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Math
Math Calculators
87 free math calculators with clear, detailed guides.
All Math Calculators
2×2 and 3×3 Matrix Calculator
Calculate matrix addition, subtraction, multiplication, determinant, inverse, and transpose for 2×2 and 3×3 matrices with full working.
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3D Shapes — Volume & Surface Area Calculator
Calculate volume and surface area of all 3D shapes: cube, cuboid, sphere, cylinder, cone, pyramid, and prism. Full working shown for any dimensions.
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Angle Converter — Degrees, Radians & Gradians
Convert angles between degrees, radians, gradians, and turns. Calculate arc length and sector area from angles. Full conversion table included.
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Area Calculator (All Shapes)
Calculate the area of any shape — rectangle, triangle, circle, trapezoid, parallelogram, ellipse, sector, and more. All formulas shown.
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Arithmetic & Geometric Sequence Calculator
Arithmetic and geometric sequence calculator: find the nth term, sum of a series, and common difference or ratio, with worked steps.
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Arithmetic & Geometric Sequence Sum Calculator
Calculate nth term, sum to n terms, and sum to infinity for arithmetic and geometric sequences. Essential for A-level maths.
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Average (Mean) Calculator
Calculate the mean, median, mode, range, and standard deviation of any set of numbers. Paste in up to 100 values.
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Binary, Decimal & Hex Converter
Convert between binary, decimal, hexadecimal, and octal number systems. See the full conversion with step-by-step working.
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Binomial Distribution Calculator
Calculate binomial probabilities P(X=r), P(X≤r), and P(X≥r). Find the mean and variance of a binomial distribution and compare to normal approximation.
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Binomial Theorem & Expansion Calculator
Expand any binomial (a+b)^n using the binomial theorem. Find specific terms, coefficients, and Pascal's triangle rows.
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Box Plot & IQR Calculator
Calculate box plot statistics: minimum, Q1, median, Q3, maximum, IQR, and identify outliers. Enter a dataset and get all five-number summary statistics.
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Chi-Squared Test Calculator
Calculate chi-squared (χ²) statistic for goodness-of-fit and independence tests. Find p-value and determine statistical significance.
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Circle Calculator
Calculate the area, circumference, diameter, and radius of any circle. Enter any one measurement to find all the others.
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Circle Equation & Geometry Calculator
Solve circle equations: find centre, radius, circumference, area, sector area, and arc length from various inputs.
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Completing the Square Calculator
Complete the square for any quadratic expression. Find the vertex form, turning point, and solve the quadratic equation by completing the square.
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Complex Number Calculator
Add, subtract, multiply, and divide complex numbers. Convert between rectangular and polar form. Calculate modulus, argument, and conjugate.
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Confidence Interval Calculator
Calculate confidence intervals for a population mean or proportion. Choose 90%, 95%, or 99% confidence levels with margin of error.
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Date Difference Calculator
Calculate the exact number of days, weeks, months, and years between any two dates. Useful for deadlines, anniversaries, and project planning.
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Differentiation & Derivatives Calculator
Calculate derivatives of polynomials, trigonometric, exponential, and logarithmic functions. Find gradients, stationary points, and rates of change.
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Ellipse Equation Calculator — Foci, Eccentricity & Area
Calculate ellipse area, perimeter, foci, eccentricity, and equations. Convert between standard and parametric forms.
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Exponent & Power Calculator
Calculate any base raised to any power. Handles large exponents, negative powers, fractional exponents, and scientific notation results.
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Exponential & Logarithmic Equation Solver
Solve exponential and logarithmic equations. Find unknowns in growth/decay, compound interest, half-life, and pH-style equations.
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Factorial, Gamma Function & Stirling Calculator
Calculate factorials up to 170!, use Stirling's approximation for large numbers, and understand the Gamma function extension to non-integers.
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Factors & Prime Factorisation Calculator
Find all factors, factor pairs, and the prime factorisation of any number. Calculate the number of factors and check if a number is prime.
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Fraction Calculator
Add, subtract, multiply, and divide fractions. Simplify fractions and convert between fractions, decimals, and percentages.
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Geometric Area & Perimeter Calculator (All Shapes)
Calculate area and perimeter of any shape: triangles, rectangles, circles, polygons, trapezia, ellipses, sectors, and more.
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Geometric Sequence & Series Calculator
Calculate terms, sum, and common ratio of geometric sequences. Find nth term, sum to n terms, and sum to infinity for converging sequences.
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Hyperbola Calculator — Vertices, Foci & Asymptotes
Calculate hyperbola properties: vertices, foci, asymptotes, eccentricity, and directrix. Covers standard form x²/a² − y²/b² = 1 and y²/a² − x²/b² = 1.
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Hypothesis Test Calculator (z-test & t-test)
Perform one-sample z-tests and t-tests. Calculate the test statistic, p-value, and make a statistical decision at any significance level.
