BODMAS Calculator
Every step in the order the rules require, with the reason for each one.
Step by step
The rule, and the two things the acronym gets wrong
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. BIDMAS and PEMDAS are the same rule with different words: indices, orders and exponents all mean powers, and parentheses means brackets. There is no disagreement between them.
The acronym is misleading in two places, and between them they account for most wrong answers.
Division does not come before multiplication
They share a rank and are worked left to right. In 12 ÷ 3 × 2, the division goes first because it is further left, giving 8. Reading the acronym literally would do the multiplication first and give 2. The same applies to addition and subtraction: 10 − 4 + 3 is 9, not 3.
A minus sign is weaker than a power
-2^2 is −4, not 4. The squaring applies to the 2, and the negative is applied to the result. If you mean the other thing, the brackets are not optional: (-2)^2 is 4. This one catches people out constantly, including in spreadsheets, where some applications deliberately break the convention.
Stacked powers go right to left
2^3^2 is 2^(3^2), which is 2 to the ninth, or 512. It is not (2^3)^2, which would be 64. Powers are the one operation that associates rightwards.
Worked examples
| Expression | Answer | The catch |
|---|---|---|
2 + 3 × 4 | 14 | Multiply before adding; 20 comes from working left to right |
12 ÷ 3 × 2 | 8 | Same rank, so left to right; the acronym suggests 2 |
10 − 4 + 3 | 9 | Same rank again; adding first would give 3 |
-2^2 | −4 | The power binds tighter than the sign |
2^3^2 | 512 | Powers group to the right |
(6 + 2) × 3 | 24 | Brackets first, always |
What the calculator accepts
Numbers, decimals, brackets, and + - * / ^. An x between two numbers is read as multiplication, since that is how the question is usually written down, and ÷ works as division. A number placed directly before a bracket multiplies, so 2(3+4) is 14.
How to use it
Type an expression and the answer appears with the working underneath. Each step shows the whole expression with the part being evaluated highlighted, and states which rule made it next in line. That is deliberately more verbose than a plain answer: the point of the page is to make the order visible.
Questions
Are BODMAS, BIDMAS and PEMDAS different rules?
No, they are the same rule with different words. Brackets and parentheses mean the same thing, and orders, indices and exponents all mean powers. The order is identical: brackets, then powers, then multiplication and division, then addition and subtraction.
Does division really come before multiplication?
No, and the acronym is misleading here. Multiplication and division share a rank and are worked left to right, as do addition and subtraction. In 12 ÷ 3 × 2, the division happens first because it is further left, giving 8 rather than 2.
What does a minus sign in front of a power do?
The power binds tighter, so -2^2 is −4, not 4: the squaring applies to the 2 and the sign is applied afterwards. Write (-2)^2 if you mean the other thing.
How are stacked powers evaluated?
Right to left, unlike every other operation. 2^3^2 is 2^(3^2), which is 512, rather than (2^3)^2, which would be 64.
Is anything sent to a server?
No. The expression is parsed and reduced inside your browser and this tool has no backend, so nothing you type is transmitted, logged or stored.
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