Math
Free math calculators for percentages, fractions, averages, standard deviation, probability, algebra, geometry, and statistics.
Covers basic to college level.
Arc Length Calculator
Numerically integrate arc length over an interval for five common function types. Applies Simpson rule with 1000 steps for accurate results on any smooth curve.
Average Absolute Deviation Calculator
Calculate the average absolute deviation (AAD) of any dataset. Enter comma-separated numbers to get the mean, each absolute deviation, and the overall AAD.
Average Value of a Function Calculator
Calculate the average value of f(x) = ax² + bx + c over an interval [a, b] using the mean value theorem for integrals. Also finds the x-value where f equals its average.
Bessel Function Calculator
Evaluate Bessel functions of the first and second kind. Computes J0, J1, Y0, and Y1 at any positive x using high-accuracy polynomial approximations.
Beta Distribution Calculator
Calculate beta distribution PDF and CDF for any alpha and beta parameters. Find probabilities, mean, variance, and mode for any value on the interval [0, 1].
Chain Rule Calculator
Differentiate composite functions using the chain rule. Choose outer and inner function types, enter parameters, and evaluate d/dx[f(g(x))] at any point x.
Chi-Square Distribution Calculator
Calculate the p-value from a chi-square test statistic and degrees of freedom. Shows the right-tail probability and plots the chi-square PDF with the critical region.
Chinese Remainder Theorem Calculator
Solve a system of congruences using the Chinese Remainder Theorem. Find the unique solution x modulo M for up to three simultaneous congruences.
Cramer's Rule Calculator
Solve a 2x2 or 3x3 system of linear equations using Cramer's Rule. Enter the coefficients and constants to get the unique solution via determinants, with each step shown.
Critical Points Calculator
Find critical points of a cubic polynomial by setting the first derivative to zero. Classifies each as a local maximum, minimum, or saddle point via the second-derivative test.
Cumulative Frequency Calculator
Convert raw data into a cumulative frequency table and ogive chart. Enter numbers, set bin count, and track running totals as counts and percentages.
Curl Calculator
Compute the curl of a 3D linear vector field. Enter six cross-variable coefficients across three component functions and get the constant curl vector.
Descartes Rule of Signs Calculator
Count possible positive and negative real roots of a polynomial using Descartes' Rule of Signs. Enter coefficients for a polynomial up to degree 5 and see the sign change analysis.
Descriptive Statistics Calculator
Calculate mean, median, mode, standard deviation, variance, range, and IQR from a list of numbers. Paste any comma-separated dataset for an instant full statistical summary.
Directional Derivative Calculator
Compute the directional derivative of a 2D scalar field at any point. Enter function coefficients, a direction vector, and evaluation point to get the result.
Divergence Calculator
Find the divergence of a 3D vector field with monomial components. Enter P(x), Q(y), R(z) coefficients and evaluation point to get the scalar result.
Double Integral Calculator
Compute a double integral of f(x,y) over a rectangular region. Choose function type, enter coefficients and bounds; uses Simpson's 2D rule for accuracy.
Error Function Calculator
Calculate erf(x), erfc(x), and the inverse error function for any real input. The error function underpins the normal CDF and Gaussian diffusion equations.
Extended Euclidean Algorithm Calculator
Find the GCD of two integers and Bezout coefficients x, y such that a*x + b*y = gcd(a, b). Shows each division step of the Extended Euclidean Algorithm.
F Distribution Calculator
Compute F distribution tail probabilities and critical values. Enter numerator and denominator degrees of freedom with an F value or significance level.
F-Test Calculator
Compare two sample variances with an F-test. Enter sample variances and sizes to get the F-statistic, p-value, and test conclusion at any significance level.
Five Number Summary Calculator
Calculate five number summary (min, Q1, median, Q3, max) and IQR from up to 10 data values. Enter values in any order — the calculator sorts them.
Frequency Distribution Calculator
Build a frequency distribution table from raw data. Enter comma-separated values, choose bin count, and get interval frequencies with a histogram.
Gamma Function Calculator
Evaluate the Gamma function for any positive real x. Returns Gamma(x) and log-gamma. For positive integers, Gamma(n) equals (n-1) factorial.
Geometric Distribution Calculator
Calculate geometric distribution probability P(X=k), cumulative P(X≤k), mean, and variance. Models the number of trials until the first success.
Golden Rectangle Calculator
Calculate the dimensions of a golden rectangle from one side. Find width or height using φ = 1.618, plus area, diagonal, and the nested square spiral.
Gradient Calculator
Compute the gradient of a 2D or 3D scalar field at any point. Choose a function type, enter coefficients and evaluation point, and get the partial derivatives.
Hypergeometric Distribution Calculator
Find exact hypergeometric probabilities P(X = k) and P(X <= k) for sampling without replacement. Inputs: population size, success count, draws, and target k.
Hypothesis Test Calculator
Run a one-sample z-test or t-test. Enter sample mean, hypothesized mean, standard deviation, and sample size to get the test statistic, p-value, and conclusion at any significance level.
Implicit Differentiation Calculator
Find dy/dx for an implicit equation F(x,y) = 0. Enter coefficients of a general conic and a point on the curve to get the slope at that point.
IQR Calculator — Interquartile Range
Calculate interquartile range, Q1, Q3, and Tukey outlier fences from up to 10 values. Uses the exclusive quartile method. Identifies mild and extreme outliers.
L'Hopital's Rule Calculator
Evaluate indeterminate limits of the form 0/0 or infinity/infinity using L'Hopital's Rule on polynomial numerators and denominators. Shows each application step.
