Math Calculators
Percentages, fractions, algebra, geometry and everyday arithmetic.
- Absolute Value Calculator Find the absolute value of a number, the distance between two numbers, or solve an absolute value equation for its two answers.
- Area Calculator Find the area of a rectangle, triangle, circle, trapezoid, parallelogram, ellipse, sector or regular polygon — one page for every common shape.
- Arithmetic Sequence Calculator Find any term of an arithmetic sequence, the sum of its first n terms, or work backwards from two known terms to the rule.
- Average Calculator Find the mean, median, mode and range of a list of numbers, and see which average actually represents your data.
- Binary Calculator Add, subtract, multiply and divide binary numbers, apply bitwise operations and shifts, and convert to decimal and hex.
- Boolean Algebra Calculator Simplify a Boolean expression to a minimal sum of products and product of sums using Quine–McCluskey, with optional don't-care conditions.
- Boolean Expression Calculator Build the truth table of a Boolean expression, list its minterms and maxterms with canonical SOP and POS, and test whether two expressions are equivalent.
- Boolean Logic Calculator Find the output of AND, OR, NOT, NAND, NOR, XOR and XNOR logic gates for your inputs, with the gate's truth table, expression and NAND-only equivalent.
- Circle Calculator Enter any one of radius, diameter, circumference or area and get the other three, plus the exact value in terms of pi.
- Cone Calculator Find a cone's volume, slant height, curved surface and total surface area from its radius and height, or from its slant height.
- Cube Root Calculator Find the cube root of any number, including negatives, in exact simplified form where possible, or cube a number.
- Cylinder Calculator Find a cylinder's volume, surface area and capacity in litres from its radius and height — or work backwards from a required volume.
- Decimal to Fraction Calculator Turn any decimal into an exact fraction in lowest terms, including repeating decimals such as 0.1666 recurring.
- Discriminant Calculator Find the discriminant of a quadratic or cubic and what it says about the roots: how many are real, whether they repeat and whether they are rational.
- Distance Formula Calculator Find the straight-line distance between two points in 2D or 3D, with the exact simplified surd as well as the decimal.
- Exponent Calculator Raise any number to any power, including negative and fractional exponents, or solve for the base or the exponent itself.
- Exponential Increase Calculator Calculate exponential increase by a fixed percentage per period: the final value, the growth rate needed or the periods to reach a target, plus doubling time.
- Factorial Calculator Work out the factorial of any whole number, exactly for large values, with the trailing-zero count and digit length.
- Fibonacci Calculator Find any Fibonacci number exactly, list the sequence, check whether a number belongs to it, and see how it approaches the golden ratio.
- Fourier Series Calculator Find the Fourier series coefficients a0, an and bn of a function on [−L, L], the first N terms of the series and its value at a point.
- Fraction Calculator Add, subtract, multiply or divide two fractions, with the result reduced to lowest terms and shown as a decimal.
- Fraction to Decimal Calculator Convert any fraction to a decimal, with repeating digits identified and the length of the repeating block shown.
- Fraction to Percent Calculator Convert a fraction to a percentage, or turn a percentage back into a fraction in lowest terms.
- GCF Calculator Find the greatest common factor of two or more numbers, by prime factorisation and by the Euclidean algorithm, with both methods shown.
- Geometric Sequence Calculator Find any term of a geometric sequence, the sum of its first n terms, or the infinite sum when the ratio is small enough to converge.
- Hex Calculator Add, subtract, multiply and divide hexadecimal numbers, convert to decimal and binary, and read hex colour codes and byte values.
- LCM Calculator Find the lowest common multiple of two or more numbers, by prime factorisation and via the greatest common factor, with both routes shown.
- Linear Equation Calculator Solve a linear equation for x, with variables on one side or both, and see the degenerate cases explained rather than hidden.
- Logarithm Calculator Find a logarithm in any base, including natural and base 10, or solve for the base or the value the logarithm is taken of.
- Long Division Calculator Divide one number by another and see every step of the long division, with a remainder or carried out to decimal places.
- Matrix Calculator Add, subtract and multiply matrices, or find the determinant, inverse and transpose of a 2×2 or 3×3, with the working shown.
