Math calculators

Plain-English tools for the kind of maths that comes up in everyday life: percentages, changes, ratios. Every tool shows its workings, so you can check the answer rather than take it on faith.

What everyday maths calculators are really for

Most of the maths people reach for in adult life is not GCSE algebra. It is percentages, ratios, fractions, and the odd standard deviation when somebody at work hands you a spreadsheet. None of it is hard, all of it is easy to get slightly wrong under time pressure, and the cost of a slightly wrong answer can be anything from a small embarrassment to a meaningful chunk of money. A calculator that shows its working is the difference between trusting the number and double-checking it.

The tools here are aimed squarely at that gap. They take the inputs as you have them, do the maths transparently, and give you a result alongside the steps that produced it, so you can see whether the answer makes sense before you act on it.

Where the inputs come from

Mostly: a price tag, a payslip, a recipe, a spreadsheet column, or whatever someone just said over the phone that you would rather verify than take on trust. A few practical pointers.

  • Percentages. Be clear about which number is the base. "20% off £80" and "£80 is 20% more than what?" are different sums with different answers. The Percentage Calculator has separate modes for each so you do not pick the wrong one by accident.
  • Discounts. Stacked discounts do not add. A 20%-off voucher on top of a 30%-off sale is not 50% off; it is 44% off, because the second cut applies to the already-reduced price. The Discount Calculator handles the order properly. Tax goes on the last step, after all the cuts.
  • Fractions. Recipe doubling, woodwork, and any imperial measurement still pulls fractions out of retirement. Convert mixed numbers (1 1/2) into improper fractions before any calculation that is not addition or subtraction, otherwise the maths gets fiddly. The Fraction Calculator does this conversion in the working.
  • Sample data. If you are computing a standard deviation, know whether you have the whole population or just a sample of it. The denominator changes (n versus n minus 1) and so does the answer. Picking the wrong one is the most common standard-deviation mistake by some distance.

Common mistakes people make with everyday maths

The most common is reversing a percentage and assuming the answer is symmetrical. It is not. If a stock price drops 20% and then rises 20%, you are not back where you started: 100 becomes 80 becomes 96. The percentage is calculated against a different base each time. This catches people out in pay rises, investment returns, and weight loss claims with depressing regularity.

The second is rounding too early. If a calculation has three steps and you round to two decimal places after each one, the final answer can drift by enough to matter. Keep the full precision in the calculator and only round the result at the end, when you are ready to communicate it.

The third is treating averages as if they tell the whole story. An average salary of £40,000 in a small company can mean everyone earns roughly £40,000, or it can mean nine people earn £30,000 and one earns £130,000. The Standard Deviation Calculator exists because that second number, the spread, is often more interesting than the average itself.

How to choose between the tools here

If you have a price and a percentage, percentage or discount calculator. If you have ingredients and a different number of portions, fraction calculator. If you have a column of numbers and want to know how much they vary, standard deviation. If you are solving a quadratic for homework or a nostalgic reason, the solver is upstairs. We will keep adding tools where the maths is short enough to do in your head if you are sharp, and embarrassing to get wrong if you are not.

  • Percentage Calculator

    Work out a percentage of a number, what percentage one number is of another, or the percentage change between two values.

  • Discount Calculator

    Sale price calculator covering single discounts, stacked discounts, sales tax or VAT, and Buy X Get Y Free deals. Currency-agnostic, with workings shown.

  • Fraction Calculator

    Add, subtract, multiply or divide fractions and mixed numbers. Returns the simplified fraction, the mixed-number form and the decimal, with every step of the working shown.

  • Standard Deviation Calculator

    Paste a list of numbers and get count, mean, median, range, variance and standard deviation, sample and population, with the working shown step by step.

  • GCD and LCM Calculator

    Find the greatest common divisor (HCF) and lowest common multiple of two or more whole numbers. Shows the Euclidean algorithm, prime factorisations and the combined-prime LCM working.

  • Quadratic Equation Solver

    Solve any quadratic ax² + bx + c = 0. Returns the two roots, the discriminant, the vertex, the axis of symmetry and the y-intercept. Handles real and complex roots with full working shown.

  • Combinations & Permutations Calculator

    Work out nCr, nPr, factorials and multinomial coefficients with arbitrary precision. Handles repetition variants and shows the formula and step-by-step working.

  • Logarithm Calculator

    Compute log base b of x for any positive base, including base 10, e and 2. Solve for the result, for x, or for the base. Change-of-base working and inverse check shown.

Frequently asked questions

What is the difference between percentage and percentage points?

A percentage is the ratio (interest of 5 per cent on a £100 loan is £5). A percentage point is the difference between two percentages (going from 5 per cent to 7 per cent is a rise of 2 percentage points, or a 40 per cent increase). News headlines mix these up constantly. The Percentage Calculator handles both views.

How do I work out a percentage discount in my head?

For 20 per cent off, knock 10 per cent off twice (so £80 becomes £64 in two steps: £80 - £8 - £8). For 25 per cent off, divide by four and subtract. For 33 per cent off, divide by three and subtract. The Percentage Calculator handles any value if mental shortcuts run out.

What is the order of operations (BIDMAS/PEMDAS)?

Brackets, Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right). Same rule, two acronyms. So 2 + 3 × 4 = 14, not 20, because the multiplication runs first. Worth knowing because it changes answers.

Why don't fractions add the way numbers do?

Because you can only add fractions with the same denominator. 1/3 + 1/4 is not 2/7. Convert to a common denominator first: 1/3 = 4/12 and 1/4 = 3/12, so 4/12 + 3/12 = 7/12. Multiplying is easier (multiply numerators, multiply denominators).

Does any of my data leave the browser?

No. Every maths tool here runs in JavaScript on your device. Numbers you enter are not logged, stored or transmitted.

Why a percentage calculator is the most-used maths tool online

Percentages are everywhere: tips, tax, sale prices, exam marks, interest rates, stock moves, tip splitting, body-fat readings, turnout figures, and anywhere a number is compared to a whole. They are also the single most common piece of maths people look up online, which tells you something about how confident most of us feel about them. That is fine. A quick tool that gives the right answer and shows the working is more useful than a reminder of year-seven lessons.

More tools are on the way in this category. The goal is the same across all of them: short, accurate, honest.