Lagrange Multiplier Calculator
Find extrema of a linear function subject to a circular or elliptic constraint. Uses the Lagrange multiplier method to solve constrained optimization.
Linear Approximation Calculator
Estimate function values near a center point using linear approximation. Choose a function type, set the center and target x, and compare the tangent-line estimate to the exact value.
Log-Normal Distribution Calculator
Compute the PDF, CDF, mean, and variance of a log-normal distribution. Enter the log-scale mean and standard deviation to evaluate at any positive x.
LU Decomposition Calculator
Decompose a square matrix A into A = LU using Doolittle's method. Get the lower-triangular L and upper-triangular U for 2x2, 3x3, or 4x4 matrices.
Matrix Power Calculator
Raise a 2x2 or 3x3 matrix to any positive integer power. Enter matrix entries and an exponent up to 20 to get the result by repeated multiplication.
Matrix Rank Calculator
Find the rank of a matrix using row reduction. Enter a 2x2, 3x3, or 4x4 matrix and get the rank, RREF form, and nullity computed step by step.
Matrix Trace Calculator
Compute trace, determinant, eigenvalues, and inverse of a 2x2 matrix. Enter the four elements to get a complete matrix analysis including classification and invertibility check.
Negative Binomial Distribution Calculator
Calculate negative binomial probabilities for failures before r successes. Enter success probability, target successes r, and observed failures k.
Normal Line Calculator
Find the normal line to a curve at a given x. Choose a function type, set parameters, and get the perpendicular slope and line equation y = mx + b.
Null Space Calculator
Find the null space (kernel) of a matrix. Enter a 2x2, 3x3, or 4x4 matrix and get the basis vectors for all solutions to Ax = 0.
Number Line Calculator
Plot a set of numbers on a number line. Enter comma-separated values, see them graphed with min, max, range, and median, and visualize spread.
Orthogonal Vectors Calculator
Check if two 3D vectors are orthogonal and find a vector orthogonal to a given one. Computes dot product, cross product, angle, and Gram-Schmidt orthogonalization.
P-Hat Calculator
Calculate the sample proportion and confidence interval for a population proportion. Enter successes, sample size, and confidence level for the CI bounds.
Partial Derivative Calculator
Compute the partial derivative of a 2D function with respect to x or y. Choose a function form, enter coefficients, and evaluate at any point.
Platonic Solids Calculator
Calculate volume, surface area, and all three radii of any Platonic solid. Covers all five from tetrahedron to icosahedron for any edge length.
Polynomial Division Calculator
Divide a polynomial by a linear divisor using synthetic division. Enter up to degree-4 coefficients and the divisor root to get the quotient and remainder.
Power Rule Calculator — Derivative of axⁿ
Apply the power rule to find the derivative of f(x) = axⁿ. Evaluate both the function and its derivative at any point x. Covers constant, linear, and polynomial terms.
Power Set Calculator
Generate all subsets of a set using the power set. Enter up to 15 comma-separated elements and get the complete list of 2^n subsets with their count.
Prediction Interval Calculator
Compute the prediction interval for a new observation from a fitted regression line. Enter regression stats and a new x value to get the interval bounds.
Product Rule Calculator
Differentiate a product of two functions using the product rule. Choose u(x) and v(x) types, set the parameters, and compute u-prime-v plus u-times-v-prime at any x.
QR Decomposition Calculator
Decompose a square matrix into A = QR with orthogonal Q and upper-triangular R using Gram-Schmidt. Works for 2x2, 3x3, and 4x4 matrices.
Quaternion Calculator
Add, subtract, multiply, or divide two quaternions. Enter a+bi+cj+dk components for each, choose an operation, and get the result with norm and conjugate.
Quotient Rule Calculator
Differentiate a ratio of two functions using the quotient rule. Choose numerator and denominator types, enter parameters, and evaluate the derivative at any point x.
R-Squared Calculator
Calculate R-squared (coefficient of determination) from x and y data pairs. Computes the regression line, correlation coefficient, and how well the line fits the data.
Rational Zeros Calculator
Apply the Rational Zero Theorem to list all possible rational roots of a polynomial. Enter integer coefficients up to degree 4 and see which candidates test as actual zeros.
Reduced Row Echelon Form Calculator
Compute the reduced row echelon form (RREF) of a square matrix using Gauss-Jordan elimination with partial pivoting. Works for 2x2, 3x3, and 4x4 matrices.
Regular Dodecahedron Calculator
Calculate volume, surface area, inradius, and circumradius of a regular dodecahedron from its edge length. Uses exact golden ratio formulas.
Relative Frequency Calculator
Convert raw counts into relative frequencies and cumulative percentages for up to 8 groups. Useful for frequency tables, surveys, and building probability distributions.
Residual Calculator
Calculate residuals from actual and predicted values. Enter y and y-hat pairs to get each residual, sum of squared errors, R-squared, and residual standard error.
Riemann Sum Calculator
Approximate a definite integral using left, right, midpoint, and trapezoidal Riemann sums for f(x) = ax² + bx + c over [a, b] with n subdivisions. Compares to exact value.
Row Echelon Form Calculator
Compute the row echelon form (REF) of a matrix using Gaussian elimination. Forward-only elimination, leaving an upper-triangular result with pivots.
Sampling Distribution Calculator
Find the standard error and probabilities for sample means using the Central Limit Theorem. Enter population mean, standard deviation, and sample size.
Secant Line Calculator
Find the secant line between two points on a curve. Computes slope and line equation for five function types, and plots the function with the secant drawn.
