Math

Plan an A/B test before you launch. Enter baseline conversion rate, minimum detectable effect, significance level and power to get the required sample size per variant, the total sample, and the test duration at your traffic.

Enter visitors and conversions for control and variant groups to calculate uplift, p-value, and confidence level with a win/lose verdict.

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.

Enter a list of numbers separated by commas, spaces, or line breaks to calculate their arithmetic mean, median, mode, range, variance, and standard deviation.

Calculate mean, median, mode, geometric mean, harmonic mean, and weighted average with complete statistical analysis, visualizations, and step-by-step solutions.

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.

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.

Calculate beta distribution probabilities from shape parameters alpha and beta. Get P(X <= x), P(X >= x) or an interval, with interactive PDF and CDF graphs, shaded regions, step-by-step solutions, mean, variance, mode and skewness.

Enter up to 10 sets of numbers. Get a box plot with quartiles, whiskers, and outliers.

Run a chi-square test of independence to see whether two categorical variables are significantly associated. Get the chi-square statistic, p-value, expected frequencies, cell contributions and Cramer's V effect size, step by step.

Calculate Coefficient of Variation (CV) with step-by-step formulas, visual comparison charts, data quality assessment, and comprehensive statistical analysis for your datasets.

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.

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.

Calculate confidence intervals for means and proportions with interactive visualization, t-distribution and z-distribution support, step-by-step calculations, and sample size recommendations.

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.

Enter categorical counts up to a 20x20 table size. Get expected frequencies, standardized residuals, Cramér's V, and chi-square test results.

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.

Enter paired x and y values. Get Pearson, Spearman, and Kendall correlations, a scatter plot, and p-values.

Calculate and visualise 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.

Calculate exponential distribution probabilities and explore its properties. Enter the rate parameter and a value to get P(X <= x), P(X > x) and interval probabilities, plus mean, variance, median, PDF and CDF curves and worked steps.

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.

Enter the four counts of a 2×2 table to get one-tailed and two-tailed Fisher's exact p-values, the odds ratio, and relative risk.

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.

Calculate geometric distribution probabilities for the number of trials until the first success. Enter the per-trial success probability and the trial number to get the PMF, CDF, cumulative probabilities and step-by-step solutions.

Calculate the geometric mean of any dataset with step-by-step formulas, interactive visualization, comparison with arithmetic mean, and comprehensive statistical analysis.

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.

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.

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.

Calculate hypergeometric probabilities for sampling without replacement. Enter population size, success states, draws and observed successes to get exact and cumulative probabilities, PMF charts, worked steps and urn visualizations.

Paste a list of numbers. See Q1, Q2, Q3, the IQR, the five-number summary, and outliers, with a box plot and steps.

Compare up to 20 independent groups to get Kruskal-Wallis H test results, rank analyses, effect sizes, and step-by-step calculations.

Calculate linear regression equation, slope, intercept, R-squared, and make predictions with interactive scatter plot visualization and step-by-step formula breakdown.

Enter initial value, growth rate, time, and base to calculate logarithmic growth curves. Generates year-by-year tables for up to 100 years.

Paste two independent samples. Get the Mann-Whitney U statistic, a p-value, an effect size, and the rank-sum steps.

Calculate Mean Absolute Deviation with step-by-step formulas, interactive visualization, and comprehensive statistical analysis. Understand data variability with our free MAD 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.

Calculate mean, median, mode and range with step-by-step formulas, interactive visualization, frequency analysis, and comprehensive statistical breakdown for any dataset.

Calculate the median absolute deviation (MAD) of a dataset with step-by-step formulas, interactive visualization, outlier detection, and robustness comparison to standard deviation.

Enter numbers separated by commas, spaces, or line breaks to calculate the median, range, minimum, and maximum with step-by-step explanations.

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.

Calculate the mode (most frequent values) of a dataset with interactive frequency visualization, step-by-step analysis, and comprehensive statistics.

Calculate probabilities for the normal (Gaussian) distribution including PDF, CDF, and inverse CDF with interactive bell curve visualization showing shaded probability areas.

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.

Enter numbers separated by commas, spaces, or line breaks to find Q1, Q3, the interquartile range, and all values outside the fences with step-by-step math.

Calculate p-values from test statistics including z-score, t-statistic, chi-square, and F-statistic for one-tailed and two-tailed hypothesis tests.

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.

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.

