BIDMAS Calculator — BODMAS Order of Operations
Enter any mathematical expression and our calculator will evaluate it following the correct BIDMAS (BODMAS) order of operations, with step-by-step working.
Try one of these examples:
What is BIDMAS?
BIDMAS is a mnemonic used in UK schools to remember the correct order of mathematical operations. Without a defined order, expressions like 3 + 4 × 2 would be ambiguous — is the answer 14 (multiplication first) or 14 (addition first)? BIDMAS resolves this by establishing a universal hierarchy.
BIDMAS stands for:
- B — Brackets: Evaluate everything inside parentheses (or brackets) first. Nested brackets are worked from the innermost outward.
- I — Indices: Calculate powers (2³ = 8), square roots, and other index operations.
- D — Division: Perform division operations, working left to right.
- M — Multiplication: Perform multiplication operations. Division and Multiplication share equal priority — work left to right.
- A — Addition: Perform addition, working left to right.
- S — Subtraction: Perform subtraction. Addition and Subtraction share equal priority — work left to right.
The critical points: D and M have equal priority (left to right), and A and S have equal priority (left to right). The mnemonic order does not imply D always before M in terms of strict precedence — it just happens to come first in the acronym.
BIDMAS vs BODMAS vs PEMDAS
Different countries use different acronyms for the same mathematical rule. The underlying order of operations is identical worldwide.
| Acronym | Used In | B/P | I/O/E | D | M | A | S |
|---|---|---|---|---|---|---|---|
| BIDMAS | UK, Australia | Brackets | Indices | Division | Multiplication | Addition | Subtraction |
| BODMAS | UK, India | Brackets | Orders | Division | Multiplication | Addition | Subtraction |
| PEMDAS | USA | Parentheses | Exponents | Multiplication | Division | Addition | Subtraction |
| BEDMAS | Canada | Brackets | Exponents | Division | Multiplication | Addition | Subtraction |
Note: In PEMDAS, M appears before D, but multiplication and division still have equal priority — work left to right. The acronyms differ in naming, not in mathematical outcome.
Worked BIDMAS Examples
Example 1: 3 + 2 × 4
Incorrect (left to right without BIDMAS): 3 + 2 = 5, then 5 × 4 = 20. WRONG.
Correct (BIDMAS — multiplication before addition): 2 × 4 = 8, then 3 + 8 = 11.
Example 2: (3 + 2) × 4
Brackets first: (3 + 2) = 5. Then 5 × 4 = 20. Brackets change the answer!
Example 3: 2³ + 4 × 2 - 1
- No Brackets.
- Indices: 2³ = 8. Expression becomes: 8 + 4 × 2 - 1
- Multiplication: 4 × 2 = 8. Expression becomes: 8 + 8 - 1
- Addition/Subtraction left to right: 8 + 8 = 16, then 16 - 1 = 15
Example 4: 10 ÷ 2 + 3 × (4 - 1)
- Brackets: (4 - 1) = 3. Expression: 10 ÷ 2 + 3 × 3
- No Indices.
- Division and Multiplication (left to right): 10 ÷ 2 = 5, then 3 × 3 = 9. Expression: 5 + 9
- Addition: 5 + 9 = 14
Common Mistakes with BIDMAS
- Treating D before M as absolute: 8 ÷ 4 × 2. Correct answer: (8 ÷ 4) × 2 = 4 (left to right). NOT 8 ÷ (4 × 2) = 1.
- Forgetting nested brackets: Work from innermost brackets outward. 2 × (3 + (4 - 1)): first (4-1)=3, then (3+3)=6, then 2×6=12.
- Negative numbers with indices: -3² = -(3²) = -9, not (-3)² = 9. Use brackets to clarify: (-3)² = 9.
BIDMAS in GCSE Maths
Order of operations is a fundamental topic in GCSE Maths (all UK exam boards: AQA, Edexcel, OCR, WJEC, CCEA). Students are expected to:
- Apply BIDMAS correctly when evaluating numerical expressions
- Use brackets to alter the order of operations
- Correctly evaluate expressions involving powers and roots
- Understand that scientific calculators automatically follow BIDMAS
- Recognise that basic (four-function) calculators may not follow BIDMAS
A common exam question type presents an expression and asks students to insert brackets to make it equal a given target value. For example: "Insert brackets into 3 + 4 × 2 to make the answer 14" — answer: (3 + 4) × 2 = 14.
Understanding BIDMAS is also essential for algebra — when substituting values into formulae, the order of operations determines the correct result.
How the BIDMAS Calculator Works
This calculator uses the current UK grading system and educational standards to help students, parents, and teachers understand academic performance. UK education follows specific grading frameworks that differ between GCSEs, A-Levels, and university degrees.
Understanding how grades are calculated and what they mean for future progression is important for making informed decisions about subject choices, university applications, and career planning.
Key Information for 2025/26
GCSEs in England use the 9-1 grading scale, where 9 is the highest and 4 is a standard pass (equivalent to the old C grade). A-Levels use the A*-E scale with UCAS tariff points ranging from 56 (A*) to 16 (E). Universities typically require grades between AAA and CCC depending on the course and institution, with highly competitive courses often asking for A*A*A.
Example Calculation
A student achieving grades of A*, A, and B at A-Level would earn UCAS tariff points of 56 + 48 + 40 = 144 points total. This exceeds the typical entry requirement for most Russell Group universities (128 points or AAB equivalent) and would make the student competitive for many courses.
Source: Based on Ofqual and UCAS 2025/26 guidelines. Last updated March 2026.
Frequently Asked Questions
What is BIDMAS?
BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction — the correct order for evaluating mathematical expressions. Brackets first, then powers/roots, then multiply/divide (left to right), then add/subtract (left to right).
Is BIDMAS and BODMAS the same thing?
Yes, BIDMAS and BODMAS are identical. BODMAS uses "Orders" instead of "Indices" — both refer to powers and roots. The mathematical rule is exactly the same.
What order do you do operations in BIDMAS?
First: Brackets. Second: Indices (powers/roots). Third: Division and Multiplication (equal priority, left to right). Fourth: Addition and Subtraction (equal priority, left to right).
What is the difference between BIDMAS and PEMDAS?
PEMDAS is the American term; BIDMAS is the UK term. Both describe the same mathematical order: Parentheses/Brackets, Exponents/Indices, then Multiplication and Division (equal priority, left to right), then Addition and Subtraction (equal priority, left to right).
Does multiplication always come before division in BIDMAS?
No. Multiplication and division have equal priority and are performed left to right. The M appearing before D in the acronym is not a ranking. Example: 12 ÷ 4 × 3 = (12 ÷ 4) × 3 = 9, not 12 ÷ (4 × 3) = 1.
Why does the order of operations matter?
Without BIDMAS, the expression 2 + 3 × 4 could give two different answers (20 or 14) depending on which operation you do first. BIDMAS gives a universal rule so everyone — and every calculator — gets the same answer: 14.