius, inner radius, and sweep angle needed to cut the unrolled template from sheet metal, cardboard, or paper. Essential for DIY, manufacturing, HVAC ductwork, and paper crafting. Featured
Conic Section Identifier - Identify the conic section type (circle, ellipse, parabola, or hyperbola) from the general second-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0. Get step-by-step classification, key properties, standard form, and an interactive graph. New
Coordinate Geometry Distance Calculator - Calculate the distance, midpoint, slope, line equation, perpendicular bisector, and angle of inclination between two points on a coordinate plane. Enter coordinates to get step-by-step solutions with an interactive diagram. New
Delaunay Triangulation Generator - Build a Delaunay triangulation from any set of 2D points and watch it form, colored by triangle quality. See the empty-circle property, overlay the Voronoi dual, and read the worst-angle and skinny-triangle stats — no spreadsheet or library needed. New
Distance Between Two Points Calculator - Calculate the Euclidean distance between two points in a 2D coordinate plane with step-by-step formulas, interactive visualization, midpoint, slope, and line equation calculations. Featured
Ellipse Circumference Calculator - Calculate the circumference (perimeter) of an ellipse using multiple approximation formulas including Ramanujan, exact series, and visualize results with an interactive SVG diagram.
Equation of a Line Calculator - Find the equation of a line from two points, a point and slope, or slope and y-intercept. Get slope-intercept, point-slope, and standard form with interactive graph, step-by-step solution, and line properties. New
Euler Characteristic Calculator - Calculate the Euler characteristic (χ = V − E + F) from vertices, edges, and faces. Identify topological structure, genus, and surface type with step-by-step solutions, interactive 3D visualization, and Platonic solid comparisons.
Frustum Calculator - Calculate the volume, lateral surface area, total surface area, and slant height of a frustum (truncated cone). Enter the top radius, bottom radius, and height to get instant results with step-by-step formulas and an interactive 3D diagram. New
General Triangle Solver - The ultimate tool to solve any triangle. Input three known values (e.g., SSS, SAS, ASA, AAS) and automatically calculate all missing sides, angles, area, and perimeter using the law of sines, law of cosines, and Heron's formula.
Golden Rectangle Calculator - Calculate golden rectangle dimensions from any side length. Visualize the golden ratio (φ ≈ 1.618) with interactive diagrams showing interior and outer rectangles, plus step-by-step formulas.
Golden Section Calculator - Calculate the missing values to complete the golden section. Enter any value (a+b, a, or b) to find the golden ratio proportions with step-by-step explanation and visual diagram.
Great Circle Distance Calculator - Calculate the shortest distance between two points on a sphere using the Haversine formula. Enter latitude and longitude coordinates to get the great circle distance in kilometers, miles, and nautical miles, plus initial and final bearing, midpoint coordinates, and step-by-step formulas with an interactive globe diagram. New
Heron's Formula Calculator - Calculate the area of a triangle using Heron's formula from three side lengths. Get the semi-perimeter, area, perimeter, inradius, circumradius, all three altitudes, interior angles, and triangle type with step-by-step formulas and an interactive triangle diagram. New
Hyperbola Calculator - Calculate the center, vertices, foci, asymptotes, eccentricity, and equations of any hyperbola. Supports standard form and general form with interactive graph and step-by-step solutions. New
Hypotenuse Calculator - Calculate the hypotenuse of a right triangle using the Pythagorean theorem. Get instant results with visual diagrams, step-by-step solutions, angles, area, and perimeter. Featured
Inscribed Circle (Incircle) Calculator - Calculate the inscribed circle (incircle) of a triangle. Enter three sides or three vertex coordinates to find the inradius, incenter, tangent points, tangent lengths, contact triangle, and see an interactive diagram with step-by-step formulas. New
Irregular Polygon Area Calculator - Calculate the area of any irregular polygon by entering vertex coordinates or drawing on an interactive canvas. Uses the Shoelace formula with step-by-step calculation, perimeter, centroid, and a visual diagram. New
Midpoint Calculator - Calculate the midpoint between two points instantly with interactive visualization, step-by-step solution, distance calculation, and comprehensive geometry analysis.
Parabola Calculator - Find the vertex, focus, directrix, axis of symmetry, and latus rectum of any parabola. Supports standard form (y=ax²+bx+c), vertex form (y=a(x-h)²+k), and general conic form ((x-h)²=4p(y-k)). Includes interactive graph with step-by-step solutions. New
Parallel and Perpendicular Line Calculator - Find equations of parallel and perpendicular lines passing through a given point. Enter a line equation and a point to get both parallel and perpendicular line equations with interactive graph, step-by-step solution, and line properties. New
Parametric Curve Grapher - Graph parametric equations x(t) and y(t) online with interactive visualization. Features animated curve tracing, speed-based coloring, osculating circle display, tangent vectors, arc length computation, and famous curve presets including Lissajous, heart, rose, butterfly, and spirograph curves. New
Parametric Curve Grapher - Graph parametric equations x(t) and y(t) online with interactive visualization. Features animated curve tracing, speed-based coloring, osculating circle display, tangent vectors, arc length computation, and famous curve presets including Lissajous, heart, rose, butterfly, and spirograph curves. New
Point-Slope Form Calculator - Find the equation of a line using point-slope form. Enter a point and slope or two points to get point-slope, slope-intercept, and standard form equations with an interactive graph and step-by-step solution. New
Point to Plane Distance Calculator - Calculate the shortest perpendicular distance from a point (x₀, y₀, z₀) to a plane Ax + By + Cz + D = 0. Get step-by-step solution, foot of perpendicular, interactive 3D visualization, and geometric analysis.
