Order of operations, done correctly
This calculator follows the standard order of operations taught as PEMDAS in the US, BODMAS or BIDMAS in the UK, and BEDMAS in Canada:
- Brackets first.
- Powers and roots next, worked right to left: 2^3^2 = 2^9 = 512.
- Multiplication and division with equal priority, left to right: 12 ÷ 3 × 2 = 8.
- Addition and subtraction with equal priority, left to right.
Under every result, the Read as line shows the expression with full brackets, so you can see exactly how it was understood. For example, 2 + 3 × 4 is read as 2 + (3 × 4) = 14.
Rules worth knowing
| Input | Result | Why |
|---|---|---|
| −3^2 | −9 | The power is applied before the minus sign, as in standard algebra. Type (−3)^2 for 9 |
| 6 ÷ 2(1 + 2) | 9 | A number next to a bracket is treated as ordinary multiplication, worked left to right. Add brackets if you mean 6 ÷ (2(1 + 2)) = 1 |
| sin(30) | 0.5 in degrees | In radians, sin(30) is −0.988. Check the Degrees/Radians switch |
| 50 + 10% | 50.1 | % means "divide by 100", as in spreadsheets. To add 10%, type 50 × 1.1 |
| log(1000) | 3 | log is base 10; ln is the natural logarithm (base e) |
Pro-tip: if a result surprises you, read the Read as line before anything else. Most "wrong" answers come from an expression being read differently from what you meant, not from an arithmetic error.
Results are shown to 12 significant digits. Very small rounding differences, such as 0.1 + 0.2, are tidied in the display. Our calculator guide explains why computers produce them.
Frequently asked questions
Does this calculator use the correct order of operations?
Yes. Brackets come first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. The "Read as" line shows how your expression was grouped.
Why does −3^2 give −9?
In standard mathematical notation the power applies before the minus sign, so −3^2 means −(3^2) = −9. Type (−3)^2 if you want 9.
How do I switch between degrees and radians?
Use the Degrees/Radians switch above the display. It affects sin, cos, tan and their inverses.
What does the % key do?
It divides the number before it by 100, as in spreadsheets, so 50 + 10% is 50.1. To increase 50 by 10%, type 50 × 1.1, or use the percentage calculator.