Order of operations calculator (BIDMAS, BODMAS, PEMDAS) with steps

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Type a calculation like $2 + 3 \times (4 + 1)^2$ and see it worked out one operation at a time, in the order taught at school: Brackets, Indices (powers), Division and Multiplication from left to right, then Addition and Subtraction from left to right. The UK calls this BIDMAS or BODMAS; the US calls it PEMDAS. Answers are exact, so $0.1 + 0.2$ gives $\tfrac{3}{10}$ , not a long decimal.

ExpressionUse + − × ÷ (or * and /), ^ for powers, and brackets ( ) [ ] { }.

Answer

2 + 3 × (4 + 1)² = 77

Working

1Brackets: add: 4 + 1 = 5 → 2 + 3 × 5²
2Indices (powers): 5² = 25 → 2 + 3 × 25
3Multiply: 3 × 25 = 75 → 2 + 75
4Add: 2 + 75 = 77 → 77

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The order, in one table

Step	BIDMAS / BODMAS	PEMDAS	Example
1	Brackets	Parentheses	$(4 + 1) = 5$
2	Indices / Orders	Exponents	$5^2 = 25$
3	Division and Multiplication, left to right	Multiplication and Division, left to right	$3 \times 25 = 75$
4	Addition and Subtraction, left to right	Addition and Subtraction, left to right	$2 + 75 = 77$

The letters differ but the rules are the same. See BIDMAS vs BODMAS vs PEMDAS.

The left-to-right rule

Multiplication and division have equal priority, and so do addition and subtraction. Work them from left to right:

$8 \div 2 \times 4 = 4 \times 4 = 16$ (not $8 \div 8 = 1$ )
$10 - 4 - 3 = 6 - 3 = 3$ (not $10 - 1 = 9$ )

This is the most common source of mistakes, and the calculator's steps show exactly which operation goes first.

Powers and negative numbers

$-2^2 = -4$ : the power applies to 2 only, then the negative sign.
$(-2)^2 = 4$ : the brackets make the whole $-2$ the base.
$2^{3^2} = 2^9 = 512$ : stacked powers are worked from the top down.

The viral questions

Questions like $6 \div 2(1 + 2)$ go viral because of implied multiplication (a number written right next to a bracket). Following the standard rules, $2(1 + 2)$ is just $2 \times 3$ , and $6 \div 2 \times 3 = 3 \times 3 = 9$ . Some people, and some older calculators, give implied multiplication a higher priority and get 1. The calculator follows the standard convention and tells you when an expression uses implied multiplication. In real maths, write it unambiguously with extra brackets.

Tips for exams

Underline the operation you'll do next before doing it.
Rewrite the whole expression after each step, as the calculator does.
On a calculator, type the expression exactly as written, with brackets, and compare with your working.

Frequently asked questions

Is BIDMAS the same as PEMDAS?

Yes. They use different words (brackets/parentheses, indices/exponents) but the order is the same.

Does multiplication come before division?

No. They have equal priority and are worked from left to right, whichever comes first.

What symbols can I use?

Numbers, decimals, + − × ÷ (or * and /), ^ for powers, and brackets ( ), [ ] and { }.

Sources

National curriculum in England: mathematics programmes of study. Department for Education.
Common Core State Standards for Mathematics. Common Core State Standards Initiative.

BIDMAS, BODMAS and PEMDAS: the order of operations explained

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