A PEMDAS and BODMAS calculator that shows each step
This order of operations calculator solves an expression the way you are taught in class and writes out every step: the operation it performs, what it equals, and the whole expression that remains. It follows PEMDAS (used in the US) and BODMAS (used in the UK, India and many other countries), which are the same rule with different names.
It is useful for homework, for checking a viral “what is 6 ÷ 2(1+2)?” puzzle, and for teachers who want a worked example in seconds. Type the expression, use the symbol buttons if you are on a phone, and read down the steps.
How to use the Order of Operations (BODMAS/PEMDAS) Step Solver
- Type or paste your expression in the box (× x * for multiply, ÷ / for divide, ^ for powers).
- Or tap one of the example buttons to see a classic case.
- Read the answer at the top.
- Follow the numbered steps: each line names the rule used, the single operation done, and the expression that is left.
- Press “Copy steps” to paste the working into your notes.
Order of Operations (BODMAS/PEMDAS) Step Solver features
One operation per step
You see exactly which operation comes next and why.
All bracket types
Round, square and curly brackets, nested to any reasonable depth.
Implicit multiplication
2(3+4) is read as 2 × (3+4).
Clear errors
Division by zero, unmatched brackets and missing numbers are explained rather than guessed.
The rule: PEMDAS = BODMAS
The letters suggest that multiplication comes before division and addition before subtraction, which is wrong: they are pairs of equal rank. 12 ÷ 3 × 2 is 4 × 2 = 8, not 12 ÷ 6 = 2.
| Priority | PEMDAS (US) | BODMAS (UK/India) | What it covers |
|---|---|---|---|
| 1 | Parentheses | Brackets | Anything inside ( ) [ ] { }, innermost first |
| 2 | Exponents | Orders (powers, roots) | x², 2^3 |
| 3 | Multiplication and Division | Division and Multiplication | Equal priority: work left to right |
| 4 | Addition and Subtraction | Addition and Subtraction | Equal priority: work left to right |
Worked example
8 + 6 × (5 − 3) ÷ 2²: brackets first, 5 − 3 = 2, leaving 8 + 6 × 2 ÷ 2². Powers next: 2² = 4, so 8 + 6 × 2 ÷ 4. Multiplication and division from the left: 6 × 2 = 12, then 12 ÷ 4 = 3. Finally 8 + 3 = 11.
Tricky cases and conventions
- Powers are right to left: 2^3^2 = 2^(3^2) = 2^9 = 512, not (2^3)^2 = 64.
- A minus before a power is read as −(2²) = −4; write (−2)^2 to get 4.
- 6 ÷ 2(1+2): this tool treats the bracketed 2(1+2) as ordinary multiplication, so the answer is 9. Some textbooks and calculators bind “2(1+2)” more tightly and get 1; the ambiguity is why careful writers add brackets.
- Decimals use floating-point arithmetic, shown to 12 significant digits, so 0.1 + 0.2 appears as 0.3.
Common mistakes to avoid
- Adding before multiplying: 2 + 3 × 4 is 14, not 20.
- Treating “M before D” as a rule: 100 ÷ 10 × 5 is 50, not 2.
- Forgetting to work inside the innermost bracket first when brackets are nested.
- Dropping a minus sign when a bracket is removed: 10 − (3 + 2) is 5, not 15.
- Squaring only the number and not its sign: −3² is −9 but (−3)² is 9.
Related tools
For general sums use the scientific calculator; the exponent calculator explains powers and the fraction calculator handles fractions exactly.
Order of Operations (BODMAS/PEMDAS) Step Solver FAQ
What is PEMDAS?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). It is the US name for the order of operations.
What is the difference between PEMDAS and BODMAS?
None in outcome. BODMAS says Brackets, Orders, Division, Multiplication, Addition, Subtraction; Orders means powers and roots. Both treat multiplication and division as equals.
Do you always multiply before you divide?
No. Multiplication and division have equal priority, so you work from left to right. The same holds for addition and subtraction.
Is BIDMAS the same?
Yes. BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) is another UK name for the same rule.
What are some BODMAS example questions?
Try 7 + 3 × 2 (answer 13), (7 + 3) × 2 (20), 18 ÷ 3 × 2 (12) and 2 + 4^2 ÷ 8 (4). Type them in and compare with the steps.
Why does my phone calculator give a different answer?
Basic calculators may evaluate left to right as you press keys. This tool applies the full order of operations to the whole expression.