Simpson's Rule Calculator
Approximate definite integrals using Simpson's 1/3 rule and 3/8 rule for f(x) = ax² + bx + c. Compares to the exact value and shows error reduction with more subdivisions.
Singular Value Decomposition Calculator
Compute the SVD A = U Σ V^T for a 2x2 matrix. Get singular values, left singular vectors (U), and right singular vectors (V) analytically.
Skewness Calculator — Distribution Shape
Compute Fisher-Pearson skewness coefficient and excess kurtosis from up to 10 data points. Shows how far a distribution departs from symmetry and normal tail weight.
Tangent Line Equation Calculator
Find the equation of the tangent line to f(x) = axⁿ at any point x₀. Returns the slope, y-intercept, and full equation in slope-intercept and point-slope form.
Trinomial Distribution Calculator
Find the exact probability of a specific three-category outcome. Enter three event probabilities, total trial count, and counts for each category.
Triple Integral Calculator
Compute a triple integral of f(x,y,z) over a rectangular box. Choose function type, enter bounds, and get the result via 3D Simpson's rule.
Two-Proportion Z-Test Calculator
Test whether two population proportions are significantly different. Enter successes and sample sizes for each group to get the z-statistic, p-value, and confidence interval.
Uniform Distribution Calculator
Calculate mean, variance, PDF, and CDF of a continuous uniform distribution on [a, b]. Enter any x to find the probability P(X ≤ x) instantly.
Cosecant Calculator
Calculate the cosecant (csc) of any angle in degrees or radians. Shows csc(θ) = 1/sin(θ), valid range, and the equivalent value in the other angle unit.
Cotangent Calculator
Calculate the cotangent (cot) of any angle in degrees or radians. Shows cot(θ) = cos(θ)/sin(θ) with domain notes and the equivalent value in both angle units.
Double Angle Formula Calculator
Calculate sin(2θ), cos(2θ), and tan(2θ) using the double angle formulas. Enter any angle in degrees or radians and see all three results instantly.
Gram-Schmidt Orthogonalization Calculator
Orthogonalize two 2D vectors using the Gram-Schmidt process. Find the orthogonal pair and the orthonormal basis, with verification of perpendicularity.
Half-Angle Formula Calculator
Compute sin(θ/2), cos(θ/2), and tan(θ/2) using half-angle identities. Enter an angle in degrees or radians and get all three values instantly.
Hexagonal Prism Calculator
Calculate the volume, lateral surface area, and total surface area of a regular hexagonal prism. Enter the side length and height to get results.
Hexagonal Pyramid Calculator
Find the volume, slant height, lateral surface area, and total surface area of a regular hexagonal pyramid from base side length and height.
Hyperbolic Functions Calculator
Calculate all six hyperbolic functions for any x. Includes inverse formulas, the cosh²-sinh²=1 identity, and applications from catenaries to neural networks.
Lateral Surface Area Calculator
Lateral surface area of cylinders, cones, and pyramids, not including the base. Enter two dimensions and get slant height plus the full lateral area formula.
Modular Arithmetic Calculator
Calculate a mod n, addition, subtraction, multiplication, and modular exponentiation. Enter two values and a modulus for instant results.
Pentagon Calculator
Calculate the area, perimeter, diagonal, apothem, and circumradius of a regular pentagon from its side length. Works in any unit — meters, cm, or inches.
Percent to Goal Calculator
Track progress toward any target. Enter your current value and goal to calculate the percentage achieved, amount remaining, and how close you are.
Power Law Distribution Calculator
Calculate Pareto and power law probabilities, mean, and percentiles. Model heavy-tailed distributions like wealth, city populations, and word frequencies.
Regular Tetrahedron Calculator
Calculate volume, surface area, height, inradius, and circumradius of a regular tetrahedron from its edge length. All five properties with exact formulas.
Relative Change Calculator
Calculate the percentage change between two values. Shows absolute difference, relative percent change, and whether the change is an increase or decrease.
Right Cone Calculator
Calculate the volume, slant height, lateral surface area, and total surface area of a right circular cone. Enter radius and height to get all results.
Right Square Pyramid Calculator
Find the volume, slant height, lateral surface area, and total surface area of a right square pyramid from base side length and height.
Secant Calculator
Calculate the secant (sec) of any angle in degrees or radians. Shows sec(θ) = 1/cos(θ), valid range, and where the function is undefined.
Sum and Difference Formulas Calculator
Calculate sin, cos, and tan of the sum and difference of two angles. Enter angles A and B to get sin(A+B), sin(A-B), cos(A+B), cos(A-B), and more.
Time Percentage Calculator
See what percentage of a time range has elapsed. Enter a start date, end date, and current date to find days elapsed, days remaining, and progress.
2D Vector Projection Calculator
Project vector A onto vector B in two dimensions. Find scalar projection, vector projection, perpendicular component, and the angle between the two vectors in degrees.
Lagrange Interpolation Calculator
Build the unique polynomial through three data points using Lagrange interpolation. Enter x and y coordinates, then evaluate the polynomial at any x value.
Taylor Series Approximation Calculator
Approximate sin(x), cos(x), e^x, and ln(1+x) using a Taylor series with 1 to 10 terms. Shows the approximation vs true value with percent error and a chart.
Catalan Number Calculator
Compute the nth Catalan number C(n) used in combinatorics for counting binary trees, balanced parentheses, polygon triangulations, and lattice paths.
Clock Angle Calculator
Calculate the angle between the hour and minute hands of an analog clock at any time. Find acute and reflex angles for any HH:MM combination.
