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.

Determine whether the difference between A/B test variants is statistically significant. Enter visitors and conversions for control and variant groups to get p-value, confidence level, uplift, and a clear win/lose verdict.

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.

Calculate the arithmetic mean (average) of a set of numbers with comprehensive statistical analysis including median, mode, range, standard deviation, variance, and interactive data visualization.

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.

Generate professional box and whisker plots with interactive visualization, comprehensive statistics, quartile analysis, outlier detection, and step-by-step calculations.

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.

Analyse categorical data with the chi-square test of independence for any R x C table. Get expected frequencies, standardized residuals, Cramer's V effect size, an animated mosaic plot, a residual heatmap and step-by-step solutions.

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.

Calculate Pearson, Spearman, and Kendall correlation coefficients with interactive scatter plot, regression analysis, p-values, and step-by-step calculation breakdown.

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.

Perform Fisher's exact test on 2×2 contingency tables. Get exact p-values (one-tailed and two-tailed), odds ratio, relative risk, step-by-step hypergeometric probability calculations, and interactive mosaic plot visualization.

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.

Calculate the interquartile range (IQR), quartiles Q1, Q2, Q3, five-number summary, and detect outliers with interactive box plot visualization and step-by-step calculations.

Perform Kruskal-Wallis H test to compare multiple independent groups. Get step-by-step calculations, rank analysis, effect size, and interactive visualization for non-parametric statistical analysis.

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

Calculate logarithmic growth over time using natural log (e), base 10, or base 2. Visualize growth curves, view year-by-year breakdowns, and understand step-by-step calculations.

Perform the Mann-Whitney U test (Wilcoxon rank-sum test) to compare two independent samples. Get U statistic, p-value, effect size, step-by-step calculations, and interactive visualizations.

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.

Calculate the median value of a set of numbers with step-by-step explanations, interactive visualizations, and comprehensive statistical insights.

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.

Identify statistical outliers in your dataset using the IQR (Interquartile Range) method. Calculate Q1, Q3, and detect values that fall outside the normal range with step-by-step calculations.

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.

Calculate relative standard deviation (RSD) and coefficient of variation (%CV) instantly, with step-by-step formulas, interactive data visualization, statistical analysis, and data quality assessment.

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.

Calculate sample standard deviation with step-by-step formulas, interactive data visualization, outlier detection, empirical rule analysis, and comprehensive statistics including variance, mean, median, and range.

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

Calculate Cp, Cpk, Pp, Ppk, sigma level, DPMO and yield from either summary stats (mean, sigma, spec limits) or raw measurement data. Includes a normal-curve overlay, capability dial, plain-language verdict, and step-by-step working.

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.

An all-in-one statistics calculator for count, sum, mean, median, mode, range, variance, standard deviation, geometric mean, harmonic mean, quartiles, outlier detection, and more.

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.

Create beautiful line charts with multiple series, smooth curves, area fills, data point markers, and custom themes. Download as PNG or SVG instantly.

Create beautiful, customizable bar charts from your data instantly. Supports vertical and horizontal bars, multiple color themes, animations, and one-click PNG/SVG download.

Create stunning pie charts with custom labels, colors, and percentages. Features animated rendering, donut mode, exploded slices, legend, and instant PNG/SVG download.

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.

Find the shortest path between nodes in a weighted graph using Dijkstra's algorithm. Features interactive graph visualization, step-by-step priority queue trace, and shortest path tree display.

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

Calculate the error function erf(x), complementary error function erfc(x), and inverse error function with interactive Gaussian curve visualization, step-by-step explanations, and comprehensive analysis for statistics and probability.

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.

Check whether a graph contains a Hamiltonian path or cycle. Runs backtracking with Warnsdorff pruning, verifies connectivity and degree prerequisites, tests the Dirac and Ore conditions, and shows the witness path on an SVG diagram.

Compute the size of a union of up to five sets with the inclusion-exclusion principle. Enter raw elements or the cardinality of every intersection to get the signed expansion, a live Venn diagram and every disjoint region's size.

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.

Calculate the Minimum Spanning Tree (MST) of a weighted graph using Kruskal's or Prim's algorithm. Features interactive graph visualization, step-by-step algorithm trace, and edge selection animation.

