Order of operations calculator

Type a sum using + − × ÷ and ^ for powers, or * and / from a keyboard. Round, square and curly brackets all work, and so do ² and ³. A number written straight against a bracket, as in 2(3 + 4), means multiply. The working does one operation per line and writes out the whole sum again after it, the way a teacher would on the board.

Answers are kept exact. 1 ÷ 3 stays as 1/3 rather than 0.333…, so 1 ÷ 3 × 3 comes back to exactly 1, and 0.1 + 0.2 is 0.3. Powers have to be whole numbers, negative ones included, so 2^-2 is 0.25. Roots and letters aren't handled.

Brackets come first, the innermost pair before the ones around it. Powers come next. Multiplication and division share a rank, so they're done together from left to right, and so are addition and subtraction after them. In 10 − 4 + 3 the subtraction goes first, because it's further left, and the answer is 9, not 3.

In the US the order is taught as PEMDAS, for parentheses, exponents, multiplication and division, addition and subtraction. Schools in the UK use BODMAS, where the O stands for orders or of, or BIDMAS, with I for indices. Canada and New Zealand often say BEDMAS. They're the same rules under different names, and Steps named as switches the labels in the working.

A minus sign in front of a power is done after the power, so −3² is −(3²), which is −9. To square −3, write (−3)². A stack of powers is worked from the top down, so 2^3^2 is 2 to the power 9, which is 512, not 8 squared.

Sums like 6 ÷ 2(1 + 2) go round the internet because people get 9 or 1. Taking × and ÷ from left to right gives 9. A number pressed against a bracket is often given a higher rank than ordinary × and ÷, done first as one piece, and that gives 1. Some calculators read it that way too, the Casio fx-82MS among them. The 2(3) after ÷ setting picks the reading, and when the two answers differ the result shows both. Written with a fraction bar, or an extra pair of brackets, there's no doubt either way.