Calculate population standard deviation (σ) with step-by-step calculations, interactive visualization, variance, mean, and data quality assessment for complete population datasets.

Calculate quartiles (Q1, Q2, Q3), interquartile range (IQR), detect outliers, and visualize data distribution with interactive box plots and step-by-step calculations.

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.

Calculate the range of any dataset instantly with visual spread analysis, step-by-step calculations, quartile breakdown, and interactive data distribution chart.

Calculate root mean square (RMS) of a set of numbers with step-by-step calculations, interactive visualization, AC/DC signal analysis, and statistical insights.

RSD describes spread relative to the mean; it does not establish accuracy or data quality. Judge acceptability using criteria for your method and purpose. A mean near zero can make this ratio unstable.

Calculate the sample mean (arithmetic average) of any dataset with step-by-step visualization, deviation analysis, data distribution chart, and comprehensive statistical insights.

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.

Enter sample values. Get the sample standard deviation and variance, plus the mean, median, range, and flagged outliers.

Create beautiful interactive scatter plots to visualize relationships between two variables. Features correlation analysis, trend lines, multiple styling options, and downloadable PNG charts.

Enter a mean, sigma, and spec limits, or paste raw measurements. Get Cp, Cpk, Pp, Ppk, sigma level, DPMO, and yield.

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.

Calculate standard deviation, variance, mean, and other statistics with step-by-step solutions and visualizations.

Calculate standard error of the mean (SEM) with step-by-step calculations, confidence intervals, data visualizations, and comprehensive statistical analysis for your dataset.

Enter numbers to get count, sum, mean, median, mode, range, variance, standard deviation, geometric and harmonic means, quartiles, and outliers.

Perform Welch's t-test to determine if there is a statistically significant difference between the means of two independent groups.

Calculate sample variance and population variance with interactive visualization, step-by-step formulas, deviation analysis, and comprehensive statistical insights.

Calculate Weibull probabilities, reliability, hazard rate and B-life percentiles. Enter the shape and scale parameters to get the PDF, CDF, mean, variance and MTTF, with step-by-step solutions and graphs showing bathtub-curve behaviour.

Calculate z-scores (standard scores) instantly with step-by-step formulas, interactive normal distribution visualization, probability lookup, percentile ranking, and statistical interpretation.

Enter labels and one or more series, up to 200 points. Make a line chart with curves, area fill, or markers, then download PNG or SVG.

Enter labels and values, up to 50 bars, and choose a direction and color theme to download a PNG or SVG.

Enter labels and values, up to 20 slices, to draw a pie or donut chart and download it as PNG or SVG.

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.

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.

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.

Calculate the absolute value (modulus) of any real or complex number. See step-by-step solutions, number line visualization, and distance-from-zero animation.

Enter two integers or one number to auto-find its partner, view step-by-step divisor sigma breakdowns, and verify amicable number pairs.

Enter two numbers and select addition or subtraction to watch column-by-column carrying and borrowing steps, including cascading borrows across zeros.

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.

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.

Solve proportions using cross multiplication. Find the unknown value in a/b = c/d equations with step-by-step solutions and visual diagrams.

Calculate the cube (n³) and cube root (∛n) of any number with step-by-step solutions, perfect cube detection, and interactive visualizations.

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.

Calculate the digital root of any number by repeatedly summing its digits until one digit remains. Supports additive and multiplicative modes, bases 2, 8, 10 and 16, an animated breakdown, formula check and persistence counter.

Enter a number and a ratio or fraction to split it into two parts, with the steps and a balance view. Decimals can run to 10 places.

Enter an integer of up to 15 digits and one or more divisors to test each, see the rules for 2 through 12 and list divisors, with up to 50 shown.

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 chosen, and learn why the trick is really binary arithmetic.

Enter an arithmetic expression to estimate it with more than one rounding method, and see the steps, a number line and the error of each estimate.

Quickly check if numbers are even or odd. Supports batch input with visual grouping, divisibility explanations, number line visualization, and detailed parity analysis.

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.

Check whether any positive integer belongs to the Fibonacci sequence. Uses Gessel's perfect-square theorem for an O(1) test, reveals the exact index, shows the Zeckendorf representation and plots the golden ratio convergence.

Enter numbers separated by commas, spaces, or new lines to find the minimum and maximum and see the set sorted.

Enter a count from 10 to 1000 to generate digits of Euler's number and calculate digit frequencies, mean values, and consecutive run lengths.