Calculate a^b mod n efficiently with the binary exponentiation algorithm. Enter the base, exponent and modulus for the result plus a step-by-step square-and-multiply breakdown, a binary decomposition visual and cryptographic context.

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.

Find all primitive roots of a modulus n - the generators of the multiplicative group. Enter any positive integer to get the primitive roots, Euler's totient, a cyclic group visualization and a step-by-step check with power tables.

Calculate probabilities of events using addition rule, conditional probability, and Bayes' theorem with interactive Venn diagrams and step-by-step solutions.

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.

Compute a topological ordering of a directed acyclic graph with Kahn's algorithm or DFS. Detects cycles and reports the cycle path, builds a parallel-execution layer view, and animates each step on an interactive graph.

Find the shortest tour that visits every city once and returns to the start. Uses exact Held-Karp dynamic programming for small instances and nearest-neighbour with 2-opt for larger ones, from coordinates or a distance matrix.

Generate truth tables for any boolean logic expression. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, and conditional operators. Visualize logic gates with animated evaluation.

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.

Check whether two positive integers form an amicable pair, or enter one number and let the tool find its partner. Includes animated divisor handshakes, step-by-step sigma-function breakdowns and aliquot-chain previews.

See carrying and borrowing happen column by column. This animated visualizer walks through every step of long addition and subtraction, including cascading borrows across zeros, so kids and learners can finally see why the trick works.

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.

Divide any number into two parts based on ratios or fractions. Interactive visual balance shows proportional splits with step-by-step calculations and downloadable results.

Test if a number is divisible by another number. Check multiple divisors at once, learn divisibility rules for 2-12, see step-by-step calculations, and explore prime factorization.

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.

Round and estimate results of arithmetic expressions. See side-by-side comparisons of rounding strategies, visual number lines, error analysis, and step-by-step estimation breakdowns.

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.

Find the minimum and maximum values in any number set with visual data distribution, sorted rankings, statistical analysis, and position indicators for comprehensive data exploration.

Generate and analyze the first n digits (up to 1000) of e (Euler's number) with comprehensive digit frequency analysis, pattern exploration, and interactive visualizations.

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.

Verify the Goldbach conjecture for any even integer above 2. Decompose your number into every pair of primes that sums to it, explore the Goldbach partition function, and view the famous Goldbach comet interactively.

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.

Solve multiplication problems step-by-step using the long multiplication method. See each partial product, carry digits, and column alignment for clear understanding.

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.

Free online multiplication calculator that multiplies any numbers instantly with detailed step-by-step solutions, visual factor breakdown, and comprehensive result analysis including sign rules and magnitude insights.

Generate printable multiplication tables for any range. Customize rows and columns, highlight specific multiples, and export as PDF for classroom or study use.

Calculate the n-th root of any number with high precision up to 1000 decimal places. Features step-by-step solutions, visual diagrams, and mathematical notation in both radical and exponential forms.

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.

Calculate the prime factors of any number with step-by-step factorization, interactive factor tree visualization, prime factorization in exponential form, and detailed mathematical analysis.

Calculate the prime factorization of any positive integer instantly. Get step-by-step breakdown, factor tree visualization, and complete analysis of prime factors.

Calculate quotient and remainder with interactive visual representations, step-by-step explanations, and comprehensive division insights.

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.

Practise on a virtual Japanese soroban with realistic bead movement. Click beads to set any value, or feed in an addition, subtraction, multiplication or division problem and watch it solved with the traditional complement rules.

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.

Apply classical Vedic maths sutras - vertically and crosswise, all from 9 and the last from 10, by one more than the previous one, and Nikhilam division - to multiply, square and divide fast. Every step is animated and explained.

Calculate the average rate of change of a function over an interval using the difference quotient. Enter any f(x) to get the secant slope, a step-by-step solution with MathJax formulas and a graph of the secant line and curve.

Solve Bernoulli differential equations step by step. Applies the v = y^(1-n) substitution to linearize the equation, builds the integrating factor, finds the closed-form solution and plots the particular curve against 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.

Calculate the curvature (κ) of a function y=f(x) or a parametric curve at a specific point, with step-by-step derivatives, osculating circle visualization, and radius of curvature.