Harmonic Mean Calculator
Calculate the harmonic mean of any list of positive numbers. Compare with arithmetic and geometric means. Used for averaging rates, speeds, and ratios.
Logistic Growth Calculator
Model population growth with carrying capacity using the logistic equation. Compute population at any time, growth rate, and inflection point.
Modular Inverse Calculator
Find the modular multiplicative inverse a⁻¹ mod m using the extended Euclidean algorithm. Used in cryptography, RSA, and number theory.
Polygon Area Calculator (Shoelace Formula)
Calculate the area of any polygon from vertex coordinates using the shoelace formula. Supports triangles, quadrilaterals, and polygons up to 8 vertices.
Pythagorean Triples Generator
Generate primitive Pythagorean triples (a, b, c) with a² + b² = c². Find triples up to a chosen hypotenuse and check whether three integers form a triple.
Solid Angle Calculator (Steradian)
Convert between steradians, square degrees, and apex angles. Compute solid angle subtended by a cone or by an area at a distance for optics and astronomy.
Stirling Approximation Calculator
Approximate n! for large n using Stirling formula and its refinement. Compare exact vs approximate factorials and see relative error for any input.
Triangular Number Calculator
Compute the nth triangular number Tₙ = n(n+1)/2 and check whether a given integer is triangular. Generates the first N values and shows the sequence.
Amicable Numbers Checker
Check whether two numbers form an amicable pair — where each equals the sum of the other's proper divisors. Shows all divisors and the classic known pairs.
Annulus Calculator
Calculate area and perimeter of an annulus — the ring between two concentric circles. Enter outer and inner radius with unit select for instant results.
Binomial Theorem Expansion Calculator
Expand (a + b)^n step by step using the binomial theorem. Shows each term, binomial coefficients, and Pascal's triangle row for any power up to 20.
Capsule Calculator
Calculate volume and surface area of a capsule — a cylinder capped with two hemispheres. Enter the radius and cylinder height for instant results.
Circular Permutations Calculator
Count circular arrangements of n distinct objects around a fixed circle using (n-1)! formula. Compare with linear permutations and necklace arrangements.
Cohen's d Effect Size Calculator
Calculate Cohen's d effect size from two group means and standard deviations. Interpret small (0.2), medium (0.5), and large (0.8) effect sizes.
Completing the Square Calculator
Rewrite any quadratic ax² + bx + c into vertex form a(x − h)² + k with step-by-step work. Finds the vertex, axis of symmetry, and roots.
Conical Frustum Calculator
Calculate volume and surface area of a conical frustum (truncated cone) from top radius, bottom radius, and height. Includes slant height formula.
Difference of Two Squares Calculator
Factor any a^2 - b^2 expression into (a+b)(a-b) with step-by-step work. Supports symbolic (px+q)(px-q) factoring and graphs the resulting parabola.
FOIL Method Calculator
Multiply two binomials step-by-step using the FOIL method. See First, Outer, Inner, and Last terms individually, then the simplified combined result.
Hazard Ratio Calculator
Calculate hazard ratio and 95% confidence interval from events and person-time for two groups. Includes p-value and interpretation for survival analysis.
Kruskal-Wallis Test Calculator
Run a Kruskal-Wallis non-parametric one-way ANOVA test. Compare 2 to 5 groups using the H statistic, chi-squared p-value, and automatic tie correction.
Mann-Whitney U Test Calculator
Calculate the Mann-Whitney U test to compare two independent samples without normality assumptions. Shows U statistic, z-score, and two-tailed p-value.
One-Way ANOVA Calculator
Run a one-way ANOVA test on up to four groups. Calculate the F-statistic and p-value to determine if group means differ significantly.
Perfect Number Checker
Check whether an integer is a perfect number — equal to the sum of its proper divisors. Lists all divisors, the sum, and known perfect numbers up to 10¹⁰.
Pyramid Frustum Calculator
Calculate volume and surface area of a pyramid frustum (truncated square pyramid) from top side, bottom side, and height. Includes slant height formula.
Rise Over Run to Degrees Converter
Convert slope rise/run ratio to angle in degrees, radians, and percent grade. Instant conversion with formulas for ramps, roofs, and roads.
Six Sigma DPMO Calculator
Convert a defect rate to a sigma level and DPMO, or enter a sigma level to see the defect rate. Includes the 1.5 sigma shift used in industry practice.
Slope Percent Grade Calculator
Convert between slope angle in degrees, percent grade, and rise/run ratio. Enter any one value to get the others. Used for roads, ramps, and drainage.
Spearman Rank Correlation Calculator
Calculate the Spearman rank correlation coefficient from two paired data sets. Measures monotonic relationships without requiring a normal distribution.
Stadium Shape Calculator
Calculate area and perimeter of a stadium shape — a rectangle with semicircular ends. Enter the radius and straight-section length for instant results.
Stem and Leaf Plot Generator
Generate a stem-and-leaf plot from your dataset. Paste numbers and get an organized plot with median, quartiles, and summary statistics instantly.
Torus Calculator
Calculate the volume and surface area of a torus (donut shape) from major and minor radii. Uses Pappus centroid theorem formulas with a worked example.
Vote Percentage Calculator
Calculate vote percentages, winner margin, and total votes for up to 4 candidates. Enter raw vote counts and get instant election result analysis.
Weibull Distribution Calculator
Calculate Weibull PDF, CDF, reliability, and hazard rate from shape and scale parameters. Find mean, median, and mode for reliability and failure analysis.
