Math Calculators

Percentage Calculator

Find what a percentage of a number is, instantly — the most fundamental everyday percentage calculation.

CAGR Calculator

Find the compound annual growth rate between a starting and ending value — a single, comparable annualized figure for evaluating growth over any time period.

Pythagorean Theorem Calculator with Steps

Find any missing side of a right triangle — hypotenuse or leg — from the other two, using a² + b² = c².

Fraction Calculator with Mixed Numbers

Add, subtract, multiply or divide two fractions or mixed numbers — fully simplified, shown as both an improper fraction and a mixed number.

Simultaneous Equation Solver with Steps

Solve a system of two linear equations with two unknowns using Cramer's rule — every determinant shown alongside the final x and y.

Percentage Change Calculator

Find the percentage increase or decrease between two numbers — a relative measure of change that's more meaningful than the raw difference alone.

Quadratic Formula Calculator with Graph

Solve ax² + bx + c = 0 and see the actual parabola plotted — roots, vertex, axis of symmetry and y-intercept, all from one graph.

Bayes Theorem Calculator with Examples

Update a probability based on new evidence — Bayes' theorem, the mathematical foundation behind medical testing, spam filters, and every 'given what we now know' probability question.

Derivative Calculator

Find the derivative of any function at a specific point — computed numerically from the actual definition of a derivative, with the step-by-step working shown.

Average Calculator

Find the average (mean) of up to five numbers — the most common single-number summary of a data set.

Gaussian Elimination Calculator with Steps

Solve a 3×3 system of linear equations via Gaussian elimination — watch each row operation reduce the system down to a direct answer.

Binomial Probability Calculator with Explanation

Find the probability of exactly k successes in n independent trials — the binomial distribution, the foundation for coin-flip, quality-control and A/B-test probability questions.

Integral Calculator with Limits and Graph

Compute a definite integral between two limits — the exact area under any curve — with the function plotted alongside the result.

Standard Deviation Calculator with Work

Find the mean, variance and standard deviation of any dataset, with every intermediate step shown — population or sample formula, your choice.

Confidence Interval Calculator from Sample Data

Find the confidence interval for a population mean from your sample's mean, standard deviation and size — with a genuine margin of error, not just a single estimate.

Quadratic Equation Calculator

Solve ax² + bx + c = 0 for its real roots, instantly — using the quadratic formula, one of algebra's most foundational tools.

Circle Calculator

Find the area and circumference of a circle from its radius — the two foundational measurements for any circular shape.

Law of Cosines Calculator for Triangles

Find a triangle's third side from two sides and the included angle — the Law of Cosines, generalizing the Pythagorean theorem to any triangle.

Completing the Square Calculator

Rewrite ax² + bx + c = 0 as a perfect square (x + p)² = q, step by step — the technique behind the quadratic formula itself.

Triangle Area Calculator

Find a triangle's area from its three side lengths, using Heron's formula — no angle or height measurement required.

Circle Area Calculator Using Diameter

Find a circle's area directly from its diameter — no need to halve it to a radius first.

Matrix Inverse Calculator (3x3)

Find the inverse of any 3×3 matrix, computed via the determinant and adjugate — the same cofactor-expansion method taught in a first linear algebra course.

Slope Calculator

Find the slope of a line between two points — the fundamental measure of steepness and direction in coordinate geometry.

Surface Area of Cylinder Calculator

Find a cylinder's total surface area — both circular ends plus the curved side — from its radius and height.

Distance Between Two Points Calculator

Find the straight-line distance between two points on a plane — a direct application of the Pythagorean theorem to coordinate geometry.

Polynomial Long Division Calculator

Divide one polynomial by another and get the quotient and remainder directly — the same long division process as arithmetic, applied to algebraic expressions.

Ratio to Percentage Calculator

Convert a ratio like 3:2 into the percentage share of each part — turning a comparative ratio into intuitive percentage figures.

Percentage Error Calculator

Find the percentage error between a measured and an actual value — a standard way to express how far an estimate or measurement is from the true figure.

Logarithm Calculator

Find the logarithm of a number to any base — the mathematical inverse of exponentiation, used across science, engineering, and finance.

Eigenvalue Calculator (3x3 Symmetric Matrix)

Find the eigenvalues of a symmetric 3×3 matrix using the Jacobi rotation method — a reliable numeric algorithm guaranteed to converge to real eigenvalues.

Exponent Calculator

Raise any number to any power, including negative and fractional exponents — the core operation behind exponential growth, scientific notation, and compound calculations.

Root Calculator

Find the nth root of any positive number — the mathematical inverse of exponentiation, covering square roots, cube roots, and beyond.

Sphere Volume Calculator

Find the volume and surface area of a sphere from its radius — the fundamental three-dimensional measurements for any spherical object.

Cylinder Volume Calculator

Find the volume of a cylinder from its radius and height — a common calculation for tanks, pipes, and cylindrical containers.

Geometric Mean Calculator

Find the geometric mean of two or three numbers — the correct way to average ratios, percentages, and growth rates.