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

Plot the slope field of any first-order ODE over a custom x-y region. Click the canvas to spawn solution curves, watch particles flow along the field, and see equilibrium nullclines, rendered as a pure SVG you can save or share.

Calculate directional derivatives of multivariable functions with step-by-step solutions, gradient computation, unit vector normalization, and interactive 3D surface visualization.

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.

Compute double integrals with detailed step-by-step solutions and 3D surface visualization. Supports definite and indefinite integrals with polynomial, trigonometric, exponential, and hyperbolic functions.

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.

Compute the discrete FFT of a real or complex signal sequence. Apply common window functions, choose FFT length and zero padding, inspect magnitude, phase, frequency bins, dominant peaks, and copy the full complex spectrum.

Solve first-order ordinary differential equations symbolically and numerically. Auto-detects separable, linear, exact and autonomous forms, applies the right technique, and draws an interactive slope field with the solution curve.

Calculate the Fourier series coefficients a0, an and bn for any periodic function. See the full integral computations, a coefficient table, the partial sum formula and a graph comparing the function with its Fourier approximation.

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.

Evaluate improper integrals with infinite limits or discontinuities. Supports Type I infinite bounds and Type II unbounded integrands, with step-by-step solutions, convergence analysis, visualizations and truncation-limit comparison.

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.

Evaluate limits of indeterminate forms (0/0, ∞/∞) using L'Hôpital's rule with step-by-step differentiation, interactive graph visualization, and detailed explanations.

Compute Laplace transforms instantly with detailed step-by-step solutions, interactive function presets, and dual visualization of time-domain and frequency-domain functions.

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.

Approximate definite integrals with Gauss-Legendre quadrature, Romberg extrapolation and adaptive Simpson quadrature. Compare estimates, error signals, function evaluations, convergence and adaptive interval placement in one workspace.

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.

Set up and solve related rates problems step by step with implicit differentiation and the chain rule. Covers the expanding sphere, sliding ladder, filling cone, ripple, shadow length, approaching cars and inflating balloon.

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.

Solve ordinary differential equations numerically with the classic 4th-order Runge-Kutta method. Enter the equation, initial conditions and step size to see the k1 to k4 computations, a solution table and the solution curve.

Solve second-order linear ODEs with constant coefficients, homogeneous or not. Derives the characteristic equation, classifies the damping as over, critical or under-damped, gives the closed form and plots the phase-plane trajectory.

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.

Solve systems of ordinary differential equations symbolically and numerically. Classifies the equilibrium as saddle, node, spiral or centre, derives eigenvalues step by step, and draws an interactive phase portrait with a trajectory.

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.

Calculate the Euclidean distance between two points in 3D space. Enter both sets of x, y, z coordinates to get the distance, midpoint, displacement vector and direction angles, with step-by-step formulas and a 3D diagram.

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.

Convert Cartesian coordinates (x, y) to polar coordinates (r, θ) with adjustable precision from 1 to 1000 decimal places. Features step-by-step solutions, interactive coordinate plane visualization, quadrant analysis, and verification.

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.

Identify the conic section type (circle, ellipse, parabola, or hyperbola) from the general second-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0. Get step-by-step classification, key properties, standard form, and an interactive graph.

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.

Build a Delaunay triangulation from any set of 2D points and watch it form, coloured by triangle quality. See the empty-circle property, overlay the Voronoi dual, and read the worst-angle and skinny-triangle statistics.

Calculate the Euclidean distance between two points in a 2D coordinate plane with step-by-step formulas, interactive visualization, midpoint, slope, and line equation calculations.

Calculate the circumference (perimeter) of an ellipse using multiple approximation formulas including Ramanujan, exact series, and visualize results with an interactive SVG diagram.

Find the equation of a line from two points, a point and slope, or slope and y-intercept. Get slope-intercept, point-slope, and standard form with interactive graph, step-by-step solution, and line properties.

Calculate the Euler characteristic (χ = V − E + F) from vertices, edges, and faces. Identify topological structure, genus, and surface type with step-by-step solutions, interactive 3D visualization, and Platonic solid comparisons.

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.