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.

Enter an even integer greater than 2 to list every pair of primes that adds up to that number.

Calculate the greatest common factor (GCF) of two or more numbers with step-by-step solutions using multiple methods.

Check if a number is prime with detailed analysis, factorization, and visual number line representation.

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.

Visualize addition and subtraction step by step with column-by-column carrying and borrowing. Color-coded animations show each digit computation for easy learning.

Solve long division problems step by step. See the full working process with quotient, remainder, and decimal expansion. Perfect for learning and verifying division.

Enter two numbers up to 999,999,999,999 to see the long multiplication solution with aligned columns, carry digits, and partial products.

Sharpen mental arithmetic with drills across five difficulty levels, from single-digit addition to two-digit multiplication. Every problem names a strategy and shows an animated coach card, and the Daily Workout is the same worldwide.

Test whether 2^p - 1 is a Mersenne prime for a given exponent p. Uses the Lucas-Lehmer test with an animated iteration trace, a binary bit-pattern visual, Euclid-Euler perfect-number pairing and the 52 known Mersenne primes.

Calculate the Mobius function for any positive integer, returning -1, 0 or +1 with full prime factorization, squarefree analysis, a step-by-step explanation, the Mertens function and a colour-coded heatmap of nearby integers.

Calculate modulo (remainder) with step-by-step division process, interactive visual diagrams, and support for integers, decimals, negative numbers, and scientific notation.

Enter numbers separated by commas, lines, or multiplication signs to get instant products with detailed step-by-step solutions and factor breakdowns.

Choose the row and column ranges and any multiples to highlight. Get a multiplication table you can print or export as a PDF.

Enter a number and an index n. Get the n-th root in radical and exponential form, with as many as 1000 decimal places, and the steps.

Generate animated number bond practice for early arithmetic. Pick a total from 5 to 100 and a Practice Quiz, Bond Chart or Fact Family mode, and each problem comes with a cherry diagram, a ten-frame and a two-colour bar model.

Calculate the number of digits in any integer, analyze digit distribution, and visualize the breakdown of each position value (ones, tens, hundreds, etc.).

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.

Solve math expressions step by step following PEMDAS/BODMAS order of operations. See each step with highlighted operations, perfect for learning operator precedence.

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.

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.

Enter a whole number up to 10^15 to see its prime factors, a factor tree, and the product in exponential form.

Enter any positive integer with up to 15 digits to get its prime factorization, step-by-step breakdown, and a factor tree visualization.

Enter a dividend and a divisor to get the quotient and remainder for whole numbers of any size, with the steps shown.

Generate fresh maths practice by grade level (K-8) and topic: addition, subtraction, multiplication, division, fractions, decimals, percentages, word problems and pre-algebra. Each has a visual aid and a reveal-on-demand solution.

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.

Compute directly with Roman numerals. Watch every step: subtractive expansion, regrouping, borrowing for subtraction, the Roman doubling method for multiplication and division, and final canonicalization of the answer.

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 and see the parities reveal the binary form of your multiplier.

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.

Set beads or enter an addition, subtraction, multiplication, or division to watch it solved on a 13-column soroban. Whole numbers up to 999,999.

Sort numbers in ascending or descending order with comprehensive statistics, visual distribution charts, and detailed analysis. Handles decimals, negatives, and thousands separators.

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.

Add long lists of numbers instantly with high precision. Paste or type your values separated by commas, spaces, or line breaks and get the total right away.

Practise multiplication tables with a live timer, streak counter and a 12x12 heatmap that pinpoints your weakest facts. Pick any tables from 2 to 12, choose Sprint, Marathon or Boss Battle, and switch between three question formats.

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.

Enter whole numbers to multiply, square, or divide with a Vedic sutra. Each step is shown, within that sutra's digit limit.

Enter a function f(x) and interval bounds [a, b] to compute the secant line slope with step-by-step MathJax formulas and a visual graph.

Enter P(x), Q(x), exponent n, and initial conditions to linearize the Bernoulli equation, find a closed-form solution, and plot the slope field.

Calculate linear, circular, and continuous convolution of signals and functions with interactive visualizations, detailed step-by-step solutions, and comprehensive mathematical analysis.

Calculate the curl of any 2D or 3D vector field with a step-by-step determinant expansion. Enter the component functions, get the symbolic curl, evaluate it at a point, spot irrotational fields and view a vorticity overlay.