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Integral Calculator (Definite & Indefinite)
Calculate definite and indefinite integrals of common functions. Find the area under a curve and antiderivatives with step-by-step power-rule working.
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Integration & Definite Integral Calculator
Calculate indefinite and definite integrals of polynomials, trig, and exponential functions. Find areas under curves and volumes of revolution.
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LCM and GCD Calculator
Calculate the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of any two or three numbers.
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LCM and HCF Calculator (Lowest Common Multiple & Highest Common Factor)
Calculate the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of any set of numbers. Shows prime factorisation working.
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Linear Equation Solver
Solve linear equations of any form — one variable, two steps, with fractions or decimals. Shows every step of the working.
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Linear Regression & Line of Best Fit Calculator
Calculate the equation of the least-squares regression line for any dataset. Find gradient, y-intercept, R-squared, and make predictions.
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Logarithm Calculator
Calculate logarithms in any base — log₁₀, ln (natural log), log₂, and custom bases. Also handles antilog and change of base.
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Logarithm Calculator (log, ln, log₂)
Logarithm calculator for log base 10, natural log (ln), log base 2, and any custom base. Also calculates antilogs, with worked examples.
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Logic Gate & Truth Table Calculator
Generate truth tables for AND, OR, NOT, NAND, NOR, XOR, and XNOR logic gates. Build complex logic expressions and see all input/output combinations.
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Matrix Determinant & Inverse Calculator
Calculate the determinant, inverse, and transpose of 2x2 and 3x3 matrices with full working shown.
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Modular Arithmetic & Congruence Calculator
Calculate modular arithmetic, find remainders, solve modular equations, and check divisibility rules. Essential for cryptography and number theory.
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Modulo Calculator
Calculate the modulo (remainder after division) for any two numbers. Includes negative numbers, real modulo, and modular arithmetic applications.
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Normal Distribution & Z-Score Probability Calculator
Calculate probabilities from the normal distribution. Find P(X < a), P(a < X < b), and percentiles for any mean and standard deviation.
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Number Base Converter (Binary, Hex, Octal)
Convert numbers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Essential for programming and computer science.
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Number Sequences & Patterns Calculator
Find the nth term of arithmetic, geometric, Fibonacci, and quadratic sequences. Identify the pattern and predict future terms.
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Numerical Integration & Area Under Curve Calculator
Calculate the approximate area under a curve using the trapezium rule and Simpson's rule. Enter function values or coordinates for any curve.
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Parabola Vertex, Focus & Roots Calculator
Calculate vertex, focus, directrix, axis, and roots of a quadratic. Convert between standard and vertex forms.
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Pearson Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient (r) and R-squared for any dataset. Test whether the correlation is statistically significant.
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Percentage Calculator
Calculate any percentage instantly — 4 types: find % of a number, what % one number is of another, what the original number was, or increase/decrease by %.
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Percentage Change Calculator
Calculate percentage increase or decrease between two values. Find out how much something has changed as a percentage.
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Percentage Error Calculator
Calculate percentage error between a measured value and the true or accepted value. Shows absolute error, relative error, and whether the result is over.
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Percentage Off Sale Price Calculator
Calculate the sale price after any percentage discount. Find the saving amount, final price, and what percentage off a price equals a target saving.
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Permutations & Combinations Calculator
Calculate permutations (nPr) and combinations (nCr) for any values of n and r. Understand when to use each and see the factored working.
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Poisson Distribution Calculator
Calculate Poisson probabilities for rare events. Find P(X=k), P(X≤k), and P(X≥k) for any Poisson distribution with mean λ.
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Polar Coordinates Converter & Calculator
Convert between polar (r, θ) and Cartesian (x, y) coordinates. Calculate distance, area, and angle in polar form.
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Prime Factorization, HCF & LCM Calculator
Find the prime factorization of any number. Calculate the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two or three numbers.
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Prime Number Checker
Check if any number is prime and find all prime factors. Includes prime factorisation and a list of primes for any positive integer.
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Probability Calculator
Calculate probability for single events, combined events (AND/OR), conditional probability, and complement. With worked examples.
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Pythagoras Theorem Calculator & Right Triangle Solver
Calculate any side of a right triangle using Pythagoras theorem. Find hypotenuse, missing side, triangle area, perimeter, and angles.
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Pythagorean Theorem Calculator
Pythagorean theorem calculator and solver: find the hypotenuse or a missing side of a right triangle using a² + b² = c². Step-by-step working shown.
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Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0 instantly. Shows full working using the quadratic formula.
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Quadratic Formula Calculator (ax² + bx + c = 0)
Solve any quadratic equation using the quadratic formula. Find real and complex roots, factorisations, and the discriminant. Shows full working.