Polar to Cartesian Converter - Convert polar coordinates (r, θ) to Cartesian coordinates (x, y) with up to 1000 decimal places precision. Features interactive visualization, step-by-step solutions, quadrant detection, and verification.
Polygon Diagonals Calculator - Calculate the number of diagonals in an n-sided polygon, find the sum of interior angles, each interior angle of a regular polygon, and visualize the polygon with all its diagonals drawn.
Pythagorean Theorem Calculator - Calculate the missing side of any right triangle using a² + b² = c². Get step-by-step solutions, interactive triangle visualization, area, perimeter, and angle calculations.
Rectangle Calculator - Calculate rectangle area, perimeter, diagonal, inscribed circle, circumscribed circle, and aspect ratio from any two known values. Includes interactive SVG diagram and step-by-step solutions.
Regular Polygon Calculator - Calculate the area, perimeter, apothem, circumradius, interior angles, exterior angles, and number of diagonals of any regular polygon. Enter the number of sides and side length to get instant results with step-by-step formulas and an interactive diagram. New
Shoelace Formula Calculator - Calculate the area of any polygon from its (x, y) vertex coordinates using the Shoelace (Gauss) algorithm. Supports triangles, quadrilaterals, and complex polygons. Ideal for surveying, GIS, land measurement, and geometry problems.
Slope Calculator - Calculate slope, gradient, angle, and line equation from two coordinate points. Features interactive graph visualization, step-by-step solutions, and multiple output formats.
Slope Intercept Form Calculator - Calculate slope intercept form (y=mx+b) from two points, point and slope, or standard form. Get step-by-step solution with interactive graph visualization.
Sphere Equation Calculator - Find the standard and general equation of a sphere given center coordinates and radius, or two endpoints of a diameter. Includes step-by-step derivation, 3D visualization, and geometric properties.
Square Calculator - Calculate all properties of a square instantly. Enter side length, area, perimeter, or diagonal to find all other measurements with step-by-step formulas and interactive visualization.
Tangent Line to Circle Calculator - Find the tangent line equations from an external point to a circle. Enter the circle equation and a point to get tangent lines, tangent length, contact points, tangent angle, and an interactive diagram with step-by-step solution. New
Torus Calculator - Calculate the volume, surface area, and geometric properties of a torus (donut shape). Enter the major radius (R) and minor radius (r) to get instant results with step-by-step formulas and an interactive 3D cross-section diagram. New
Triangle Centroid Calculator - Calculate the centroid (center of mass) of any triangle given its three vertex coordinates. Get step-by-step solution, triangle properties, and an interactive visual diagram with medians.
Triangle Orthocenter Calculator - Calculate the orthocenter (intersection of the three altitudes) of any triangle given its three vertex coordinates. Get step-by-step solution, altitude equations, triangle classification, and an interactive visual diagram.
Linear Algebra
Angle Between Vectors Calculator - Calculate the angle between two 2D or 3D vectors using the dot product formula cos(θ) = (a·b)/(|a||b|). Get step-by-step solutions, results in both degrees and radians, interactive vector diagram, and geometric interpretation. New
Characteristic Polynomial Calculator - Calculate the characteristic polynomial det(A − λI) of a square matrix. Supports 2×2 to 6×6 matrices with step-by-step cofactor expansion, eigenvalue extraction, coefficient analysis, and interactive polynomial visualization. New
Cholesky Decomposition Calculator - Decompose a symmetric positive-definite matrix into A = LLᵀ with animated step-by-step computation. See each element of the lower-triangular matrix L derived with full formulas, verify the result, and explore the factorization visually. New
Column Space Calculator - Find the column space and basis of any matrix using row reduction. See each row operation step by step with pivot column highlighting, rank, dimension, and interactive visualization for 2D/3D column spaces. New
Cramer's Rule Calculator - Solve systems of 2 or 3 linear equations using Cramer's rule. Enter coefficients, get step-by-step determinant calculations with animated matrix visualization, geometric interpretation graph, and the complete solution. New
Cross Product Calculator - Calculate the cross product (vector product) of two 3D vectors using the determinant formula. Get step-by-step expansion, the perpendicular result vector, its magnitude (parallelogram area), direction verification, and an interactive 3D visualization. New
Determinant Calculator - Calculate the determinant of any square matrix with detailed step-by-step cofactor expansion, matrix properties analysis, and visual solutions.
Dot Product Calculator - Calculate the dot product (scalar product) of two vectors in 2D, 3D, or higher dimensions. Get the angle between vectors, magnitudes, scalar and vector projections, geometric interpretation, and step-by-step formulas with an interactive vector diagram. New
Eigenvalue and Eigenvector Calculator - Calculate eigenvalues and eigenvectors of 2x2 and 3x3 matrices with detailed step-by-step solutions, characteristic polynomial derivation, interactive visualization, and matrix property analysis.
Gram-Schmidt Calculator - Orthonormalize a set of linearly independent vectors using the Gram-Schmidt process. Get step-by-step projections, orthogonal and orthonormal bases, verification of orthogonality, and an interactive vector visualization.
Jacobian Matrix Calculator - Calculate the Jacobian matrix of multivariable vector-valued functions. Enter transformation components like F(x,y) = (x²+y, xy), get the full Jacobian matrix with all partial derivatives, the determinant, eigenvalues, step-by-step solution with MathJax, and an interactive grid deformation visualization showing how the transformation distorts space. New
Jordan Normal Form Calculator - Compute the Jordan canonical form J of a square matrix, plus the transition matrix P such that P^(-1)AP = J. Handles defective (non-diagonalizable) matrices via generalized eigenvectors, with step-by-step kernel-chain analysis and a visual Jordan-block diagram. New
Matrix Calculator - Calculate matrix operations with step-by-step solutions: addition, subtraction, multiplication, inverse, transpose, and determinant. Visual matrix display with detailed explanations.