Adding & Subtracting Fractions Calculator
Add or subtract two fractions with full step-by-step working. Finds the LCD, converts fractions, and simplifies the result to lowest terms.
Equivalent Fractions Calculator
Find equivalent fractions for any fraction and check whether two fractions are equivalent. Shows simplified form and a full list of equivalents.
Odds Calculator
Convert between probability (%) and odds formats. Calculate odds for/against, decimal odds, and "1 in N" from probability or event counts.
Quartile Calculator
Calculate Q1, Q2 (median), Q3, IQR, and outlier bounds from any dataset. Includes a 5-number summary chart and Tukey fence outlier detection.
Rounding Calculator
Round any number to a specified decimal places, significant figures, or to the nearest integer, 10, 100, or 1,000. Instant results with explanation.
2×2 Matrix Eigenvalue and Eigenvector Calculator
Calculate eigenvalues and eigenvectors of a 2x2 matrix. Find the characteristic polynomial, determinant, trace, and diagonalizability with full solution.
Adjacency Matrix to Edge List Converter
Convert an adjacency matrix to an edge list. Calculate vertex degrees, detect weighted graphs, and analyze graph structure from matrix input.
Bayes' Theorem Calculator
Calculate conditional probability with Bayes' theorem from prior, likelihood, and evidence. Includes a worked medical test sensitivity and specificity example.
Best Rational Approximation Calculator
Find the best fraction approximation for any decimal number using continued fractions. Shows the top 5 rational approximations within a denominator limit.
Bisection Method Calculator
Find roots of equations using the bisection method. Enter an interval [a, b] and a function to get iterative root approximations with step-by-step output.
Conic Sections Calculator
Calculate properties of ellipses, hyperbolas, and parabolas. Find foci, vertices, eccentricity, directrix, and semi-axes for any conic section equation.
Continued Fraction Expansion Calculator
Calculate the continued fraction expansion of any real number or fraction. Find convergents and representations of the golden ratio, pi, e, and sqrt(2).
Coterminal Angle Calculator
Find coterminal angles, reference angles, quadrant location, and trig values for any angle in degrees or radians. Shows positive and negative coterminals.
Expected Value in Game Theory Calculator
Calculate mixed strategy Nash equilibrium for 2×2 zero-sum games. Find optimal mixed strategies and expected payoffs for both players.
Fourier Series Calculator
Calculate Fourier series coefficients for square, sawtooth, and triangle waves. Find an and bn coefficients, partial sums, and convergence behavior.
Game Theory Payoff Matrix Solver
Find Nash equilibria, dominant strategies, minimax values, and mixed strategy equilibria for 2×2 and 2×3 payoff matrices in normal-form games.
Golden Ratio Calculator
Calculate golden ratio dimensions, golden rectangles, and Fibonacci sequences. Discover how phi (φ = 1.618) appears in nature, art, and architecture.
Graph Chromatic Number Estimator
Estimate the chromatic number of a graph using the Welsh-Powell greedy coloring algorithm. Enter edges and find the minimum colors needed.
Graph Properties Calculator
Calculate graph density, average degree, edge count, and analyze degree sequences. Check Euler path conditions and tree/complete graph status.
Growth Rate Calculator
Calculate simple growth rate, CAGR (compound annual growth rate), or continuous growth rate — plus doubling time using the Rule of 72.
Interval Notation Converter
Convert between inequality, interval, and set-builder notation. Visualize number line representations and find unions, intersections, and complements.
Laplace Transform Calculator
Look up Laplace transforms for common functions. Select function type, enter parameters, and get both f(t) and F(s) in formatted form.
Markov Chain Steady State Calculator
Find the steady-state (stationary) distribution of a 2×2 or 3×3 Markov chain transition matrix. Calculate long-run probabilities for any Markov process.
Minimax Algorithm Visualizer
Visualize the minimax algorithm for game trees. Enter leaf values and see how Max and Min players choose optimally in a 2-level or 3-level tree.
Möbius Function Calculator
Calculate the Mobius function for any integer: check squarefreeness, compute values for a range, and explore connections to the Riemann zeta function.
Numerical Differentiation Calculator
Approximate derivatives of functions using forward, backward, and central difference methods. Compare accuracy, step size effects, and higher-order formulas.
ODE Euler Method Solver
Numerically solve first-order ODEs using Euler's method. Choose a preset dy/dx function, set initial conditions, and see a step-by-step solution table.
Partial Fraction Decomposition Calculator
Decompose rational functions into partial fractions with support for linear, repeated linear, and quadratic factors for integration and Laplace transforms.
Shortest Path Calculator (Dijkstra's Algorithm)
Find the shortest path between two vertices in a weighted graph using Dijkstra's algorithm. Shows the path, total distance, and step-by-step table.
Base64 Encoder / Decoder
Encode any text to Base64 or decode Base64 back to readable text. Used in email attachments, data URLs, authentication tokens, and API credentials.
Diamond Problem Solver
Solve algebra diamond problems instantly. Enter the product (top) and sum (bottom) to find the two numbers. Essential for factoring trinomials.
Euler's Totient Function Calculator
Calculate Euler's totient function phi(n) — the count of integers from 1 to n that are coprime to n. Essential for RSA cryptography and number theory.
Fractal Dimension Calculator
Calculate the fractal (Hausdorff) dimension of self-similar fractals using box-counting. Covers coastlines, snowflakes, and strange attractors with examples.