- Midpoint Calculator Find the midpoint between two points, or work backwards from a midpoint and one endpoint to find the missing endpoint.
- Mixed Number Calculator Convert between mixed numbers and improper fractions, or add, subtract, multiply and divide two mixed numbers.
- Multiplication Table Generator Generate the times table for any number, or a full grid up to any size, with the patterns that make each table easier to learn.
- Number Base Converter Convert a number between any two bases from 2 to 36, with every common base shown alongside and exact arithmetic at any size.
- Percent Error Calculator Compare a measured or estimated value against the accepted true value, and express how far off it was as a percentage.
- Percentage Calculator Work out a percentage of a number, what percentage one number is of another, or the percentage change between two values.
- Percentage Decrease Calculator Find the percentage drop between two values, take a percentage off a number, or work backwards to the price before a discount.
- Percentage Difference Calculator Compare two values where neither is a baseline. Divides by their average, so the answer is the same whichever order you enter them.
- Percentage Increase Calculator Find the percentage increase between two values, or apply an increase to a number to see what it becomes.
- Perimeter Calculator Find the perimeter of a rectangle, triangle, circle, parallelogram, trapezoid, regular polygon or ellipse — the distance all the way round.
- Polygon Calculator Find the area, perimeter, angles, apothem and radius of a regular polygon from its side length, apothem or circumradius.
- Polynomial Multiplication Calculator Multiply two or three polynomials and expand the product, with every term-by-term product, FOIL for binomials and the degree of the result.
- Prime Factorization Calculator Break any whole number into its prime factors, with the factor tree, the exponent form, and every divisor it produces.
- Prime Number Checker Check whether a number is prime, see the divisor that rules it out, and find the nearest primes on either side.
- Proportion Calculator Solve a proportion for its missing term by cross-multiplying, check whether two ratios match, or work with inverse proportion.
- Pythagorean Theorem Calculator Find a missing side of a right triangle, or check whether three lengths form one, with the exact answer and both acute angles.
- Quadratic Equation Calculator Solve any quadratic equation, with the discriminant, the exact surd roots, the vertex and the factored form.
- Quotient Rule Calculator Differentiate f(x) = u(x)/v(x) with the quotient rule, showing u′, v′, the substituted formula, the slope at a point and the tangent line.
- Radians to Degrees Calculator Convert between radians, degrees, gradians and turns, with the exact multiple of pi shown wherever there is one.
- Ratio Calculator Simplify a ratio, scale it up or down, find a missing term, or split a total amount in a given ratio.
- Rational Algebraic Expressions Calculator Add, subtract, multiply or divide two rational expressions in x, reduce the result to lowest terms and list the excluded values of x.
- Rectangle Calculator Find a rectangle's area, perimeter and diagonal from its sides — or work backwards from the area, perimeter or diagonal to a missing side.
- Remainder Calculator Find the remainder when one number is divided by another, check divisibility, or work with modular arithmetic including large powers.
- Right Triangle Calculator Solve a right triangle from any two of its measurements, including sides, angles, the altitude to the hypotenuse and both circle radii.
- Rounding Calculator Round a number to any number of decimal places or to the nearest ten, hundred or thousand, using the rounding rule you need.
- Scientific Notation Calculator Convert between ordinary numbers and scientific notation, or multiply and divide two numbers written in it.
- Significant Figures Calculator Count the significant figures in a number, or round it to a chosen number of them, with the reason each digit counts explained.
- Simplest Radical Form Calculator Write a square root, cube root or any nth root in simplest radical form, with prime factors shown and fractions under the root rationalised.
- Simplify Fraction Calculator Reduce any fraction to its lowest terms, with the greatest common divisor and the full chain of equivalent fractions shown.
- Simplify Radical Expressions Calculator Add, subtract and multiply square roots: simplify each term, combine like radicals and get an exact answer such as 17√3 with a decimal check.
- Simpson's Rule Calculator Approximate a definite integral with Simpson's 1/3 or 3/8 rule, showing each point, its weight, the step size and an estimated error.
- Sine Cosine Tangent Calculator Find all six trigonometric ratios for any angle, or work backwards from a ratio to the angle, with exact values at the special angles.