Enter y=f(x) or a parametric curve and a point to get curvature, the radius of curvature and the osculating circle, with derivative steps.

Calculate derivatives instantly with step-by-step solutions. Supports single-variable, partial, implicit, and directional derivatives with interactive visualizations.

Enter a first-order ODE and an x-y window to plot the slope field, add up to 8 solution curves and see the equilibrium nullclines.

Enter a multivariable function, a point and a direction to get the directional derivative and gradient, with steps. The maximum equals the gradient's magnitude.

Calculate the divergence of any 2D or 3D vector field with step-by-step partial derivatives. Enter the component functions, get the symbolic divergence, evaluate it at a point, identify sources and sinks, and view a heat map.

Enter a function, integration variables, and optional limits to compute double integrals with step-by-step solutions and 3D surface plots.

Solve any first-order ODE numerically with Euler's method. See the iteration table, the Euler polygon drawn on the slope field, and a convergence comparison at h, h/2 and h/4, with optional error analysis against a closed form.

Enter real or complex samples and a sample rate to compute discrete FFT magnitude, phase, frequency bins, and dominant peaks.

Enter dy/dx = f(x, y), initial values, and an x range to solve the differential equation and generate a slope field with a solution curve.

Enter a periodic function and its interval to calculate Fourier coefficients a0, an, and bn. Up to 20 terms are computed at once.

Calculate the gradient vector of a multivariable function. Enter f(x, y) or f(x, y, z) to get every partial derivative, evaluate the gradient at a point, read its magnitude and direction, and view a 2D gradient field.

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.

Enter an integrand and bounds, including infinity. Evaluate Type I and Type II improper integrals and see whether they converge, with steps.

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.

Calculate the instantaneous rate of change of any function at a point using the limit definition. Get step-by-step solutions with MathJax formulas, an interactive tangent line graph and a convergence table as h approaches zero.

Calculate definite and indefinite integrals with detailed step-by-step solutions, interactive function visualization, and comprehensive explanations for calculus students and professionals.

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.

Enter a numerator, a denominator, and the point, including infinity. Evaluate 0/0 or infinity-over-infinity forms by differentiating, with steps.

Enter a function of t. See its Laplace transform with steps and both the time-domain and s-domain pictures.

Calculate limits of mathematical functions with detailed step-by-step solutions. Supports one-sided limits, indeterminate forms, and L'Hospital's Rule.

Calculate line integrals of scalar and vector fields along parametric curves in 2D and 3D. Enter the field, parametric equations and bounds for symbolic results with step-by-step solutions, arc length and a curve visualization.

Compute the Maclaurin series expansion of common functions at x = 0. Get the nth-order polynomial terms, a Lagrange remainder estimate, the radius of convergence and an animated graph of partial sums converging to the function.

Find roots of equations with the Newton-Raphson method. Enter any function and an initial guess to see step-by-step iterations with tangent line approximations, convergence analysis and a graph tracing the path to the root.

Enter a function and the interval. Compare Gauss-Legendre, Romberg, and adaptive Simpson results, with error and evaluation counts.

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 an interactive graph with worked steps.

Compute partial derivatives of multivariable functions with detailed step-by-step solutions, interactive examples, and geometric visualization of tangent planes.

Find the power series representation of a function centred at any point. Compute Taylor and Maclaurin coefficients, determine the radius and interval of convergence with endpoint analysis, and watch partial sums converge.

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.

Pick a setup such as a sliding ladder, filling cone, expanding sphere, or balloon, and enter the known rates. Get the related rate with steps.

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.

Enter an equation, initial conditions, and a step size. See each k1-to-k4 step and a solution table, for at most 1000 steps.

Enter coefficients, forcing expression, initial values, and x range to find the closed-form ODE solution, damping classification, and phase-plane plot.

Test whether an infinite series converges using the Ratio, Root, Integral, Comparison, Limit Comparison, Alternating Series and p-Series tests, with step-by-step solutions and animated partial sum graphs.

Approximate definite integrals with Simpson's 1/3 rule, 3/8 rule and the composite rule. Includes an interactive parabolic visualization, error estimation, convergence analysis, method comparison and step-by-step solutions.

Compute derivatives of any single-variable function with step-by-step solutions, differentiation rule identification, interactive graph, and critical point analysis.