Logistic Map & Bifurcation Calculator
Explore the logistic map and chaos theory. Calculate iterations, detect period-doubling bifurcations, and see the transition to chaos as parameter r increases.
Monty Hall Problem Simulator
Simulate the famous Monty Hall probability puzzle. See why switching doors wins 2/3 of the time through hands-on simulation.
Nash Equilibrium Calculator
Find the Nash Equilibrium for 2x2 payoff matrix games. Solve game theory problems including Prisoner's Dilemma and coordination games.
Newton's Method Root Finder
Find roots of equations using Newton's Method (Newton-Raphson). Enter a function and starting guess to iteratively find where f(x) = 0.
Numerical Integration Calculator (Simpson's, Trapezoidal, Midpoint)
Approximate definite integrals using Simpson's Rule, the Trapezoidal Rule, and the Midpoint Rule. Compare accuracy between methods and understand error bounds.
Pascal's Triangle Generator
Generate Pascal's Triangle up to any row count. See binomial coefficients, row sums, diagonal sequences, and patterns including the Fibonacci numbers.
Polar to Cartesian Coordinate Converter
Convert between polar (r, θ) and Cartesian (x, y) coordinates in both directions. Supports degrees and radians with formulas for trig, calculus, and physics.
Text to Binary Converter
Convert any text to binary code and back. Displays 8-bit binary for each character with its ASCII decimal and hex values. Supports all printable symbols.
Truth Table Generator
Generate truth tables for logical expressions with AND, OR, NOT, XOR, NAND, and NOR operations. Perfect for computer science and discrete math.
URL Encoder / Decoder
Encode special characters in URLs (percent-encoding) or decode encoded URLs back to readable text. Essential for developers, SEO, and web tools.
Venn Diagram Calculator
Calculate set operations including union, intersection, complement, and difference for 2 or 3 sets. Find cardinalities and region sizes.
Area of Shapes Calculator
Calculate the area of any 2D shape — circle, rectangle, triangle, trapezoid, parallelogram, ellipse, and more. Supports metric and imperial units.
Box Plot & Five-Number Summary Calculator
Calculate the five-number summary, quartiles, IQR, and outliers for any data set. Generate box plot data for statistics and data analysis.
Circumference Calculator
Calculate the circumference and area of a circle from the radius or diameter. Also find the radius or diameter from a known circumference.
Distance Formula Calculator
Calculate the distance between two points in 2D or 3D coordinate space. Also finds the midpoint, slope, and Manhattan distance.
Expected Value Calculator
Calculate the expected value (mathematical expectation) of a probability distribution. Enter outcomes and probabilities to find the long-run average result.
Golden Angle Calculator
Calculate the golden angle and explore its link to the golden ratio and Fibonacci spirals in nature. See cumulative angles for leaves and seeds.
Law of Sines Calculator
Solve triangles using the Law of Sines. Find unknown sides and angles for ASA, AAS, and SSA triangle configurations with step-by-step results.
Linear Regression Calculator (Least Squares)
Calculate the linear regression line (line of best fit) for a data set using the least squares method. Find slope, y-intercept, and R² correlation.
Mean Absolute Deviation (MAD) Calculator
Calculate the Mean Absolute Deviation (MAD) of a data set. A simple, intuitive measure of data spread easier to interpret than standard deviation.
Percent Error Calculator
Calculate the percent error between an experimental and theoretical value. Essential for lab reports and evaluating the accuracy of measurements.
Percentage Difference Calculator
Calculate the percentage difference between two values. Unlike percent change, percentage difference treats both values symmetrically for equal comparison.
Triangle Solver
Solve any triangle — find all sides and angles from any combination of known values. Supports SSS, SAS, ASA, AAS, and SSA using Law of Sines and Cosines.
Variance Calculator
Calculate population variance and sample variance from a data set. Understand how spread out your data is with this fundamental statistics measure.
Volume of Shapes Calculator
Calculate the volume of any 3D shape — sphere, cylinder, cone, rectangular prism, pyramid, and more. Includes unit conversion for all common units.
Geometric Mean Calculator
Calculate the geometric mean of a set of numbers. Used in finance for average investment returns, population growth rates, and other multiplicative processes.
Heron's Triangle Area Calculator
Calculate triangle area from three side lengths using Heron's formula. Works for any triangle — no height or angles needed. Shows full step-by-step work.
Law of Cosines Calculator
Solve any triangle with the Law of Cosines c² = a² + b² − 2ab·cos(C). Enter sides and angles to find unknown measurements, area, and perimeter.
Prime Factorization Calculator
Break any integer into its prime factors with exponent notation. Returns complete factorization, factor tree, all divisors, and total divisor count.
2x2 Matrix Multiplication Calculator
Multiply two 2x2 matrices instantly. Enter values for both matrices to get the product with all four elements using the row-by-column dot product method.
Binomial Probability Calculator
Calculate binomial distribution probabilities. Find the probability of exactly k successes in n trials with a given success probability.
Chi-Square Calculator
Perform a chi-square goodness-of-fit test. Enter observed and expected frequencies to calculate the chi-square statistic and p-value.
Confidence Interval Calculator
Calculate confidence intervals for population means. Enter your sample data or summary statistics to find the margin of error and interval bounds.
Derivative Calculator
Calculate derivatives of common functions step by step. Enter a function type and coefficients to find the derivative using standard differentiation rules.
Equation Solver
Solve linear and quadratic equations step by step. Enter your equation coefficients to find the solution with detailed working.
Fraction Simplifier Calculator
Simplify any fraction to its lowest terms. Enter a numerator and denominator to find the greatest common divisor and reduced fraction.