- Slope Calculator Find the slope between two points, or the angle and grade it corresponds to, along with the full equation of the line.
- Sphere Calculator Find a sphere's volume, surface area, radius, diameter or circumference from any one of them, with the working shown.
- Square Root Calculator Find the square root of any number, simplified into exact surd form where possible, with the decimal value alongside.
- Surface Area Calculator Find the surface area of a box, cube, sphere, cylinder, cone, pyramid, prism or hemisphere, with each face listed separately.
- System of Equations Calculator Solve two or three simultaneous linear equations, with the determinant, the elimination steps, and the parallel and coincident cases explained.
- Trapezoid Calculator Find the area, perimeter and median of a trapezoid from its two parallel sides and either the height or the two slanted legs.
- Trapezoidal Approximation Calculator Estimate a definite integral with the trapezoidal rule from a function or from a table of data with uneven spacing, with left, right and midpoint sums.
- Triangle Calculator Solve any triangle from three sides, two sides and the angle between them, or two angles and a side — with area, heights and classification.
- Trigonometric Identities Calculator Evaluate and check the main trigonometric identities at your angles: Pythagorean, double angle, half angle, and sum and difference formulas.
- Trigonometry Calculator Solve any triangle by the law of sines or cosines — including the ambiguous SSA case, where two different triangles can fit the same measurements.
- Volume Calculator Find the volume of a box, cube, sphere, cylinder, cone, pyramid, prism or hemisphere — with the answer converted to litres and gallons.
A Guide to Math Calculators
A maths calculator that only returns an answer is almost useless for the people who need it most. If you are checking homework, revising, or trying to understand why a method works, the answer is the least interesting part. Every calculator in this category shows its steps, so you can find the line where your own working went wrong rather than just learning that it did.
Seventy-four calculators, grouped below by topic.
Percentages
The group people arrive for most, and the one where the wording causes the most trouble. The Percentage Calculator handles the ordinary forms: what is X percent of Y, X is what percent of Y, and so on.
The rest exist because "increase", "decrease", "difference" and "error" are four different calculations that get used interchangeably. Percentage Increase and Percentage Decrease are directional and not symmetric: a rise of 50 percent followed by a fall of 50 percent does not return you to where you started. Percentage Difference is symmetric, because it divides by the mean of the two values rather than by one of them, which is why it gives a different answer from either. Percent Error divides by the true value specifically, which is what makes it the right one for lab work.
Fractions
Six calculators. The Fraction Calculator does arithmetic on fractions and the Mixed Number Calculator handles whole-and-part forms. Simplify Fraction reduces to lowest terms by dividing out the greatest common factor, and shows which factor it used.
The three converters cover the forms a question can ask for: Fraction to Decimal, Decimal to Fraction and Fraction to Percent. The decimal-to-fraction direction is the interesting one, because it has to recognise a repeating decimal to give an exact answer rather than a close approximation.
Geometry
Fourteen calculators, the largest group. For plane figures there are dedicated calculators for the Circle, Rectangle, Triangle, Trapezoid and regular Polygon, plus general Area and Perimeter calculators when you want to pick the shape rather than the page.
Right triangles get two: the Pythagorean Theorem Calculator for the side-length relation on its own, and the Right Triangle Calculator for the full solution including angles and area.
For solids, the Sphere, Cylinder and Cone calculators each give volume and surface area together, with general Volume and Surface Area calculators covering the rest.
Coordinate geometry and trigonometry
Three coordinate calculators that work together on the same pair of points: Distance, Midpoint and Slope. The slope calculator reports an undefined slope for a vertical line rather than dividing by zero and returning infinity, which is the kind of refusal that matters more than it looks.
For trigonometry, the Sine Cosine Tangent Calculator gives the individual ratios, the Trigonometry Calculator solves triangles from mixed given values, and Radians to Degrees converts between the two angle measures. The Trigonometric Identities Calculator verifies and rearranges identities rather than evaluating a number.
Algebra
The Linear Equation Calculator and System of Equations Calculator cover one and several unknowns, with the system calculator reporting no solution or infinitely many instead of forcing a single answer out of a degenerate system. The Quadratic Equation Calculator gives real and complex roots, and the Discriminant Calculator tells you which kind to expect before you solve. The Matrix Calculator handles arithmetic, determinants and inverses.