Matrix Diagonalization Calculator - Diagonalize a square matrix by computing eigenvalues, eigenvectors, and the decomposition A = PDP⁻¹. Supports 2×2 to 5×5 matrices with step-by-step solutions, characteristic polynomial, multiplicity analysis, and interactive visualization. New
Matrix Exponential Calculator - Compute the matrix exponential e^(At) for square matrices and use it as the state transition matrix for linear ODE systems x'(t)=Ax(t). Enter a matrix A, a time t, and optionally an initial vector x(0) to get e^(At), x(t), Padé scaling details, trace and determinant identities, 2×2 eigenvalue classification, and an animated phase-plane flow diagram. New
Matrix Inverse Calculator - Calculate the inverse of a square matrix using Gauss-Jordan elimination with detailed step-by-step row operations. Supports 2×2 to 6×6 matrices with exact fractional arithmetic, determinant calculation, and A×A⁻¹=I verification. New
Matrix LU Decomposition Calculator - Calculate LU decomposition of any square matrix with partial pivoting. Get lower triangular (L), upper triangular (U), and permutation (P) matrices with step-by-step Gaussian elimination and verification.
Matrix Multiplication Calculator - Multiply two matrices with detailed step-by-step element computation. See each dot product broken down, with color-coded row × column visualization. Supports matrices up to 5×5 with interactive dimension controls. New
Matrix Power Calculator - Calculate the power of a square matrix A raised to any integer exponent n. See each multiplication step animated, intermediate matrices A¹ through Aⁿ, determinant and trace properties, with MathJax formulas and interactive visualization. New
Matrix Rank Calculator - Calculate the rank of any matrix using Gaussian elimination (row echelon form). Get step-by-step row reduction, pivot analysis, column space and null space dimensions, and visual heatmap. Supports matrices up to 10×10.
Matrix Trace Calculator - Calculate the trace of a square matrix (sum of diagonal elements), verify its equality with the sum of eigenvalues, explore trace properties, and visualize the diagonal with an interactive heatmap. Supports matrices up to 10×10.
Null Space Calculator - Find the null space (kernel) of any matrix by solving Ax = 0 using Gaussian elimination. Get the basis vectors, nullity, step-by-step RREF reduction, and rank-nullity theorem verification with exact fractional arithmetic. New
Partial Fraction Decomposition Calculator - Decompose rational functions into partial fractions with detailed step-by-step solutions, coefficient analysis, and visual decomposition breakdown.
QR Decomposition Calculator - Decompose any matrix A into an orthogonal matrix Q and upper triangular matrix R using the Gram-Schmidt process. Supports 2×2 to 5×5 matrices with animated step-by-step orthogonalization, orthogonality verification QᵀQ = I, and interactive visualization. New
RREF Calculator (Row Echelon Form) - Reduce any matrix to reduced row echelon form (RREF) with detailed step-by-step row operations. Enter your matrix, see every pivot, swap, and elimination step visualized. Identify rank, nullity, pivot columns, free variables, and solution type instantly. New
Singular Value Decomposition (SVD) Calculator - Calculate the Singular Value Decomposition (SVD) of any matrix. Decompose A = UΣVᵀ with step-by-step solutions, interactive 3D visualization, rank analysis, condition number, and applications in data compression and dimensionality reduction.
Tensor Product Calculator - Compute the tensor product, also called the Kronecker product, of two rectangular matrices with exact fraction arithmetic, block-by-block visualization, copyable results, and SEO-friendly linear algebra explanations. New
Unit Vector Calculator - Calculate the unit vector (normalized vector) in the direction of a given 2D, 3D, or n-dimensional vector. Get the magnitude, each normalized component, direction angles, step-by-step normalization process, and visual verification that the result has length 1. New
Vector Calculator - Free online vector calculator with step-by-step solutions. Calculate dot product, cross product, magnitude, unit vector, angle between vectors, projection, and more with interactive 3D visualization.
Vector Magnitude Calculator - Calculate the magnitude (length or Euclidean norm) of a 2D, 3D, or n-dimensional vector. Get step-by-step computation showing each squared component, the sum under the radical, and the final square root result, with an interactive vector diagram. New
Vector Projection Calculator - Calculate the vector projection and scalar projection of one vector onto another. Supports 2D and 3D vectors with step-by-step formulas, interactive diagram, and orthogonal decomposition.
Logarithm Calculators
Log Base 10 Calculator - Calculate the common logarithm (log base 10) of any positive number with detailed step-by-step solutions, interactive graphs, and real-world applications including pH scale, decibels, and Richter scale. Featured
Log Base 2 Calculator - Calculate the binary logarithm (log base 2) of any positive number with detailed step-by-step explanations, visual representations, and comprehensive insights into logarithmic properties. Featured
Log (Logarithm) Calculator - Calculate logarithm for any base with step-by-step solutions, interactive visualization, and conversion between common log types (natural log, log base 10, log base 2).
Natural Log Calculator - Calculate the natural logarithm ln(x) of any positive number with step-by-step derivation, interactive visualization, logarithm properties, related calculations, and mathematical insights.
Number System Converters
Base Converter - Convert integers between any number bases from binary (base-2) to base-36 with multi-base preview, step-by-step conversion breakdown, and digit position analysis.
Base-N Calculator - Convert integers between any number bases from 2 to 36 with step-by-step calculation breakdown and digit position analysis.
Binary Calculator - Perform binary arithmetic (add, subtract, multiply, divide) and bitwise operations (AND, OR, XOR, NOT, shifts). Interactive step-by-step solutions with multi-base results in binary, decimal, and hexadecimal.
Binary Converter - Convert binary numbers to decimal, hexadecimal, octal, and any base (2-36). Get instant results with visual bit diagrams, step-by-step explanations, and grouped formatting for easy reading.