Evaluate surface integrals of scalar fields and flux integrals of vector fields over parametric surfaces. Choose a preset - sphere, cylinder, cone, paraboloid or torus - or enter your own, with normal vectors and a 3D visualization.

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.

Enter differential equations or matrix coefficients to classify equilibrium points, compute eigenvalues step by step, and generate trajectory phase portraits.

Calculate the Taylor series expansion of any function around a point with step-by-step derivative calculations, interactive comparison graph, and educational explanations.

Approximate definite integrals with the trapezoidal rule, with an interactive trapezoid visualization, error estimation, Richardson extrapolation, convergence analysis and a per-trapezoid area breakdown. Accepts functions or data points.

Compute triple integrals with detailed step-by-step solutions and 3D visualization. Supports definite and indefinite integrals with symbolic computation.

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.

Calculate the Wronskian determinant of a set of functions to test linear independence. See the full matrix with derivatives, a step-by-step determinant expansion, and a verdict on whether the functions form a fundamental set.

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.

Enter both x, y, z coordinates to get Euclidean distance, the midpoint, the displacement vector, and direction angles.

Plot interactive 3D surfaces z = f(x, y) with mouse rotation, zoom and pan. Adjust the x/y domain, mesh resolution, colour map, wireframe and lighting to explore saddle points, ripples, paraboloids and the sinc surface.

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.

Calculate arc length, radius, or central angle of a circle sector with interactive diagram, step-by-step solution, and support for degrees and radians.

Enter x and y coordinates and precision up to 1000 decimals to get polar coordinates (r, θ) with quadrant analysis and step-by-step verification.

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.

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.

Generate the 2D flat pattern of a cone or truncated cone. Calculates the outer radius, inner radius and sweep angle you need to cut the unrolled template from sheet metal, cardboard or paper for DIY, HVAC ductwork and crafting.

Enter coefficients A through F of a second-degree polynomial. Instantly identify circles, ellipses, parabolas, or hyperbolas with step-by-step properties.

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.

Enter 2D points to build a Delaunay mesh coloured by triangle quality, check the empty-circle property and overlay the Voronoi dual.

Enter the coordinates of two points to get the Euclidean distance, the midpoint, the slope and the line equation, with formula steps.

Enter the semi-major and semi-minor axes to calculate the perimeter of an ellipse using Ramanujan and infinite series formulas with an SVG diagram.

Enter two points, a point and a slope, or a slope and y-intercept to get all three line forms, with a graph and the steps.

Enter vertices, edges and faces to compute V − E + F, then see the genus, the surface type and a comparison with the Platonic solids.

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.

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.

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.

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.

Enter two latitudes and longitudes to get the distance in kilometres, miles, and nautical miles, plus bearings and the midpoint.

Calculate the area of a triangle from its three sides with Heron's formula. Get the semi-perimeter, area, perimeter, inradius, circumradius, all three altitudes, interior angles and triangle type, with an interactive diagram.

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.

Enter the lengths of side a and side b to calculate the hypotenuse, internal angles, perimeter, and area of a right triangle with step-by-step solutions.

Calculate the incircle of a triangle. Enter three sides or three vertex coordinates to find the inradius, incenter, tangent points, tangent lengths and contact triangle, with an interactive diagram and step-by-step formulas.

Input up to 100 vertex coordinates or draw on the canvas to find polygon area, perimeter, and centroid with step-by-step calculations.

Calculate the midpoint between two points instantly with interactive visualization, step-by-step solution, distance calculation, and comprehensive geometry analysis.

Find the vertex, focus, directrix, axis of symmetry and latus rectum of any parabola. Supports standard form, vertex form and general conic form, with an interactive graph and step-by-step solutions for each property.

Enter a line equation and a point to get the parallel and perpendicular lines through that point, with a graph and steps.

Graph parametric equations x(t) and y(t) interactively. Features animated curve tracing, speed-based colouring, the osculating circle, tangent vectors, arc length, and presets for Lissajous, heart, rose, butterfly and spirograph curves.

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.

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.

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.

Enter the number of sides to get the diagonal count, the interior-angle sum, and each interior angle of a regular polygon.

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.

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.

Calculate the area, perimeter, apothem, circumradius, interior and exterior angles and number of diagonals of any regular polygon. Enter the number of sides and side length for results with step-by-step formulas and a diagram.

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.

Calculate slope, gradient, angle, and line equation from two coordinate points. Features interactive graph visualization, step-by-step solutions, and multiple output formats.