Greatest Common Factor (GCF) Calculator
Find the greatest common factor (GCF) of two or more numbers using prime factorization and the Euclidean algorithm. Used to simplify fractions and ratios.
Integral Calculator
Calculate integrals (antiderivatives) of common functions. Find both indefinite and definite integrals with step-by-step solutions.
Least Common Multiple (LCM) Calculator
Find the least common multiple of two or more numbers using prime factorization. Returns step-by-step working for fractions and scheduling problems.
Limit Calculator
Calculate limits of common functions as x approaches a value. Evaluate one-sided and two-sided limits with step-by-step explanations.
Long Division Calculator
Perform long division with step-by-step working. See the quotient, remainder, and decimal result with a complete division breakdown.
Matrix Determinant Calculator
Calculate the determinant of 2x2 and 3x3 matrices with step-by-step working. Uses cofactor expansion and applies to linear algebra and eigenvalue problems.
Normal Distribution Calculator
Calculate probabilities for the normal (Gaussian) distribution. Find the probability between, above, or below any value given the mean and standard deviation.
Number Base Converter
Convert numbers between binary, octal, decimal, hexadecimal, and any base from 2 to 36. Shows full conversion steps for programming and computer science.
P-Value Calculator
Calculate the p-value from a z-score, t-statistic, or chi-square statistic. Determine statistical significance for your hypothesis test.
Percentage Off / Sale Price Calculator
Calculate final sale price and dollar savings after any percentage discount. Enter price and discount to see savings and total paid, with optional sales tax.
Polynomial Evaluator
Evaluate any polynomial at a given x by entering degree and coefficients. Computes the result step-by-step using the Horner method for algebra and calculus.
Radian to Degree Converter
Convert between radians and degrees instantly using the formula degrees = radians × 180 / π. Includes a reference table of common angles from 0° to 360°.
Sample Size Calculator
Calculate the required sample size for your survey or study. Determine how many responses you need for reliable results at your desired confidence level.
Systems of Equations Solver (3 Variables)
Solve a 3×3 system of linear equations using Gaussian elimination. Returns exact x, y, z values, no-solution detection, and infinite solution identification.
T-Test Calculator
Perform a one-sample or two-sample t-test. Enter your data to calculate the t-statistic, p-value, and determine statistical significance.
Z-Score Calculator
Calculate the z-score (standard score) from a raw value, mean, and standard deviation. Find how many standard deviations a value is from the mean.
Age Difference Calculator
Calculate the exact age difference between two people in years, months, and days. Shows current ages and how old each person was when the other was born.
Coin Flip Probability Calculator
Calculate the probability of any heads/tails count in a series of flips using the binomial distribution. Returns exact and cumulative probabilities.
Cross Multiplication Calculator
Solve proportions by cross multiplication. Enter three values in a/b = c/d and find the unknown instantly with a step-by-step cross-multiplication solution.
Days Between Dates
Calculate exact days, weeks, months, and years between any two dates. Also counts business days excluding weekends and US federal holidays.
Dice Roll Probability Calculator
Calculate probability of rolling any sum with multiple dice. Supports d4, d6, d8, d10, d12, d20, and custom dice for tabletop RPGs and board games.
Fraction/Decimal/Percent Converter
Convert between fractions, decimals, and percentages instantly. Enter any fraction, decimal, or percentage and see all three forms with simplification.
Mean Calculator
Calculate the arithmetic mean of any set of numbers. Enter comma-separated values and get the mean instantly with sum and count shown for verification.
Number Sequence Finder
Enter a number sequence to identify arithmetic, geometric, or quadratic patterns. Returns the rule, common difference or ratio, and next predicted terms.
Number to Words Converter
Convert any number up to 999 trillion into written English words. Handles integers, decimals, and negatives — perfect for checks, legal documents, and invoices.
Percentage of Total Calculator
Calculate what percentage a part is of a total and find the reverse. Handles percent change for grades, discounts, and tax with step-by-step results.
Surface Area Calculator
Calculate surface area of cubes, rectangular prisms, spheres, cylinders, cones, and pyramids. Returns total and lateral area in square inches, cm, and meters.
Time Addition/Subtraction Calculator
Add or subtract hours, minutes, and seconds with automatic carrying and borrowing. Enter up to 10 time values to get total duration in HH:MM:SS format.
2D Vector Calculator
Add, subtract, and compute dot product, cross product magnitude, unit vector, and angle between two 2D vectors. Shows component-by-component working.
2x2 Matrix Calculator
Perform 2x2 matrix operations including addition, subtraction, multiplication, determinant, and inverse with step-by-step arithmetic shown for each calculation.
3x3 Matrix Calculator
Calculate determinant using Sarrus rule, transpose, and inverse of any 3x3 matrix. Returns all results for linear algebra and 3D graphics transformations.
Absolute Value Calculator
Calculate the absolute value of any real number or expression. Shows the result as a distance from zero on the number line with step-by-step explanation.
Average Calculator
Calculate mean, median, mode, range, and sum for any set of numbers. Returns descriptive statistics for homework, data analysis, and grade averaging.
Binary / Decimal / Hex Converter
Convert numbers between binary, decimal, and hexadecimal instantly. Enter any value in any base to see all three conversions with optional octal output.
Circle Calculator
Enter radius, diameter, circumference, or area of a circle and calculate all other measurements instantly. Returns all four values with full formulas shown.
Complex Number Calculator
Perform arithmetic on complex numbers in rectangular (a+bi) and polar form. Add, subtract, multiply, divide, find modulus, argument, and conjugate.