Binary to Decimal Converter - Convert binary (base-2) numbers to decimal (base-10) with an interactive bit-by-bit breakdown showing how each digit contributes to the final value through powers of 2.
Binary to Hex Converter - Convert binary (base-2) numbers to hexadecimal (base-16) with visual bit grouping, step-by-step conversion process, interactive diagrams, and comprehensive number system education.
Binary to Octal Converter - Convert binary numbers to octal with interactive visualization showing bit grouping, step-by-step conversion process, and comprehensive number system education.
Decimal to Binary Converter - Convert decimal (base-10) numbers to binary (base-2) instantly. Get step-by-step division method breakdown, visual bit diagrams, grouped binary output, and multi-base conversions including octal and hexadecimal.
Decimal to Hex Converter - Convert decimal (base-10) numbers to hexadecimal (base-16) with interactive visualization, step-by-step conversion process, and detailed explanations for programming and digital electronics. Featured
Decimal to Octal Converter - Convert decimal (Base-10) numbers to octal (Base-8) instantly with visual step-by-step division method, binary-octal grouping, bit pattern visualization, and comprehensive number system education.
Decimal to Percent Converter - Convert decimal numbers to percentages with visual representation, step-by-step calculation, batch conversion support, and precision control. Perfect for math, finance, and data analysis.
Decimal to Scientific Notation Converter - Convert any decimal number to scientific notation with step-by-step visualization, multiple output formats including E-notation and engineering notation, and interactive examples for learning.
Degree to Radian Converter - Convert degrees to radians instantly with interactive unit circle visualization, step-by-step formulas, common angle references, and bidirectional conversion support.
HEX Calculator - Perform hexadecimal addition, subtraction, multiplication, division, and bitwise operations (AND, OR, XOR, NOT, shifts). Get step-by-step solutions with multi-base results in hex, decimal, and binary.
HEX Converter - Convert hexadecimal numbers to decimal, binary, octal, and any base from 2 to 36. Get instant multi-format results with visual digit breakdown and step-by-step conversion process.
Hex to Binary Converter - Convert hexadecimal (Base-16) numbers to binary (Base-2) with visual digit mapping, step-by-step conversion breakdown, and one-click copy.
Hex to Decimal Converter - Convert hexadecimal (base-16) numbers to decimal (base-10) instantly. See step-by-step conversion process, positional notation breakdown, and results in multiple bases. Featured
Hex to Octal Converter - Convert hexadecimal (base-16) numbers to octal (base-8) instantly. Get step-by-step conversion breakdown, visual diagrams, and multi-base results including decimal and binary.
Octal Calculator - Perform addition, subtraction, multiplication, and division on octal (base-8) numbers with step-by-step visual explanations and instant decimal conversions. Featured
Octal Converter - Convert octal (base-8) numbers to binary, decimal, hexadecimal, and any base from 2 to 36 instantly. Free online octal number system converter with step-by-step conversion explanations.
Octal to Binary Converter - Convert octal (base-8) numbers to binary (base-2) instantly with visual step-by-step conversion showing each digit mapping, interactive reference table, and educational breakdown.
Octal to Decimal Converter - Convert octal (base-8) numbers to decimal (base-10) with visual digit-by-digit breakdown, step-by-step calculations, and educational explanations.
Octal to Hex Converter - Free online tool to convert octal numbers to hexadecimal with step-by-step calculation, binary representation, and digit breakdown visualization.
Percent to Decimal Converter - Convert percent to decimal instantly with step-by-step calculation, visual diagram, batch conversion for multiple values, and interactive examples. Free online percentage to decimal converter.
Radian to Degree Converter - Convert radians to degrees instantly with interactive unit circle diagram, step-by-step calculation, common angle reference, DMS output, and batch conversion. Free online angle converter for math, physics, and engineering.
Ratio to Percentage Calculator - Convert any ratio to percentage with step-by-step solution, visual pie chart representation, and support for multiple ratio formats including fractions and decimals. Featured
Roman Numerals Converter - Convert Roman numerals to Arabic numbers and vice versa with detailed visual explanations. Understand the meaning of Roman numeral dates and sequences like "X XXIII XVII" with our interactive step-by-step converter. Featured
Scientific Notation to Decimal Converter - Convert numbers from scientific notation (exponential form) to ordinary decimal notation with step-by-step explanation and visual decimal point movement. Featured
Percentage
Percentage Calculator - Free online percentage calculator with 6 calculation modes: find percentages, calculate percentage of a number, percentage change, difference, increase, and decrease. Features visual charts, step-by-step solutions, and instant results.
Percentage Change Calculator - Calculate percentage change between two values with step-by-step breakdown, visual comparison charts, and detailed analysis. Find percentage increase, decrease, or difference instantly.
Percentage Decrease Calculator - Calculate the percentage decrease between two values with step-by-step solutions, interactive SVG diagrams, and multiple calculation modes including reverse calculations.
Percentage Error Calculator - Calculate percentage error between estimated and actual values with step-by-step formula breakdown, visual comparison chart, error interpretation, and detailed analysis.
Percentage Increase Calculator - Calculate percentage increase from one number to another with step-by-step solution, visual comparison charts, and instant verification. Perfect for business analytics, academic calculations, and financial analysis.
Seed Germination Rate Calculator - Calculate seed germination percentage from a germination test, classify seed lot viability, estimate confidence range, and plan how many seeds to sow for a target number of seedlings. New
Sequence Tools
Arithmetic Sequence Calculator - Calculate the nth term and sum of arithmetic sequences with step-by-step solutions, interactive visualizations, and high-precision results up to 1000 decimal places. Featured
Catalan Number Generator - Generate the n-th Catalan number with step-by-step formula derivation, interactive visualizations of parenthesizations and polygon triangulations, a full sequence table, and deep combinatorial interpretation for mathematics, computer science, and competitive programming.