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.

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.

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.

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.

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.

Enter the (x, y) coordinates of three vertices to calculate the triangle's centroid with step-by-step formulas and median diagrams.

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.

Solve equations involving absolute values step by step. Shows both positive and negative cases with detailed explanations and verification.

Solve inequalities involving absolute values (e.g., |x+a| < b, |x-2| > 3). Understand 'and' vs 'or' conditions with detailed step-by-step solutions.

Solve classic age word problems step by step: one person N years older than another, ratios in Y years, three-person age ratios and father-son puzzles. Sets up the algebra, solves the system, verifies it and draws a timeline.

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.

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.

Solve classic coin word problems step by step: N coins totalling a given amount, twice as many quarters as dimes, three-coin mixtures with count relationships, and fewest coins to make an amount. Animates the coin stacks.

Enter quadratic coefficients a, b, and c to solve quadratic equations by completing the square, find the vertex form, and view step-by-step algebra.

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.

Enter a polynomial's coefficients, up to degree 20, to see the sign changes and possible counts of positive and negative real roots.

Solve for distance, speed or time given the other two. Pick the unknown on an interactive triangle, mix units freely, enter time as 1h 30m or 5400 sec, and use bonus modes for multi-leg average and round-trip harmonic-mean speed.

Enter a function such as 1/(x-2), sqrt(x) or log(x) to get its domain and range in interval notation, with the analysis steps.

Multiply and expand polynomials (binomials, trinomials, and higher-degree expressions) using FOIL method and Binomial Theorem. Get step-by-step solutions with detailed explanations.

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.

Enter f(x) and g(x) to calculate both compositions, with algebraic steps for (f ∘ g)(x) and (g ∘ f)(x).

Enter up to three functions and your axis ranges to plot curves and find up to 10 intercepts and 5 vertical asymptotes.

Determine whether a function is even, odd or neither, with a step-by-step algebraic proof, symmetry graph, numerical verification table and even-odd decomposition. Handles polynomial, trig, exponential, log and absolute value functions.

Solve linear, quadratic, polynomial, and rational inequalities with step-by-step solutions. Display results graphically on a number line and in interval notation.

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.

Solve single-variable linear equations (e.g., ax + b = c) with detailed step-by-step solutions. Shows all algebraic manipulations and verifies the answer.

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.

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.

Choose a problem type and enter concentrations and amounts. Solve a blend, a dilution with water, adding pure solute, or draining and replacing part of a mix.

Plot polar equations interactively: r = sin(3t), Archimedean spirals, cardioids, limacons, lemniscates and butterfly curves, with adjustable range, resolution, palettes and grid. Overlay up to three equations and export SVG or PNG.

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.

Divide one polynomial by another using long division. Shows the complete step-by-step process, quotient, and remainder with detailed explanations.

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.

Enter an equation with square roots or cube roots to solve it step by step and check for extraneous solutions.

Simplify square roots and higher-order radicals into simplest radical form - sqrt(50) becomes 5*sqrt(2) - including rationalizing the denominator, with step-by-step solutions built on prime factorization.

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.

Simplify, add, subtract, multiply, or divide rational expressions (fractions involving polynomials). Features step-by-step solutions, factoring visualization, domain analysis, and detailed explanations.

Use the Rational Root Theorem to find every possible rational root of a polynomial with integer coefficients. Enter the coefficients for the full candidate list, verification of the actual roots and step-by-step factoring.

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.

Divide polynomials by linear binomials (x - a) using the streamlined synthetic division method. Shows step-by-step process with coefficients and remainder.

Enter two or more linear inequalities and the axis window to graph each boundary and shade the overlapping feasible region.

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.

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.

Enter speeds, gap, head start, and train lengths to solve head-on meetings, overtaking, and platform crossing problems step by step.

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.

Calculate the vertex (maximum or minimum point) and the axis of symmetry for any quadratic function (parabola) with detailed step-by-step solutions.

Solve a combined time, a missing solo time, fill-versus-drain pipes, alternating shifts, or the time when a second worker joins midway.

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.

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.

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.

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.

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.

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.

Enter two 3D vector coordinates to calculate their cross product, perpendicular vector, and parallelogram area with step-by-step determinant expansion.

Enter a square matrix of up to 10 by 10 to get its determinant by cofactor expansion, with the steps and matrix properties.