Decimal to Fraction Converter
Convert any decimal to a fraction in lowest terms or any fraction to a decimal. Handles terminating and repeating decimals with step-by-step simplification.
Elapsed Time Calculator
Calculate time difference between two timestamps in hours, minutes, and seconds. Supports AM/PM and 24-hour formats with overnight span detection.
Exponent Calculator
Calculate any base raised to any exponent including negative and fractional powers. Includes a table of common squares, cubes, and powers of 2 and 10.
Factorial Calculator
Calculate factorial n!, permutations P(n,r), and combinations C(n,r) with step-by-step working. Returns exact values up to 20! for probability problems.
Fibonacci Calculator
Find the nth Fibonacci number and generate the first N terms. See the golden ratio approximation (1.61803) and Fibonacci in nature, art, and spiral patterns.
Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step working. Returns a simplified fraction, mixed number, and decimal with LCM denominator.
Geometric Series Calculator
Calculate the sum of a geometric series given the first term, common ratio, and number of terms. Also shows infinite sum when |r| < 1.
GPA Calculator
Calculate cumulative and semester GPA on a 4.0 scale. Enter letter grades and credit hours to find your average and the grades needed to hit a target GPA.
Hex Color Converter
Convert colors between hex, RGB, and HSL with a live preview. Enter any hex code or RGB values to instantly get all three formats for web and design work.
Interest Rate Finder
Find the implied interest rate when you know the present value, future value, and number of periods. Reverse-engineer any growth rate.
LCM & GCD Calculator
Calculate the LCM and GCD for two or more numbers using prime factorization. Essential for adding fractions and solving divisibility problems.
Logarithm Calculator
Calculate logarithms with any base using the change-of-base formula. Returns ln (base e), log (base 10), and lb (base 2) with step-by-step working.
Markup & Markdown Calculator
Calculate selling price from cost and markup percentage, or find the sale price from markdown percentage. Essential for retail pricing.
Mean, Median, Mode Calculator
Enter a set of numbers to find the mean, median, and mode with explanations of which measure is most appropriate for your data.
Mixed Number / Improper Fraction Converter
Convert between mixed numbers and improper fractions and simplify results. Add, subtract, multiply, and divide mixed numbers with step-by-step working.
Modulo Calculator
Calculate the modulo (remainder) of any two integers: a mod n = r. Shows quotient, remainder, step-by-step division, and clock arithmetic examples.
Number Base Converter
Convert numbers between any base from 2 to 36 including binary, octal, decimal, and hex. Returns the converted value with digit-by-digit working shown.
Numerical Integration Calculator
Approximate the area under a curve using the trapezoidal rule and Simpson rule. Enter function f(x), integration bounds, and number of intervals.
Percentage Calculator
Calculate percentages three ways: find what percent of a number is, percentage of a total, and percentage increase or decrease between any two values.
Percentage Change Calculator
Calculate the percentage increase or decrease between any two values with the formula shown. Find percent change for prices, scores, population, and revenue.
Permutation & Combination Calculator
Calculate P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!) with step-by-step factorial working. Covers card hands, lottery, and committee formation problems.
Prime Number Checker
Check if any number is prime. If not, see its full prime factorization. Also shows the nearest primes above and below for quick number theory reference.
Probability Calculator
Calculate probability, odds, and expected value from events and outcomes. Covers single event, multiple events, and complementary probability.
Proportions Solver
Solve a/b = c/d proportions by entering any three values to find the fourth. Handles scaling recipes, map distances, unit rates, and similar-triangle problems.
Pythagorean Theorem Calculator
Calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²). Find the hypotenuse or either leg.
Quadratic Formula Calculator
Solve ax2 + bx + c = 0 using the quadratic formula. Returns real and complex roots, vertex, discriminant, and axis of symmetry with step-by-step working.
Ratio Calculator
Simplify ratios to lowest terms and find the missing value in a proportion (a:b = c:?). Covers part-to-part and part-to-whole for cooking, maps, and mixing.
Real-World Combinations Calculator
Calculate the total number of possible combinations for lottery numbers, PIN codes, passwords, and more. Understand your odds.
Roman Numeral Converter
Convert between decimals and Roman numerals in both directions. Supports 1 to 3,999 using standard subtractive notation for I, V, X, L, C, D, and M.
Rule of Three Calculator
Solve proportions with the rule of three: if A gives B, then C gives what? Uses cross-multiplication to find the unknown fourth value in any ratio.
Scientific Notation Converter
Convert between standard numbers and scientific notation. Also multiply and divide numbers in scientific notation with coefficient and exponent shown.
Significant Figures Calculator
Count the significant figures in any number and round to a specific number of sig figs. Essential for science and engineering.
Slope Calculator
Calculate slope, y-intercept, line equation, distance, and midpoint from two points. Returns slope-intercept form for algebra, geometry, and graphing.
Square Root Calculator
Calculate square root and cube root of any number. Checks for perfect squares, shows simplified radical form, and displays step-by-step working.
Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any data set. Returns population (σ) and sample (s) values with step-by-step working for up to 50 values.
Trigonometry Calculator
Calculate all six trig values — sin, cos, tan, sec, csc, and cot — from any angle in degrees or radians. Shows unit circle coordinates and reference angle.
Unit Rate Calculator
Calculate the price per unit or compare two rates to find the better deal. Essential for grocery shopping and cost comparisons.
Weighted Average Calculator
Calculate the weighted average (weighted mean) of values with different weights. Useful for grades, investments, and surveys.