Collatz Conjecture Calculator - Explore the Collatz conjecture (3n+1 problem) by generating the hailstone sequence for any positive integer. Visualize the trajectory, analyze stopping time, peak values, and sequence statistics with interactive charts.
Cube Numbers List - Generate and explore cube numbers with interactive visualizations, 3D cube diagrams, step-by-step calculations, and multiple export formats. Perfect for students, teachers, and math enthusiasts.
First n Prime Numbers - Generate and explore the first n prime numbers with interactive visualization, twin prime detection, gap analysis, and distribution charts. A powerful prime number generator for math education, cryptography research, and number theory exploration.
Geometric Sequence Calculator - Calculate the nth term, sum of first n terms, and infinite sum of any geometric sequence with step-by-step solutions and interactive visualization.
Happy Number Calculator - Determine if a number is a happy number by repeatedly replacing it with the sum of the squares of its digits. Visualize the happiness journey, explore patterns, and find all happy numbers in any range.
List of Fibonacci Numbers - Generate Fibonacci numbers with golden ratio visualization, spiral diagram, and sequence analysis. Create lists of the first N Fibonacci numbers instantly.
List of Prime Numbers - Generate a comprehensive list of prime numbers from 2 to any specified number up to 10,000. Discover the building blocks of mathematics with instant results and detailed statistics. Featured
Magic Square Generator - Generate magic squares of any order N where every row, column, and diagonal sums to the same magic constant. Includes step-by-step construction, interactive visualization, and mathematical properties.
Partition Function Calculator - Compute the partition function p(n), the number of ways to write n as a sum of positive integers. Enumerate every partition for small n with animated Young (Ferrers) diagrams, compare distinct-parts q(n) vs. odd-parts o(n) (Euler's theorem), plot the growth curve, and benchmark against the Hardy-Ramanujan asymptotic approximation. New
Pascal's Triangle Generator - Generate Pascal's triangle up to 30 rows. Explore patterns like Fibonacci numbers, Sierpinski triangle, powers of 2, and binomial coefficients with interactive highlighting and animations. New
Product Notation Calculator (Pi Notation) - Evaluate product (Π) pi notation expressions with step-by-step factor expansion, running product visualization, and growth analysis. Supports polynomial, exponential, trigonometric, and custom expressions. New
Recurrence Relation Solver - Solve linear homogeneous recurrence relations with constant coefficients. Enter the recurrence and initial values to get the closed-form solution from the characteristic equation, the first N terms, roots on the complex plane, and automatic growth classification. New
Sigma Notation Calculator (Summation) - Evaluate sigma (Σ) summation notation expressions with step-by-step term expansion, running total visualization, and convergence analysis. Supports polynomial, exponential, trigonometric, and custom expressions. New
Square Numbers List - Generate list of square numbers (perfect squares), find squares in a range, or check if a number is a perfect square. Interactive visualization with step-by-step calculations.
Twin Prime Finder - Find every twin prime pair (primes p and p+2) up to any limit you choose. Get the complete list, totals, density per decade, the predicted Hardy-Littlewood count, largest pair found, and an interactive visualization — all in one place. New
Statistics And Data Analysis
A/B Test Sample Size Calculator - Plan an A/B test before you launch. Enter your baseline conversion rate, the minimum detectable effect (MDE), significance level (alpha) and power (1 minus beta) to get the required sample size per variant, total sample size, and how long the test will take given your daily traffic. New
A/B Test Significance Calculator - Determine whether the difference between A/B test variants is statistically significant. Enter visitors and conversions for control and variant groups to get p-value, confidence level, uplift, and a clear win/lose verdict. New
ANOVA Calculator - Perform one-way ANOVA test to determine if there are significant differences among group means. Includes complete ANOVA table, effect size (eta-squared, omega-squared), interactive visualizations, and step-by-step hypothesis testing.
Arithmetic Mean Calculator - Calculate the arithmetic mean (average) of a set of numbers with comprehensive statistical analysis including median, mode, range, standard deviation, variance, and interactive data visualization.
Average Calculator - Calculate mean, median, mode, geometric mean, harmonic mean, and weighted average with complete statistical analysis, visualizations, and step-by-step solutions. Featured
Average Deviation Calculator - Calculate the average absolute deviation (AAD) of a dataset from the mean or median. Includes step-by-step calculations, visual distribution chart, and comprehensive statistical analysis.
📊 Bar Graph Maker - Create beautiful, customizable bar charts from your data instantly. Supports vertical and horizontal bars, multiple color themes, animations, and one-click PNG/SVG download. New
Bayes' Theorem Calculator - Calculate posterior probability using Bayes' theorem. Enter prior probability, likelihood, and false positive rate to get step-by-step solutions with probability tree diagrams and natural frequency visualizations. New
Beta Distribution Calculator - Calculate probabilities for the beta distribution with shape parameters α and β. Get P(X ≤ x), P(X ≥ x), or P(a ≤ X ≤ b), with interactive PDF/CDF graphs, shaded probability regions, step-by-step MathJax solutions, and distribution properties including mean, variance, mode, and skewness. New
Box and Whisker Plot Maker - Generate professional box and whisker plots with interactive visualization, comprehensive statistics, quartile analysis, outlier detection, and step-by-step calculations.
Chi-Square Test Calculator - Perform a chi-square test of independence to determine if there is a significant association between two categorical variables. Get chi-square statistic, p-value, expected frequencies, cell contributions, and Cramer's V effect size with step-by-step calculations.
Coefficient of Variation Calculator - Calculate Coefficient of Variation (CV) with step-by-step formulas, visual comparison charts, data quality assessment, and comprehensive statistical analysis for your datasets.