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Random Number Generator
Generate random numbers within any range. Choose integers or decimals, generate multiple numbers, and create random lists for raffles, games, and statistics.
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Ratio Calculator
Simplify ratios, scale ratios, and solve proportions. Works for any ratio — cooking, mixing, scale models, map distances and more.
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Roman Numeral Converter
Convert any number to Roman numerals or convert Roman numerals back to numbers. Works for all values from 1 to 3,999 with rules explained.
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Rounding Calculator (Decimals, Significant Figures)
Round numbers to decimal places, significant figures, or the nearest 10, 100, or 1000. Shows the rounded result and the rounding rule applied.
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Sample Size Calculator
Calculate the minimum sample size needed for your survey, experiment, or study. Set your confidence level, margin of error, and population size.
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Scientific Notation Calculator
Convert numbers to and from scientific notation. Perform multiplication, division, addition, and subtraction with numbers in scientific notation.
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Set Theory & Venn Diagram Calculator
Calculate union, intersection, and complement of sets. Solve Venn diagram problems with 2 or 3 sets using inclusion-exclusion.
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Simultaneous Equations Solver
Solve simultaneous linear equations (two equations, two unknowns) using substitution or elimination. Shows full working step by step.
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Slope, Gradient & Angle Calculator
Calculate slope, gradient, angle, and equation of a line from two points or from rise and run. Convert between degrees, percent grade, and ratio.
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Slope, Gradient & Line Equation Calculator
Calculate the slope (gradient), y-intercept, and equation of a line from two points. Find parallel and perpendicular line equations.
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Square Root & Cube Root Calculator
Calculate square roots, cube roots, and nth roots of any number. Shows step-by-step working and checks for perfect squares.
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Standard Deviation Calculator
Calculate mean, median, mode, variance, and standard deviation for any data set. Enter up to 50 numbers for a full statistical summary.
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Standard Error & Confidence Interval Calculator
Calculate the standard error of the mean, confidence intervals (95%, 99%), and margin of error for any sample size.
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Standard Form (Scientific Notation) Calculator
Convert numbers to and from standard form (scientific notation). Multiply, divide, and add numbers in standard form with full working shown.
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Statistics Calculator (Mean, SD)
Calculate mean, median, mode, range, variance, and standard deviation for any data set. Shows all working for GCSE and A-level statistics.
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Statistics Calculator: Mean, Median, Mode & Range (Datasets)
Calculate mean, median, mode, range, variance, and standard deviation for any dataset. Essential for GCSE statistics and data analysis.
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Taylor & Maclaurin Series Calculator
Calculate the Taylor or Maclaurin series expansion for common functions. Find polynomial approximations for sin(x), cos(x), eˣ, ln(1+x), and more.
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Time Calculator (Add & Subtract Hours)
Add or subtract hours, minutes, and seconds. Calculate elapsed time, total hours worked, and convert between time formats.
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Triangle Calculator
Calculate the area, perimeter, angles, and height of any triangle. Works for right-angled, equilateral, isosceles, and scalene triangles.
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Trigonometric Identities & Equations Solver
Apply key trigonometric identities: double angle, sum/difference, Pythagorean. Solve trig equations and simplify trig expressions.
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Trigonometry Calculator — Sine, Cosine & Tangent
Calculate sine, cosine, tangent and their inverses. Solve right triangles and apply the sine rule and cosine rule for any triangle.
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Vector Cross Product & Triple Product Calculator
Calculate vector cross product, scalar triple product, and vector triple product. Find magnitude, direction, and applications.
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Vector Magnitude & Direction Calculator
Calculate the magnitude, direction, and unit vector of any 2D or 3D vector. Add, subtract, and find dot products of vectors with full working.
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Vector Magnitude, Addition & Dot Product Calculator
Calculate vector magnitude, addition, subtraction, dot product, cross product, and angle between vectors in 2D and 3D.
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Volume Calculator — Cube, Sphere, Cylinder & More
Calculate the volume of any 3D shape: cube, cuboid, sphere, cylinder, cone, pyramid, prism, and hemisphere. Full working shown.
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Z-Score & Standard Normal Calculator
Calculate z-scores, find percentiles, and determine the probability of values in a normal distribution. Convert between raw scores and z-scores.
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About our math calculators
These maths calculators cover arithmetic, algebra, geometry, trigonometry, statistics, sequences, and number theory — from solving quadratics and simultaneous equations to finding the area of a triangle, computing standard deviation, converting number bases, or checking whether a number is prime. Each shows the working, not just the answer.
Good maths tools teach as well as compute, so every calculator here explains the formula and method, with worked examples and the common pitfalls to watch for. The guides cover the reasoning behind the result — useful for checking homework, revising for exams, or refreshing a half-remembered method.
From primary and GCSE level through to A-level and beyond, these calculators are free, need no sign-up, and are written to make the maths clear rather than hide it behind a black box.