What Is BODMAS? Rule, Formula & Examples

📅 2025-09-05 ⏱ 7 min read

BODMAS is a rule that defines the correct order of operations in math: Brackets, Orders, Division, Multiplication, Addition, Subtraction. Learn the formula, explore interactive visualizers, and see worked examples.

What Is BODMAS?

BODMAS is a set of rules that determines the correct sequence for solving mathematical expressions. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. These 6 operations must be performed in this specific order to get the right answer every time. If you want to solve or verify any expression instantly, you can use our free BODMAS calculator to see every step computed in real time.

The expression 8 + 2 × 5 equals 18, not 50. Multiplication comes before addition in BODMAS. Without BODMAS, the same expression can produce 2 different answers — only 1 is correct.

Why BODMAS Matters

✗ Without BODMAS

8 + 2 × 5

8 + 2 = 10

10 × 5 = 50

= 50 ✗

✓ With BODMAS

8 + 2 × 5

M first: 2 × 5 = 10

A next: 8 + 10 = 18

= 18 ✓

BODMAS Full Form and Rule

The BODMAS full form breaks down into 6 operations arranged by priority level:

BBrackets( ), { }, [ ] — solved first

OOrdersPowers, square roots, exponents

DDivision÷ — left to right with multiplication

MMultiplication× — left to right with division

AAddition+ — left to right with subtraction

SSubtraction− — left to right with addition

The BODMAS rule groups Division and Multiplication at the same priority level, and Addition and Subtraction at the same priority level. Within each group, operations are solved from left to right.

Hierarchy Explorer

Interactive BODMAS Priority Ladder

Click any operation letter below to inspect its precedence rank, rules, and live calculation behavior.

Highest Priority — Rank 1

B — Brackets: Parentheses ( ), Braces , Brackets [ ]

Any expression enclosed inside brackets must be solved completely before any other operations. If brackets are nested (brackets within brackets), always evaluate the innermost bracket first: ( ) then then [ ].

Live Example:

5 × (3 + 4) ➔ Solve (3 + 4) = 7 ➔ 5 × 7 = 35

💡 Pro Tip: Never distribute multiplication into brackets before checking if the inside expression can be simplified first.

The BODMAS Formula

The BODMAS formula has 4 priority levels:

Priority 1: Brackets — ( ), { }, [ ]
Priority 2: Orders — exponents and roots
Priority 3: Division and Multiplication — left to right
Priority 4: Addition and Subtraction — left to right

⚡ Interactive Visual Tool

Live BODMAS Step-by-Step Evaluator

Click "Next Step" to watch the BODMAS rule resolve operations in order of mathematical precedence.

Try Examples:

Current Expression State: Initial Expression

Rule: Ready

Click "Next Step ▶" to start solving using BODMAS order of precedence.

Step Breakdown Summary

3 Worked BODMAS Examples

Example 1: Basic BODMAS

Solve: 6 + 3 × 4

Step 1 — Multiplication: 3 × 4 = 12

Step 2 — Addition: 6 + 12 = 18

6 + 3 × 4 = 18

Example 2: Brackets and Orders

Solve: (5 + 3)² − 10

Step 1 — Brackets: (5 + 3) = 8

Step 2 — Orders: 8² = 64

Step 3 — Subtraction: 64 − 10 = 54

(5 + 3)² − 10 = 54

Example 3: All BODMAS Operations

Solve: 12 × 3 + (4 − 2) − 4² + 18 ÷ 3

Step 1 — Brackets: (4 − 2) = 2
Expression: 12 × 3 + 2 − 4² + 18 ÷ 3

Step 2 — Orders: 4² = 16
Expression: 12 × 3 + 2 − 16 + 18 ÷ 3

Step 3 — Division & Multiplication (left to right):
12 × 3 = 36, then 18 ÷ 3 = 6
Expression: 36 + 2 − 16 + 6

Step 4 — Addition & Subtraction (left to right):
36 + 2 = 38, then 38 − 16 = 22, then 22 + 6 = 28

12 × 3 + (4 − 2) − 4² + 18 ÷ 3 = 28

💡 Key Rule

Division does not always come before Multiplication. D and M have equal priority. Solve them in the order they appear from left to right. The same rule applies to Addition and Subtraction.