Cohen's d Calculator - Calculate Cohen's d effect size to measure the standardized difference between two group means. Features step-by-step calculations, interactive visualization, effect size interpretation, and support for both raw data and summary statistics.
Compound Growth Calculator - Calculate compound annual growth rate (CAGR), future value, initial value, or time periods with interactive growth charts, detailed breakdowns, and comprehensive analysis for investments and business growth. Featured
Confidence Interval Calculator - Calculate confidence intervals for means and proportions with interactive visualization, t-distribution and z-distribution support, step-by-step calculations, and sample size recommendations.
Confidence Interval for Proportion Calculator - Calculate confidence intervals for population proportions using Wald (normal approximation) or Wilson score methods. Get step-by-step solutions, visual diagrams, margin of error analysis, and practical interpretation guidance.
Contingency Table Calculator - Analyze categorical data relationships with the chi-square test of independence. Supports any R×C contingency table with expected frequencies, standardized residuals, Cramér's V effect size, animated mosaic plot, residual heatmap, and step-by-step solutions. New
Conversion Rate Calculator - Calculate the conversion rate from visitors to conversions, with Wilson, Wald, and Agresti-Coull confidence intervals, margin of error, sample-adequacy check, and an animated funnel to gauge reliability for A/B testing and funnel analysis. New
Correlation Coefficient Calculator - Calculate Pearson, Spearman, and Kendall correlation coefficients with interactive scatter plot, regression analysis, p-values, and step-by-step calculation breakdown.
Effect Size Calculator - Calculate and visualize effect sizes including Cohen's d, Hedges' g, Glass's delta, eta-squared, omega-squared, and Cohen's f. See animated distribution overlap, step-by-step formulas, CLES probability, and interpretation guidelines for your statistical research. New
Exponential Distribution Calculator - Calculate probabilities, visualize the PDF and CDF curves, and explore properties of the exponential distribution. Enter the rate parameter λ (lambda) and a value x to get P(X ≤ x), P(X > x), P(a ≤ X ≤ b), mean, variance, median, and step-by-step solutions with interactive graphs. New
F-Test / F-Distribution Calculator - Calculate F-statistic and p-value for ANOVA, two-sample variance tests, and regression analysis. Get step-by-step solutions with interactive F-distribution curve visualization, critical value tables, and hypothesis test conclusions. New
Fisher's Exact Test Calculator - Perform Fisher's exact test on 2×2 contingency tables. Get exact p-values (one-tailed and two-tailed), odds ratio, relative risk, step-by-step hypergeometric probability calculations, and interactive mosaic plot visualization. New
Five Number Summary Calculator - Calculate the five-number summary (minimum, Q1, median, Q3, maximum) for any dataset. Features an interactive box-and-whisker plot, step-by-step quartile calculations, outlier detection, and multiple calculation methods. New
Geometric Distribution Calculator - Calculate geometric distribution probabilities for the number of trials until the first success. Enter the probability of success per trial and the trial number to get exact PMF, CDF, cumulative probabilities, step-by-step solutions, interactive PMF/CDF charts, and animated trial sequence visualizations. New
Geometric Mean Calculator - Calculate the geometric mean of any dataset with step-by-step formulas, interactive visualization, comparison with arithmetic mean, and comprehensive statistical analysis.
Gini Coefficient Calculator - Calculate the Gini coefficient to measure inequality of a distribution using the Lorenz curve approach. Features step-by-step calculation, interactive Lorenz curve visualization, quintile analysis, and inequality interpretation.
Harmonic Mean Calculator - Calculate the harmonic mean of a data set with step-by-step formulas, comparison with arithmetic and geometric means, interactive visualization, and practical examples for rates, speeds, and financial analysis.
Histogram Maker - Create beautiful histograms online with comprehensive statistical analysis including mean, median, mode, skewness, kurtosis, and distribution shape detection. Supports auto-optimal bin calculation and PNG export.
Hypergeometric Distribution Calculator - Calculate hypergeometric distribution probabilities for sampling without replacement. Enter population size, success states, draws, and observed successes to get exact probabilities, cumulative values, PMF charts, step-by-step solutions, and urn visualizations. New
Interquartile Range Calculator - Calculate the interquartile range (IQR), quartiles Q1, Q2, Q3, five-number summary, and detect outliers with interactive box plot visualization and step-by-step calculations.
Kruskal-Wallis Test Calculator - Perform Kruskal-Wallis H test to compare multiple independent groups. Get step-by-step calculations, rank analysis, effect size, and interactive visualization for non-parametric statistical analysis.
📈 Line Graph Maker - Create beautiful line charts with multiple series, smooth curves, area fills, data point markers, and custom themes. Download as PNG or SVG instantly. New
Linear Regression Calculator - Calculate linear regression equation, slope, intercept, R-squared, and make predictions with interactive scatter plot visualization and step-by-step formula breakdown.
Logarithmic Growth Calculator - Calculate logarithmic growth over time using natural log (e), base 10, or base 2. Visualize growth curves, view year-by-year breakdowns, and understand step-by-step calculations.
Mann-Whitney U Test Calculator - Perform the Mann-Whitney U test (Wilcoxon rank-sum test) to compare two independent samples. Get U statistic, p-value, effect size, step-by-step calculations, and interactive visualizations.
Mean Absolute Deviation (MAD) Calculator - Calculate Mean Absolute Deviation with step-by-step formulas, interactive visualization, and comprehensive statistical analysis. Understand data variability with our free MAD calculator.
Mean Calculator - Calculate the arithmetic mean (average) of any dataset with interactive visualization, step-by-step formula breakdown, and comprehensive statistics including sum, median, range, and standard deviation.