Calculate the shortest distance between two points on a sphere with the Haversine formula. Enter latitude and longitude to get the distance in kilometres, miles and nautical miles, plus initial and final bearing 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.

Calculate the hypotenuse of a right triangle using the Pythagorean theorem. Get instant results with visual diagrams, step-by-step solutions, angles, area, and perimeter.

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.

Calculate the area of any irregular polygon by entering vertex coordinates or drawing on an interactive canvas. Uses the Shoelace formula with step-by-step calculation, perimeter, centroid, and a visual diagram.

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.

Find equations of parallel and perpendicular lines passing through a given point. Enter a line equation and a point to get both parallel and perpendicular line equations with interactive graph, step-by-step solution, and line properties.

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.

Calculate the number of diagonals in an n-sided polygon, find the sum of interior angles, each interior angle of a regular polygon, and visualize the polygon with all its diagonals drawn.

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.

Calculate the centroid (center of mass) of any triangle given its three vertex coordinates. Get step-by-step solution, triangle properties, and an interactive visual diagram with medians.

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.

Solve quadratic equations by completing the square. Get detailed step-by-step algebraic work, vertex form, geometric visualization, and interactive parabola graph.

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.

Use Descartes' Rule of Signs to determine the possible number of positive and negative real roots of any polynomial. Enter coefficients and see step-by-step sign change analysis with visual diagrams.

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.

Determine the domain (possible inputs) and range (possible outputs) of algebraic functions with step-by-step analysis and interval notation.

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.

Calculate the composition of two functions (f ∘ g)(x) and (g ∘ f)(x) with detailed step-by-step instructions showing how to compose functions algebraically.

Visualize algebraic functions on an interactive coordinate system. Plot multiple equations, identify key features like intercepts, asymptotes, and analyze function behavior.

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.

Solve concentration and mixture word problems step by step. Blend two solutions, find how much stock to add for a target concentration, dilute with water, strengthen with pure solute, or drain and replace part of a mixture.

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.

Solve equations containing radicals (square roots, cube roots, etc.) with step-by-step solutions. Automatically checks for extraneous solutions to ensure accuracy.

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.

Visualize the feasible region (solution set) for a system of two or more linear inequalities. Graph each inequality on a coordinate plane and identify the intersection region.

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.

Solve classic two-train word problems step by step: trains meeting head-on, overtaking in the same direction, crossing each other with lengths, passing a pole, or crossing a platform, with animated track visuals and relative-speed maths.

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-and-B-working-together rate problems in five forms: combined time, the missing solo time of one worker, fill-versus-drain pipes, alternating shifts, and partial completion when one worker joins midway. Fully explained.

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.

Calculate the cross product of two 3D vectors with the determinant formula. Get a step-by-step expansion, the perpendicular result vector, its magnitude as the parallelogram area, a direction check and a 3D visualization.

Calculate the determinant of any square matrix with detailed step-by-step cofactor expansion, matrix properties analysis, and visual solutions.

Calculate the dot product of two vectors in 2D, 3D or higher dimensions. Get the angle between them, magnitudes, scalar and vector projections, the geometric meaning and step-by-step formulas with an interactive diagram.

Calculate eigenvalues and eigenvectors of 2x2 and 3x3 matrices with detailed step-by-step solutions, characteristic polynomial derivation, interactive visualization, and matrix property analysis.

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.

Calculate the Jacobian matrix of a vector-valued multivariable function. Enter the transformation components to get every partial derivative, the determinant, eigenvalues, worked steps and a grid deformation visualization.

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.

Calculate the inverse of a square matrix using Gauss-Jordan elimination with detailed step-by-step row operations. Supports 2×2 to 6×6 matrices with exact fractional arithmetic, determinant calculation, and A×A⁻¹=I verification.

Calculate LU decomposition of any square matrix with partial pivoting. Get lower triangular (L), upper triangular (U), and permutation (P) matrices with step-by-step Gaussian elimination and verification.

Multiply two matrices with detailed step-by-step element computation. See each dot product broken down, with color-coded row × column visualization. Supports matrices up to 5×5 with interactive dimension controls.

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.