Beyond that, the Polynomial Multiplication Calculator expands products term by term and the Rational Algebraic Expressions Calculator simplifies algebraic fractions, including stating the values that must be excluded. The Exponential Increase Calculator covers growth by a constant factor.
Powers, roots and radicals
Exponent, Square Root, Cube Root and Logarithm calculators cover the basic operations, the logarithm calculator taking any base rather than only 10 and e.
Two more work in exact form rather than decimals, which is what an exam usually wants: Simplest Radical Form and Simplify Radical Expressions.
Number theory
Six calculators on the properties of whole numbers. GCF and LCM are the pair most school work needs, and Prime Factorization shows the decomposition that both of them rest on. The Prime Number Checker tests a single number, the Factorial Calculator handles the rapid growth that breaks ordinary arithmetic quickly, and the Remainder Calculator gives quotient and remainder together.
Sequences
Arithmetic Sequence and Geometric Sequence calculators find terms and sums, with the geometric one stating whether an infinite sum converges rather than returning a number for a series that diverges. The Fibonacci Calculator covers the best-known recursive sequence.
Ratios and proportions
The Ratio Calculator simplifies and scales ratios, including the three-part forms that recipes and mixing instructions use. The Proportion Calculator solves for the missing term when two ratios are set equal, which is the single most widely applicable technique in school maths: it is the same operation behind scaling a recipe, converting a unit, reading a map and working out a discount.
The two are easy to confuse because both take ratios as input. The ratio calculator rewrites one ratio into an equivalent form. The proportion calculator uses a known ratio to find an unknown quantity, and reports it with the cross-multiplication shown, because that step is where sign and placement errors creep in.
Number bases
The Number Base Converter handles any base, while the Binary Calculator and Hex Calculator do arithmetic directly in the bases that matter in computing, showing the working in that base rather than converting to decimal and back.
Boolean logic
Three calculators for the algebra of true and false. The Boolean Logic Calculator evaluates expressions, the Boolean Expression Calculator builds a truth table, and the Boolean Algebra Calculator simplifies an expression using the algebraic laws, showing which law it applied at each step.
Calculus and numerical methods
Four calculators at the level where showing the steps matters most. The Quotient Rule Calculator differentiates a ratio and lays out the substitution, which is where this rule is usually got wrong.
The other three are numerical. Simpson's Rule and the Trapezoidal Approximation estimate a definite integral, and comparing them on the same function is the clearest way to see why Simpson's rule converges faster: it fits parabolas where the trapezoidal rule fits straight lines. Simpson's rule also requires an even number of intervals, and the calculator says so rather than quietly adjusting your input. The Fourier Series Calculator decomposes a periodic function into its harmonics.
Arithmetic and number handling
Seven calculators for the operations that underpin everything else. Long Division and the Multiplication Table Generator are built for learning rather than for speed. Average covers the mean and its relatives, and Absolute Value the sign-stripping operation.
Three deal with how a number is written rather than its value. Rounding covers the several rounding conventions, which do not agree on halfway cases. Significant Figures applies the rules that scientific work uses, where trailing zeros may or may not count depending on the notation. Scientific Notation converts in both directions.
How to get the most from these
Turn the steps on. Every calculator here can show its working, and the working is the part that teaches you something. If your answer and the calculator's disagree, comparing the steps tells you which line to look at, and that is a faster route to understanding than being handed a correct result.
It is also worth knowing which calculator answers which form of a question before you start. Much of the difficulty in school maths is not the arithmetic but working out what is being asked: whether a question wants a percentage difference or a percentage change, an exact radical or a decimal, the greatest common factor or the lowest common multiple. The groups above are arranged around those distinctions rather than around difficulty, so the calculator that matches your question is usually in the same section as the ones you have already tried.
Where a question has no answer, these calculators say so: a vertical line has no slope, a divergent series has no sum, a degenerate system has no unique solution. An answer returned in those cases would be wrong in a way that is hard to notice, which is exactly the kind of error worth refusing to make.