Mean Median Mode Calculator - Calculate mean, median, mode and range with step-by-step formulas, interactive visualization, frequency analysis, and comprehensive statistical breakdown for any dataset.
Median Absolute Deviation Calculator - Calculate the median absolute deviation (MAD) of a dataset with step-by-step formulas, interactive visualization, outlier detection, and robustness comparison to standard deviation.
Median Calculator - Calculate the median value of a set of numbers with step-by-step explanations, interactive visualizations, and comprehensive statistical insights. Featured
Midrange Calculator - Calculate the midrange of any dataset with step-by-step visualization showing the midpoint between maximum and minimum values, plus comprehensive statistics including mean, median, and range comparison.
Mode Calculator - Calculate the mode (most frequent values) of a dataset with interactive frequency visualization, step-by-step analysis, and comprehensive statistics.
Normal Distribution Calculator - Calculate probabilities for the normal (Gaussian) distribution including PDF, CDF, and inverse CDF with interactive bell curve visualization showing shaded probability areas. New
Odds Ratio Calculator - Calculate odds ratio, relative risk, confidence intervals, and number needed to treat from a 2×2 contingency table. Features animated forest plot, step-by-step solution with MathJax formulas, and clinical interpretation. New
Outlier Calculator - Identify statistical outliers in your dataset using the IQR (Interquartile Range) method. Calculate Q1, Q3, and detect values that fall outside the normal range with step-by-step calculations. Featured
p-Value Calculator - Calculate p-values from test statistics including z-score, t-statistic, chi-square, and F-statistic for one-tailed and two-tailed hypothesis tests. New
Pareto Chart Generator - Build Pareto charts that combine ranked bars with a cumulative-percent line so the "vital few" causes behind 80% of any problem jump out instantly. Paste data, pick a threshold, and read the takeaway sentence — no spreadsheet needed. New
Percentile Calculator - Calculate the value at any percentile in a dataset, or determine the percentile rank of a specific value. Supports linear, nearest rank, and exclusive interpolation methods with step-by-step breakdown and visualization. New
🥧 Pie Chart Maker - Create stunning pie charts with custom labels, colors, and percentages. Features animated rendering, donut mode, exploded slices, legend, and instant PNG/SVG download. New
Population Standard Deviation Calculator - Calculate population standard deviation (σ) with step-by-step calculations, interactive visualization, variance, mean, and data quality assessment for complete population datasets.
Quartile Calculator - Calculate quartiles (Q1, Q2, Q3), interquartile range (IQR), detect outliers, and visualize data distribution with interactive box plots and step-by-step calculations.
Quartile Deviation Calculator - Calculate the quartile deviation (semi-interquartile range) of a dataset with interactive box plot visualization, complete quartile analysis (Q1, Q2, Q3, IQR), outlier detection, and step-by-step calculation breakdown.
Range Calculator - Calculate the range of any dataset instantly with visual spread analysis, step-by-step calculations, quartile breakdown, and interactive data distribution chart.
Relative Standard Deviation Calculator - Calculate relative standard deviation (RSD) and coefficient of variation (%CV) with step-by-step formulas, interactive data visualization, statistical analysis, and data quality assessment. Featured
Root Mean Square Calculator - Calculate root mean square (RMS) of a set of numbers with step-by-step calculations, interactive visualization, AC/DC signal analysis, and statistical insights. Featured
Sample Mean Calculator - Calculate the sample mean (arithmetic average) of any dataset with step-by-step visualization, deviation analysis, data distribution chart, and comprehensive statistical insights.
Sample Size Calculator - Calculate the required sample size for surveys, research studies, and statistical analysis with confidence level, margin of error, and finite population correction. Get step-by-step formula breakdowns and visual confidence intervals.
Sample Standard Deviation Calculator - Calculate sample standard deviation with step-by-step formulas, interactive data visualization, outlier detection, empirical rule analysis, and comprehensive statistics including variance, mean, median, and range.
Scatter Plot Maker - Create beautiful interactive scatter plots to visualize relationships between two variables. Features correlation analysis, trend lines, multiple styling options, and downloadable PNG charts.
Six Sigma Process Capability Calculator - Calculate Cp, Cpk, Pp, Ppk, sigma level, DPMO and yield from either summary stats (mean, sigma, spec limits) or raw measurement data. Includes a normal-curve overlay, capability dial, plain-language verdict, and step-by-step working. New
Spearman Rank Correlation Calculator - Calculate Spearman's rank correlation coefficient (ρ) with step-by-step ranking, tied rank handling, scatter plot visualization, significance testing, and detailed interpretation of monotonic relationships. New
Standard Deviation Calculator - Calculate standard deviation, variance, mean, and other statistics with step-by-step solutions and visualizations.
Standard Error Calculator - Calculate standard error of the mean (SEM) with step-by-step calculations, confidence intervals, data visualizations, and comprehensive statistical analysis for your dataset. Featured
Statistics Calculator - An all-in-one statistics calculator for count, sum, mean, median, mode, range, variance, standard deviation, geometric mean, harmonic mean, quartiles, outlier detection, and more.
t-Test Calculator - Perform Welch's t-test to determine if there is a statistically significant difference between the means of two independent groups.
Variance Calculator - Calculate sample variance and population variance with interactive visualization, step-by-step formulas, deviation analysis, and comprehensive statistical insights.
Weibull Distribution Calculator - Calculate Weibull distribution probabilities, reliability R(t), hazard rate h(t), and B-life percentiles. Enter shape β and scale η to get PDF, CDF, mean, variance, MTTF, and step-by-step solutions with interactive graphs showing the bathtub curve behavior. New
Z-Score Calculator - Calculate z-scores (standard scores) instantly with step-by-step formulas, interactive normal distribution visualization, probability lookup, percentile ranking, and statistical interpretation.