Calculate the rank of any matrix using Gaussian elimination (row echelon form). Get step-by-step row reduction, pivot analysis, column space and null space dimensions, and visual heatmap. Supports matrices up to 10×10.

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.

Find the null space (kernel) of any matrix by solving Ax = 0 using Gaussian elimination. Get the basis vectors, nullity, step-by-step RREF reduction, and rank-nullity theorem verification with exact fractional arithmetic.

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.

Calculate the singular value decomposition of any matrix, factoring A into U, Sigma and V transpose. Includes step-by-step solutions, an interactive 3D visualization, rank analysis, condition number and data compression uses.

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.

Calculate the unit vector in the direction of any 2D, 3D or n-dimensional vector. Get the magnitude, each normalized component, direction angles, the step-by-step normalization and visual proof that the result has length 1.

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.

Convert any decimal number to scientific notation with step-by-step visualization, multiple output formats including E-notation and engineering notation, and interactive examples for learning.

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.

Convert hexadecimal numbers to decimal, binary, octal, and any base from 2 to 36. Get instant multi-format results with visual digit breakdown and step-by-step conversion process.

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.

Free online tool to convert octal numbers to hexadecimal with step-by-step calculation, binary representation, and digit breakdown visualization.

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.

Generate and explore the first n prime numbers with an interactive visualization, twin prime detection, gap analysis and distribution charts. Useful for maths lessons, cryptography research and number theory exploration.

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.

Generate Fibonacci numbers with golden ratio visualization, spiral diagram, and sequence analysis. Create lists of the first N Fibonacci numbers instantly.

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.

Solve linear homogeneous recurrence relations with constant coefficients. Enter the recurrence and initial values to get the closed form from the characteristic equation, the first N terms, the roots and a growth classification.

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.

Convert angles from DMS (Degrees, Minutes, Seconds) format to decimal degrees with interactive visualization, batch conversion, and smart format parsing. Perfect for GPS, GIS, navigation, and surveying.

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.

Graph sine, cosine, tangent, cotangent, secant and cosecant interactively. Adjust amplitude, frequency, phase shift and vertical shift in the form y = A*f(B(x-C)) + D and watch the curve update in real time.

Calculate all trigonometric function values using Pythagorean, Double Angle, and Half Angle identities. Enter any known trig value and quadrant to find sin, cos, tan, csc, sec, cot with step-by-step solutions.

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.

Express any proper fraction as a sum of distinct unit fractions the ancient Egyptian way. Run the Greedy, Binary and Practical algorithms side by side, watch an animated pie converge, and explore Rhind Papyrus expansions.

Generate equivalent fractions with visual fraction bars, number line diagrams, and pattern highlighting. Check if two fractions are equivalent or find up to 100 equivalent fractions instantly.

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.

Convert any decimal, repeating decimal, or mixed number to a simplified fraction. See step-by-step GCD reduction, visual fraction bar, and verification with long division.

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.

Calculate the area of a circle from radius, diameter, or circumference. Get instant results with step-by-step calculations, interactive diagrams, and comprehensive circle metrics.

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.

Calculate the total surface area of a cube with step-by-step solutions. Find surface area from edge length, space diagonal, face diagonal, or volume with interactive 3D visualization and comprehensive measurements.

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.

Calculate the surface area of a sphere from radius or diameter with step-by-step formula breakdown, interactive visualization, and unit conversions. Perfect for geometry, engineering, and science.

Calculate how many gallons or litres your swimming pool holds. Supports rectangular, round, oval and kidney shapes with separate shallow and deep-end depths, and gives surface area, water weight and an estimated 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.

Calculate the volume of a cone instantly with step-by-step solutions. Enter radius and height to get volume, surface area, and slant height. Perfect for students, engineers, and educators.

Calculate the volume of a cube instantly with our free calculator. Enter the edge length to get volume, surface area, space diagonal, and step-by-step formula breakdown with interactive 3D visualization.

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.

Calculate logarithm for any base with step-by-step solutions, interactive visualization, and conversion between common log types (natural log, log base 10, log base 2).

Calculate the common logarithm (log base 10) of any positive number with detailed step-by-step solutions, interactive graphs, and real-world applications including pH scale, decibels, and Richter scale.

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.