Enter two vectors in 2D, 3D or up to 50 dimensions to get the dot product, the angle between them and the scalar and vector projections.

Enter a 2×2 or 3×3 matrix to get its eigenvalues and eigenvectors, the characteristic polynomial and the solution steps.

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.

Enter function components and variables (up to 6 each) to calculate the Jacobian matrix, determinant, eigenvalues, and worked steps.

Compute the Jordan canonical form of a square matrix plus the transition matrix P with P inverse A P = J. Handles defective, non-diagonalizable matrices via generalized eigenvectors, with kernel-chain analysis and a block diagram.

Calculate matrix operations with step-by-step solutions: addition, subtraction, multiplication, inverse, transpose, and determinant. Visual matrix display with detailed explanations.

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.

Compute the matrix exponential e^(At) and use it as the state transition matrix for linear ODE systems. Enter A, a time t and an optional initial vector to get x(t), Pade scaling details and an animated phase-plane flow diagram.

Enter a square matrix from 2x2 to 6x6. Get the inverse by Gauss-Jordan elimination, the determinant, and a check that A times A^-1 is I.

Enter a square matrix up to 8x8. Get the lower, upper, and permutation matrices from Gaussian elimination with partial pivoting.

Multiply two matrices up to 5x5 with step-by-step element computation and row-by-column breakdown.

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.

Enter a matrix up to 10x10. Get its rank from row echelon form, plus the column-space and null-space dimensions.

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.

Enter a matrix. Get a basis for the solutions of Ax = 0, the nullity, the row-reduction steps, and a rank-nullity check in exact fractions.

Decompose rational functions into partial fractions with detailed step-by-step solutions, coefficient analysis, and visual decomposition breakdown.

Decompose any matrix into an orthogonal Q and an upper triangular R with the Gram-Schmidt process. Handles 2x2 to 5x5 matrices with animated step-by-step orthogonalization and a check that Q transpose times Q equals the identity.

Reduce any matrix to reduced row echelon form with detailed step-by-step row operations. Enter your matrix and see every pivot, swap and elimination, then read off rank, nullity, pivot columns, free variables and solution type.

Enter a matrix of at most 10 by 10. Get U, Sigma, and V transpose, plus the rank and the condition number.

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.

Enter a 2D, 3D, or longer vector, up to 50 dimensions, for its magnitude, unit vector, and direction angles.

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.

Calculate the magnitude, or Euclidean norm, of a 2D, 3D or n-dimensional vector. Get a step-by-step computation showing each squared component, the sum under the radical and the final square root, with a vector diagram.

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.

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.

Convert integers between any number bases from 2 to 36 with step-by-step calculation breakdown and digit position analysis.

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.

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.

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.

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.

Convert binary numbers to octal with interactive visualization showing bit grouping, step-by-step conversion process, and comprehensive number system education.

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.

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.

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.

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.

Enter a decimal to get scientific notation, E-notation and engineering notation, with the steps that shift the decimal point.

Convert degrees to radians instantly with interactive unit circle visualization, step-by-step formulas, common angle references, and bidirectional conversion support.

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.

Enter a hexadecimal number to convert it to decimal, binary, octal or another base from 2 to 36. See the value of each digit and the conversion steps.

Convert hexadecimal (Base-16) numbers to binary (Base-2) with visual digit mapping, step-by-step conversion breakdown, and one-click copy.

Convert hexadecimal (base-16) numbers to decimal (base-10) instantly. See step-by-step conversion process, positional notation breakdown, and results in multiple bases.

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.

Perform addition, subtraction, multiplication, and division on octal (base-8) numbers with step-by-step visual explanations and instant decimal conversions.

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.

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.

Convert octal (base-8) numbers to decimal (base-10) with visual digit-by-digit breakdown, step-by-step calculations, and educational explanations.

Enter an octal number of up to 21 digits. Get the hexadecimal form, the binary in between, and the digit breakdown.

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.

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.

Convert any ratio to percentage with step-by-step solution, visual pie chart representation, and support for multiple ratio formats including fractions and decimals.

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.

Convert numbers from scientific notation (exponential form) to ordinary decimal notation with step-by-step explanation and visual decimal point movement.

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.

Generate the n-th Catalan number with a step-by-step formula derivation, interactive parenthesization and polygon-triangulation visuals, a full sequence table and the combinatorial meaning behind each interpretation.

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.

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.

