Math calculators
Solve the everyday math that comes up in school, work, and DIY — with every step shown, not just the answer.
- Percentage CalculatorWork out what X% of a number is, what percent one number is of another, and any percentage increase or decrease, with every step shown.
- Percentage Change CalculatorFind the percentage increase or decrease between two numbers, with the absolute difference, direction, and multiplier worked out step by step.
- Fraction CalculatorAdd, subtract, multiply or divide two fractions and see the answer reduced to lowest terms, plus the mixed number and decimal equivalents.
- Average CalculatorPaste a list of numbers to get the mean, median, mode, range, minimum, maximum, count, and both sample and population standard deviation.
- Quadratic Equation CalculatorSolve any quadratic equation ax² + bx + c = 0 with the quadratic formula. Shows real or complex roots, the discriminant, the vertex, and the axis of symmetry.
- Right Triangle CalculatorEnter the two legs of a right triangle to get the hypotenuse, area, perimeter and both acute angles in degrees, with every step shown.
- Circle CalculatorEnter any one circle measurement — radius, diameter, circumference or area — and get the other three instantly, with every step of the working shown.
- GCD & LCM CalculatorFind the greatest common divisor and least common multiple of two whole numbers, with the full Euclidean algorithm and prime factorisation shown.
- Ratio CalculatorSimplify a ratio to its lowest terms and solve the proportion A : B = C : X for the missing value, with the decimal form and percentage split.
- Area CalculatorFind the area of a rectangle, triangle, circle, trapezoid, parallelogram or ellipse, converted into square feet, square metres, acres and more.
- Volume CalculatorWork out the volume of a box, cylinder, sphere, cone, capsule or pyramid, and read it off in litres, cubic metres, cubic feet and gallons.
- Probability CalculatorFind P(A and B), P(A or B), P(neither) and the complements for two events, independent or mutually exclusive, plus the odds of it happening at least once.
- Z-Score CalculatorFind the z-score of a value from the mean and standard deviation, then see its percentile, the area in each tail, and the two-tailed p-value.
- Slope CalculatorFind the slope between two points, with the line equation, y-intercept, angle, distance, midpoint, and the percentage grade and ratio builders use.
- Logarithm CalculatorWork out log to any base, with log10, ln and log2 shown alongside. Includes the change-of-base formula, a b^y check, and the inverse antilogarithm.
- Combination & Permutation CalculatorWork out nCr and nPr — how many ways to choose or arrange r items from n, with or without repetition — and see which of the four formulas your question needs.
- Prime Number CalculatorCheck whether a number is prime, see its prime factorisation in exponent form, list every divisor, and find the nearest primes above and below it.
- Square Root CalculatorFind the square root or any nth root, in simplified radical form as well as decimal. √72 = 6√2, with the perfect-square factor extraction shown step by step.
- Exponent CalculatorWork out b to the power n for any base and exponent, including negative, fractional and zero powers, with the answer in scientific notation.
- Factorial CalculatorWork out n! exactly, with every digit, up to 10,000!. Shows the full integer, its digit count, scientific notation and how many zeros it ends in.
- Distance CalculatorDistance between two latitude and longitude points by the haversine formula, in km and miles, plus 3D straight-line and Manhattan taxicab distance.
- Confidence Interval CalculatorBuild a confidence interval for a mean from the sample mean, standard deviation and size. Uses Student’s t when σ is estimated, z when it is known.
- Half-Life CalculatorSolve exponential decay in any direction — remaining amount, half-life, elapsed time or starting amount — with the decay constant and mean lifetime.
Every step, not just the answer
An answer you cannot check is only useful once. Each calculator here shows the working — the substitution, the intermediate values, the formula that produced them — so the result can be verified, reproduced by hand, or handed in as method. That constraint shaped which calculators exist: a page that can only emit a number without being able to justify it does not earn a place here.
It also changes what the tool is for. Seeing that a percentage change of 25 percent followed by a fall of 25 percent lands at 93.75 rather than back at 100 is the sort of thing that stops being surprising once you have watched the arithmetic happen rather than been told the result.
Where exactness matters
Some of these problems have exact answers that decimals destroy. A third is not 0.333, a surd is not its rounded value, and a fraction result printed as a decimal has thrown away the very thing that made it a fraction. Where an exact form exists — a reduced fraction, a factorisation, a simplified radical — it is what gets shown, with the decimal alongside rather than instead.
The number theory pages lean on the same principle. A prime factorisation, a greatest common divisor, a least common multiple: these are exact structural facts about an integer, and they are the foundation under fraction arithmetic, modular problems and a good deal of cryptography.
Frequently asked questions
What is the difference between a percent and a percentage point?
A percentage point is an absolute difference between two percentages; a percent is a relative one. If a rate rises from 4 percent to 5 percent, that is a rise of one percentage point, but a relative rise of 25 percent. Both statements are true and they differ by a factor of 25, which is why the distinction matters in any reporting of rates. When a source says a figure rose by 1 percent, it is often worth checking which of the two was meant.
Why does a 25 percent rise followed by a 25 percent fall not return to the start?
Because each change is applied to a different base. A rise of 25 percent takes 100 to 125. The subsequent fall of 25 percent is taken from 125, not from 100, so it removes 31.25 and lands at 93.75. Percentage changes multiply rather than add: 1.25 times 0.75 is 0.9375. Reversing a percentage rise requires a smaller percentage fall, and the gap widens as the percentages grow.
What does a z-score actually tell me?
A z-score expresses how far a value sits from the mean, measured in standard deviations. A z of 2 means the value is two standard deviations above average. Its usefulness is that it strips away the original units, so a test score and a height can be compared on the same scale. Where the underlying data is roughly normal, a z-score also maps directly onto a percentile, which is how it turns into a statement about how unusual the value is.
Why does a computer say that 0.1 plus 0.2 is not 0.3?
Because binary floating point cannot represent 0.1 or 0.2 exactly, in the same way decimal cannot represent a third exactly. Each is stored as the nearest representable value, and the tiny errors survive the addition, giving 0.30000000000000004. This is a property of the representation rather than a bug. It is also why exact arithmetic here is done on fractions and integers wherever the answer is meant to be exact.