Trigonometry Calculators
Arccos (Inverse Cosine) Calculator - Calculate arccos (inverse cosine) instantly with interactive unit circle visualization, step-by-step solutions, degree and radian outputs, and up to 1000 decimal places precision.
Arcsin Calculator - Calculate the inverse sine (arcsin) of any value between -1 and 1. Get results in degrees or radians with adjustable precision up to 1000 decimal places, interactive unit circle diagram, step-by-step solution, and general solution formulas.
Arctan2 Calculator - Calculate the angle between the positive x-axis and a point (x, y) using atan2. Features interactive SVG visualization, step-by-step solution, and high-precision output (1-1000 decimal places). Essential for programming, robotics, navigation, and game development.
Arctan Calculator - Calculate arctan (inverse tangent) with high precision. Get the angle whose tangent equals your input value, displayed in both degrees and radians with interactive unit circle visualization and step-by-step solution.
Cosine Calculator - Calculate the cosine of any angle with high precision, interactive unit circle visualization, cosine wave graph, step-by-step solutions, and special angle recognition. Supports degrees and radians.
Cosecant/Secant/Cotangent Calculator - Calculate the reciprocal trigonometric functions with adjustable precision from 1 to 1000 decimal places: Cosecant (1/sin), Secant (1/cos), and Cotangent (1/tan). Interactive unit circle visualization, domain validation, step-by-step explanation, and copy-to-clipboard functionality.
Decimal Degrees to DMS Converter - Convert angles from decimal degrees (e.g., 30.263889°) to Degrees, Minutes, Seconds (DMS) format (e.g., 30° 15' 50"). Supports GPS coordinates, navigation, and surveying applications with step-by-step conversion and visual breakdown.
DMS to Decimal Degrees Converter - Convert angles from DMS (Degrees, Minutes, Seconds) format to decimal degrees with interactive visualization, batch conversion, and smart format parsing. Perfect for GPS, GIS, navigation, and surveying.
Hyperbolic Functions Calculator - Calculate hyperbolic functions (sinh, cosh, tanh) and their inverses (asinh, acosh, atanh) with adjustable precision from 1 to 1000 decimal places. Features step-by-step solutions, interactive graphs, and identity verification.
Interactive Unit Circle Visualizer - A premium interactive unit circle tool. Drag to explore angles, snap to special values, see all 6 trig functions live, copy values instantly, and learn with step-by-step breakdowns and exact fractional values.
Law of Cosines Calculator - Solve triangles using the Law of Cosines. Supports SAS (Side-Angle-Side) and SSS (Side-Side-Side) cases. Get step-by-step solutions, interactive triangle visualization, area, perimeter, and triangle classification!
Law of Sines Calculator - Use the Law of Sines to find unknown sides or angles in a triangle. Supports ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSA (Side-Side-Angle) cases with ambiguous case detection. Get step-by-step solutions with detailed explanations!
Right Triangle Calculator - Solve right triangles by entering any two known values (sides or angles). Calculate all missing sides, angles, area, and perimeter with detailed step-by-step explanations and visual diagrams.
Sine Calculator - Calculate the sine of any angle with high precision, interactive unit circle visualization, sine wave graph, step-by-step solutions, and special angle recognition. Supports degrees and radians.
Tangent Calculator - Calculate the tangent of any angle with adjustable precision from 1 to 1000 decimal places. Supports degrees and radians, shows step-by-step solutions with MathJax formulas, interactive unit circle visualization, and clearly flags vertical asymptotes. Includes a special angles reference table and trigonometric identity cards.
Trigonometric Function Grapher - Interactive trigonometric function grapher for visualizing sine, cosine, tangent, cotangent, secant, and cosecant. Customize amplitude, frequency, phase shift, and vertical shift (y = A·f(B(x-C)) + D) with real-time parameter adjustment. Perfect for students, teachers, and engineers.
Trigonometric Identities Calculator - Calculate all trigonometric function values using Pythagorean, Double Angle, and Half Angle identities. Enter any known trig value and quadrant to find sin, cos, tan, csc, sec, cot with step-by-step solutions.
Volume Calculators
Volume Calculator - Calculate the volume of 11 different 3D shapes including sphere, cylinder, cone, cube, cuboid, triangular prism, pyramid, tetrahedron, ellipsoid, torus, and frustum. Get instant results with detailed step-by-step solutions.
Volume of a Cone Calculator - Calculate the volume of a cone instantly with step-by-step solutions. Enter radius and height to get volume, surface area, and slant height. Perfect for students, engineers, and educators.
Volume of a Cube Calculator - Calculate the volume of a cube instantly with our free calculator. Enter the edge length to get volume, surface area, space diagonal, and step-by-step formula breakdown with interactive 3D visualization.
Volume of a Cylinder Calculator - Calculate the volume and surface area of a cylinder with step-by-step formulas, interactive 3D visualization, unit conversions, and educational diagrams. Supports high-precision calculations.
Volume of a Pyramid Calculator - Calculate the volume of pyramids with rectangular, square, or triangular bases. Features interactive 3D visualization, step-by-step calculations, surface area, and multiple unit support.
Volume of a Rectangular Prism Calculator - Calculate the volume, surface area, and diagonal of a rectangular prism (box) with step-by-step formulas, 3D visualization, and unit conversions. Perfect for construction, packaging, and education.
Volume of Ellipsoid Calculator - Calculate the volume of an ellipsoid with step-by-step solution, interactive 3D diagram, surface area estimation, and unit conversions. Supports all common measurement units.
Volume of Sphere Calculator - Calculate the volume of a sphere with high precision using radius, diameter, or circumference. Features step-by-step calculations, interactive 3D visualization, unit conversions, and real-world size comparisons.
All MiniWebtools