Enter a number from 1 to 10,000 to get a list of consecutive prime numbers, identify twin primes, and view the gaps between each prime.

Calculate the nth term, sum of first n terms, and infinite sum of any geometric sequence with step-by-step solutions and interactive visualization.

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.

Choose a count, a maximum value, or a start and end index. See that Fibonacci list, with a golden-ratio view and a spiral diagram.

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.

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.

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 Young diagrams, compare distinct-parts and odd-parts counts, and plot the growth curve.

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.

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.

Enter a linear homogeneous recurrence with constant coefficients and its initial values. Get the closed form and up to 60 terms.

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.

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.

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.

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.

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.

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.

Calculate the angle between the positive x-axis and a point (x, y) using atan2, with an interactive diagram, a step-by-step solution and high-precision output up to 1000 decimal places for programming, robotics and navigation.

Calculate cosecant, secant and cotangent with precision from 1 to 1000 decimal places. Includes an interactive unit circle, domain validation, a step-by-step explanation and one-click copy of any result.

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.

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.

Enter DMS coordinates or batch paste up to 50 lines to convert degrees, minutes, and seconds into decimal degrees for GPS and GIS mapping.

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.

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.

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!

Use the Law of Sines to find unknown sides or angles in a triangle. Supports the ASA, AAS and SSA cases with ambiguous-case detection, and gives step-by-step solutions with a detailed explanation of each stage.

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.

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.

Calculate the tangent of any angle with precision from 1 to 1000 decimal places. Supports degrees and radians, shows step-by-step solutions, an interactive unit circle, and clearly flags vertical asymptotes with a special angles table.

Choose sine, cosine, tangent, cotangent, secant, or cosecant and set A, B, C, and D in y = A*f(B(x-C)) + D to graph the curve.

Enter a known trig value, quadrant, and identity type to calculate sin, cos, tan, csc, sec, and cot with step-by-step solutions up to 100 decimal places.

Compare two fractions with step-by-step explanations, visual pie charts, and interactive diagrams to see which fraction is larger or smaller.

Convert any decimal number to a fraction with step-by-step visual explanation, multiple output formats, and interactive fraction visualization.

Enter a numerator and denominator to write the fraction as distinct unit fractions, comparing the greedy, binary and practical methods.

Enter one fraction to list equivalents, up to 100 of them, or enter two fractions to test whether they are equivalent, with bars and a number line.

Perform fraction arithmetic with our interactive calculator. Get step-by-step solutions, visual diagrams, and results in multiple formats including mixed numbers and decimals.

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.

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.

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.

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.

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.

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.

Type a percent such as 75%, a repeating decimal, or a mixed number. Get the simplified fraction, the GCD steps, and a long-division check.

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.

Enter a radius, diameter, or circumference to get the circle's area and its other measurements, with the steps.

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.

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.

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.

Calculate ellipse area instantly with our free tool. Get area, perimeter (Ramanujan formula), eccentricity, and interactive visualization. Perfect for geometry, engineering, and design calculations.

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.

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.

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.

Enter an edge, space diagonal, face diagonal, or volume to calculate a cube's total surface area.

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.

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.

Enter the radius or diameter of a sphere to calculate its total surface area with step-by-step formulas and unit conversions.

Enter your pool shape, dimensions, and depths to calculate total water volume in gallons or litres, surface area, water weight, and hose fill time.

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.

Enter the radius and height of a cone for its volume, surface area, and slant height, with the formula steps shown.

Enter the edge length for the cube's volume, surface area, and space diagonal, with the formula steps shown.

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.

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.

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.

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.

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.

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.

Calculate percentage change between two values with step-by-step breakdown, visual comparison charts, and detailed analysis. Find percentage increase, decrease, or difference instantly.

Calculate the percentage decrease between two values with step-by-step solutions, interactive SVG diagrams, and multiple calculation modes including reverse calculations.

Calculate percentage error between estimated and actual values with step-by-step formula breakdown, visual comparison chart, error interpretation, and detailed analysis.

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.

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.

Enter a number and a base, or choose natural log, log base 10, or log base 2. See the logarithm with steps.

Calculate common logarithms and inverse powers of 10 with adjustable display precision, batch input, calculation steps and conditional scientific interpretations.

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.

Calculate the natural logarithm ln(x) of any positive number with step-by-step derivation, interactive visualization, logarithm properties, related calculations, and mathematical insights.