Free Online Math Calculators & Unit Converters
Free arithmetic, percentage, square and square root calculators plus length, temperature and time unit converters that work in any web browser.
Convert between metres, kilometres, centimetres, inches, feet, yards, miles and nautical miles instantly, with the conversion factors shown.
Convert between Celsius, Fahrenheit, Kelvin, Rankine and Reaumur, with the formula for each conversion and a quick reference table of key points.
Convert between nanoseconds, seconds, minutes, hours, days, weeks, months and years, with exact factors and worked examples. Free online tool.
Square any number, including decimals and negatives, and see the working. Includes a squares reference table and the rules for squaring fractions.
Calculate the square root of any number, exact or decimal, with simplified radical form where one exists and a table of common perfect squares.
Add two or more numbers, including decimals and negatives, and see the running total. Free online addition calculator with column-addition examples.
Subtract one number from another, including decimals and negatives, and see the difference and the working. Free online subtraction calculator.
Multiply two or more numbers, including decimals and negatives, and see the product with the working. Free online multiplication calculator.
Divide any two numbers and get the quotient, remainder and decimal result, with long-division working shown. Free online division calculator.
Work out percentage of a number, percentage change, increase, decrease and reverse percentages, each with the formula and a full worked example.
Arithmetic, powers and unit conversion
Eleven tools covering three things: the four basic operations plus percentages, the square and square root pair, and unit conversion for length, temperature and time. Each one shows the working rather than just the answer, because the point of using a calculator on the web instead of the one on your phone is usually to check a method, not to get a number.
Percentages: the four questions people actually ask
"Percentage calculator" covers four distinct calculations that get muddled constantly.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 240 = 36 |
| X is what percent of Y? | X ÷ Y × 100 | 36 of 240 = 15% |
| Percentage change from X to Y | (Y − X) ÷ X × 100 | 240 → 300 = +25% |
| Reverse: Y is X% more than what? | Y ÷ (1 + X ÷ 100) | 300 is 25% more than 240 |
The mistake almost everyone makes
A 25% increase followed by a 25% decrease does not return you to where you started. 100 rises to 125, then falls by 25% of 125, which is 31.25, leaving 93.75. Percentage changes compound against a moving base, and the base for the second change is the result of the first.
The same trap appears in reverse-percentage problems. If a price of £120 includes 20% VAT, the VAT is not £24 — that would be 20% of the pre-tax price if the pre-tax price were £120, which it is not. Divide by 1.20 to get £100, so the VAT is £20. Getting this backwards is one of the most common bookkeeping errors there is.
Temperature: the one conversion that is not a simple factor
Length, mass and time conversions are multiplications: one inch is always 2.54cm, whatever the value. Temperature scales have different zero points as well as different degree sizes, so every conversion needs an offset too.
- °C to °F: (C × 9/5) + 32
- °F to °C: (F − 32) × 5/9
- °C to K: C + 273.15 — the degree is the same size, only the zero moves
- °F to °R: F + 459.67 — Rankine is to Fahrenheit as Kelvin is to Celsius
The scales cross at −40, which is the same temperature in Celsius and Fahrenheit. It is a useful sanity check: if your conversion does not agree at −40, you have the formula wrong. The temperature converter also handles Kelvin, Rankine and Réaumur, and refuses temperatures below absolute zero.
Squares and square roots
Squaring is trivial arithmetic; the interesting part is what happens in the other direction. Every positive number has two square roots, one positive and one negative — both 5 and −5 square to 25. By convention the radical symbol denotes only the positive (principal) root, which is why √25 is 5 and not ±5. When you solve x² = 25 as an equation, though, both answers count.
Most square roots are irrational: √2 = 1.41421356… never terminates or repeats. Where a root simplifies to an exact radical form — √72 = 6√2 — the square root calculator shows that form alongside the decimal, because in algebra the exact form is usually the answer you are expected to give.
Why unit conversion still causes accidents
NASA lost the Mars Climate Orbiter in 1999 because one team supplied thrust data in pound-force seconds and another expected newton seconds. The arithmetic was fine; the units were not. Two habits prevent this: carry the unit alongside every number in your working, and check that the answer moves in the direction you expect. Converting metres to feet should produce a bigger number, because a foot is smaller than a metre. If it produced a smaller one, you multiplied where you should have divided.
The length converter shows the factor it applied for exactly that reason — so you can see the conversion, not just trust it.