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BODMAS — Order of Operations

What is BODMAS?

BODMAS is a rule that tells us which part of a mathematical expression to evaluate first. Follow the letters in the order shown — when two operations have the same priority (for example Division and Multiplication), evaluate from left to right.

BODMAS Rule — Full form
Letter Full form Symbols / Examples What it means / How to apply
B Brackets ( ), { }, [ ] Evaluate expressions inside brackets first. Work from innermost brackets outward.
O Order (Indices / Exponents / Roots) Square roots, indices, powers — e.g., ^, √ Evaluate powers and roots (orders) after brackets and before multiplication/division.
D Division ÷, / Division and multiplication have equal priority — perform left to right.
M Multiplication ×, * See Division row — treat together and evaluate left to right.
A Addition + Addition and subtraction have equal priority — perform left to right after multiplication/division.
S Subtraction − See Addition row — treat together and evaluate left to right.
Step-by-step explanation (how to apply BODMAS)
  1. Look for brackets. If there are any, evaluate the innermost bracketed expressions first.
  2. Within the expression (or after brackets are removed), evaluate Orders — exponents and roots.
  3. Next, handle Division and Multiplication. They are equal priority: read left to right and perform each operation in order as they appear.
  4. Finally, perform Addition and Subtraction. They are equal priority: read left to right.
  5. If at any stage new brackets or orders appear (e.g., after simplification), repeat the steps accordingly.
Worked example — step by step

Expression: 8 + 2 × 5 − (3 ^ 2)

  1. Brackets: evaluate (3 ^ 2) first — because brackets have top priority.
    3 ^ 2 = 9 → expression becomes 8 + 2 × 5 − 9
  2. Orders: none remain outside brackets (we already evaluated the power inside brackets).
  3. Division & Multiplication (left to right): evaluate 2 × 5.
    2 × 5 = 10 → expression becomes 8 + 10 − 9
  4. Addition & Subtraction (left to right): first 8 + 10 = 18, then 18 − 9 = 9.
    Final result = 9

Tip: when in doubt, rewrite the expression step-by-step replacing evaluated parts with their results — this helps avoid mistakes.

Step-by-step evaluator

Enter a simple arithmetic expression using numbers, + - * / ^ and parentheses.

Quick examples: 8 + 2 * 5 (8 + 2) * 5 4 + 18 / (3 * 3)
Steps
Result:  
Examples explained
Example 1

8 + 2 × 5

  1. Multiply first: 2 × 5 = 10
  2. Add: 8 + 10 = 18
Example 2

(8 + 2) × 5

  1. Brackets first: (8 + 2) = 10
  2. Multiply: 10 × 5 = 50
Example 3 — powers

3 + 2 ^ 3 × 2

  1. Orders first: 2 ^ 3 = 8
  2. Then multiply: 8 × 2 = 16
  3. Add: 3 + 16 = 19