Advanced Math Operations

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.

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.

Calculate the beta function B(x, y) with step-by-step calculations, gamma function relationship, interactive visualization, and detailed mathematical explanations.

Calculate binomial coefficients C(n, k) with step-by-step solutions, Pascal's triangle visualization, and real-world probability applications.

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.

Perform bitwise operations (AND, OR, XOR, NOT) and bit shift operations on integers with interactive visual bit diagrams showing each bit position.

Simplify Boolean expressions with algebraic laws, Quine-McCluskey and Karnaugh maps. Enter any AND, OR, NOT, XOR, NAND or NOR expression to get the minimal SOP/POS form, truth table, K-map, gate diagram and NAND-only equivalents.

Calculate probabilities using the Central Limit Theorem (CLT) with interactive visualizations, step-by-step solutions, and Z-score calculations for sample means.

Solve systems of simultaneous congruences with the Chinese Remainder Theorem. Find the smallest x satisfying several modular equations, with an Extended Euclidean Algorithm breakdown, a number-line visual and verification.

Calculate combinations C(n,k) with step-by-step solutions, Pascal's Triangle visualization, interactive diagrams, and detailed formula breakdowns for combinatorics problems.

Calculate the complementary error function erfc(x) with interactive visualization, step-by-step solution, and comprehensive erfc table for values from -3 to 3.

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.

Convert any decimal, fraction, or square root to its continued fraction representation with convergents, step-by-step Euclidean algorithm, and interactive visualization.

Calculate the number of derangements (subfactorial !n) of n elements, where nothing stays in its original position. Includes a step-by-step inclusion-exclusion formula, a visualization, a derangement table and probability analysis.

Enter a weighted graph and the start and end to get the shortest path, a priority-queue trace and the path tree. Limited to 50 nodes and 200 edges.

Calculate Shannon entropy of probability distributions with step-by-step formulas, interactive visualizations, entropy classification, and educational insights for information theory analysis.

Choose erf, erfc or the inverse, then enter x and a precision up to 15 decimal places, to get the value with steps on a Gaussian curve.

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.

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.

Calculate exponential growth and decay with step-by-step solutions, interactive growth curve visualization, and high-precision results for population, investment, and scientific modeling.

Calculate the exponential integral Ei(x) with high precision, interactive visualization, and detailed step-by-step mathematical derivation.

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.

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.

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.

Calculate the Gamma function with step-by-step solutions, interactive graphs, and factorial comparison tables. Supports both positive and negative real numbers.

Start with a total length, larger segment or smaller segment. Calculate the matching golden ratio lengths and golden rectangle dimensions.

Find the chromatic number and a valid vertex colouring for any undirected graph. Enter edges or an adjacency list to get the minimum number of colours, a colour assignment, an animated DSATUR walkthrough and a graph visualization.

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.

Compute the order of every element in a finite group, check whether it is abelian or cyclic, render the Cayley table as a colour-coded heatmap, and view the subgroup lattice as a Hasse diagram. Covers cyclic, dihedral and symmetric groups.

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.

Enter a graph of up to 20 vertices to check for a Hamiltonian path or cycle. A witness route is shown when one exists.

Enter elements or intersection sizes for up to five sets. See the union size, the signed expansion, and each region of the Venn diagram.

Minimize Boolean functions with Karnaugh maps. Enter minterms, maxterms or toggle a truth table to get the simplified sum-of-products or product-of-sums expression, colour-coded groupings, prime implicants and worked steps.

Solve linear programming problems with the simplex method. Supports maximize or minimize objectives, mixed constraints and up to eight decision variables, and for two-variable problems plots the feasible region with the optimum marked.

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.

Enter a weighted graph with up to 50 nodes and 200 edges to find the minimum spanning tree using Kruskal's or Prim's algorithm with visual steps.

Enter a base, an exponent, and a modulus. Get a^b mod n and the binary square-and-multiply steps.

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.

Calculate negative binomial probabilities for the number of trials or failures needed to reach a target number of successes. Get the exact PMF and CDF, step-by-step solutions, interactive charts and trial sequence visualizations.

Compute the maximum flow from source to sink in a capacitated directed network using Ford-Fulkerson with Edmonds-Karp. Animates every augmenting path and shows residual capacities, saturated edges and the proving min-cut.

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.

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.

Calculate permutations with repetition - ordered arrangements with replacement - using n^r. Enter the number of items and positions for the result, worked steps, slot-machine visuals and examples from passwords, PINs and licence plates.

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.

Check whether a graph is planar - drawable without edge crossings - using Kuratowski's theorem. Detects K5 and K3,3 subdivisions, verifies Euler's inequality, and highlights the forbidden minor when the graph is non-planar.

Calculate Poisson probabilities P(X=k), cumulative probabilities, and visualize PMF/CDF distributions with detailed step-by-step solutions.

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.

Enter a positive integer modulus to find all primitive roots, calculate Euler's totient, and view power tables with cyclic group visualizations.

Enter event probabilities to compute conditional probability, intersections, unions, and Bayes' theorem with interactive Venn diagrams and steps.

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.

Solve any proportion a/b = c/d for the missing value with cross multiplication, clear step-by-step solutions, and a visual diagram. Free, instant, and accurate.

Solve quadratic equations using the quadratic formula with step-by-step solutions, discriminant analysis, vertex form conversion, and interactive parabola visualization.

Compute addition, subtraction, multiplication, division, inverses and powers in modular rings and Galois finite fields. Visualise Cayley tables, classify units, zero divisors, nilpotents and idempotents, and inspect the group structure.

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.

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.

Convert numbers to scientific notation, perform arithmetic operations (+, -, ×, ÷), compare values, and visualize results with step-by-step explanations and interactive diagrams.

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.

Round numbers to significant figures, count sig figs with digit-by-digit analysis, and perform arithmetic with proper significant figure rules.

Solve the stable marriage problem with the Gale-Shapley algorithm. Paste ranked preference lists for two equal groups to get the guaranteed-stable pairing, with a proposal-by-proposal trace and blocking-pair verification.

Calculate Stirling numbers of the first kind (permutations into cycles) and second kind (set partitions into non-empty subsets). Includes an interactive triangle, a step-by-step recurrence derivation and full triangle tables.

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.

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.

Calculate the sum of consecutive square numbers (1² + 2² + ... + n²) with step-by-step formulas, interactive charts, and visual geometric representations.

Enter a directed graph to get a topological order with Kahn's algorithm or DFS, or the cycle path if the graph is not acyclic.

Enter city coordinates or a distance matrix to find a tour that visits each city once and returns. Exact Held-Karp up to 12 cities; 2-opt up to 40.

Enter a Boolean expression using letters A through H, eight at most. Get a truth table for AND, OR, NOT, XOR, NAND, NOR, XNOR, and conditionals.

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.