🔢 Mathematics

Math Calculator

Free online math and statistics calculators — percentages, fractions, averages, standard deviation and ratios. Every tool shows the formula, a worked example and step-by-step results.

✓ Step-by-step

✓ Formulas shown

✓ Statistics tools

✓ 100% Free

Math & statistics calculators

Pick a calculator below. Each opens a dedicated page with the formula, a worked example and instant step-by-step output.

Percentage Calculator

Percent of a number, percent change and "what % of".

Quadratic Equation

Solve ax²+bx+c=0 — roots, discriminant, vertex.

Log to any base, plus ln, log₁₀ and log₂.

Permutation & Combination

nPr and nCr with factorials.

Average Calculator

Mean, median and mode of any data set.

Standard Deviation

Population & sample standard deviation and variance.

Ratio Calculator

Simplify ratios and solve proportions A:B = C:D.

Scientific Notation

Convert to a × 10ⁿ, E-notation & engineering notation.

Exponent Calculator

Powers and roots — base^exponent, negative & fractional.

Greatest common divisor & least common multiple.

Single & combined events — and, or, neither, complement.

Area Calculator

Rectangle, circle, triangle, square & parallelogram.

Volume Calculator

Box, cube, sphere, cylinder & cone.

Fraction Calculator

Add, subtract, multiply, divide and simplify fractions.

Gradient, angle, y-intercept and line equation from two points.

Distance & midpoint between two points (distance formula).

Pythagorean Theorem

Find a right-triangle side with a²+b²=c².

Midpoint of a segment, plus distance and slope.

Radius, diameter, area and circumference from any one.

Area from three sides with Heron's formula, plus angles.

√n, both roots, cube root and a perfect-square check.

Exact n! with digits, scientific notation and trailing zeros.

Prime check, factorization, divisor count and next prime.

Round to decimals or nearest 10/100 — half-up, floor, ceiling, banker's.

Remainder of a ÷ b, quotient and positive floored modulo.

Mean / Median / Mode

Averages, mode and range of a pasted data set.

Convert between binary, octal, decimal and hexadecimal.

Numbers to Roman numerals and back, with breakdown.

Quotient, remainder, decimal and step-by-step working.

Solve A/B = C/D for any missing term by cross-multiplication.

Rectangle, square, triangle and circle perimeter, plus area.

Cube, box, sphere, cylinder and cone surface area and volume.

Standard score and percentile from value, mean and SD.

Population & sample variance and standard deviation.

Measured vs true value — percent, absolute & signed error.

Decimal to Fraction

Exact simplified fraction & mixed number from a decimal.

|x| from zero, plus distance |a − b| between two numbers.

Percentage Change

Percent increase or decrease from an old to a new value.

∛x for any number, negatives included, perfect-cube flag.

Significant Figures

Round to N sig figs and count significant figures.

Arithmetic Sequence

nth term and series sum from first term & common difference.

Geometric Sequence

nth term and sum from first term & common ratio.

ⁿ√x for any degree — 4th, 5th, higher roots.

(max + min) / 2, plus min, max and range of a data set.

Fraction to Percent

Convert any fraction to a percent and decimal, with working shown.

Quotient & Remainder

Integer division with remainder and the a = q×b + r check.

Sum of Integers

Add all consecutive integers a to b — total, terms and average.

Percent to Fraction

Convert any percent to a fraction in lowest terms, decimal and mixed number.

All factors and factor pairs of a number, with count, sum and prime/square check.

Ratio Simplifier

Reduce a ratio to lowest terms with the GCD, decimal and 1:n form.

About these math calculators

This is the mathematics hub of AI Calculator. It brings together the everyday and academic math tools people search for most — working out a percentage, combining fractions, finding an average, measuring how spread out a data set is, or simplifying a ratio. Each calculator is a standalone page that states the formula plainly, runs the numbers instantly in your browser, and walks through a worked example so the method is clear, not just the answer.

The statistics tools — average and standard deviation — pair naturally: the average tells you the centre of a data set while the standard deviation tells you how tightly the values cluster around it. For everyday arithmetic, the percentage, fraction and ratio calculators cover the operations students and professionals reach for daily. More math tools are added regularly.