Maths / Calculate
Order of Operations Calculator: PEMDAS and BODMAS Steps
Work through an arithmetic expression with highlighted reduction steps, exact fractions, brackets, right-associative powers and left-to-right multiplication and division.
Order of Operations Calculator: PEMDAS and BODMAS Steps: This calculator helps you explain how an arithmetic answer is reached. It highlights the next sub-expression and shows the expression after that calculation, so you can compare the working with your own. Brackets come first, then powers, then multiplication and division together from left to right, then addition and subtraction together from left to right. BODMAS and PEMDAS are names for the same ordering; neither means that multiplication always precedes division. Powers associate to the right, so 2^3^2 becomes 2^(3^2) and gives 512. A leading minus applies after a power: −3^2 gives −9, whereas (−3)^2 gives 9. Fractions remain exact for rational calculations. Implicit multiplication has the same priority as division here. Thus 6 ÷ 2(1+2) gives 9. Some textbook conventions give implied multiplication higher priority, producing 1; explicit brackets remove the ambiguity. The working inserts brackets to show how the expression was grouped. For functions and more advanced calculations, use the scientific calculator, or practise ratios with the fraction calculator. Runs 100% locally in your browser with zero server file uploads.
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PEMDAS and BODMAS name the same order: brackets, powers, multiplication and division from left to right, then addition and subtraction from left to right. Powers associate to the right: 2^3^2 means 2^(3^2). A leading minus applies after powers: −3^2 = −9.
Implicit multiplication has the same priority as division here: 6 ÷ 2(1+2) = 9. Some textbooks give implied multiplication priority and obtain 1. Write (6 ÷ 2) × (1+2) or 6 ÷ (2 × (1+2)) to make your intention clear.
Result: 14
Each highlight shows the next operation. Exact fractions remain exact.
2 + 3 × 4× ÷ left to right2 + 12+ − left to right14
Arithmetic conventions
OpenStax Prealgebra 2e, order of operations, describes parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. Its text is available under Creative Commons Attribution.
Clear notation
OpenStax Elementary Algebra 2e uses grouping symbols to state the intended order. PEMDAS and BODMAS describe the same hierarchy. Chained powers here associate to the right; explicit parentheses avoid disagreements over implied multiplication.
How to use it
- Enter numbers with brackets and +, −, ×, ÷ or ^.
- Read the highlighted calculation and its rewritten expression below.
- Follow each reduction to the exact result; use explicit brackets where implicit multiplication could be ambiguous.
Privacy & limitations
Expressions are calculated in your browser.
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Frequently asked questions
Are PEMDAS and BODMAS different?
No. Both put grouping first, then powers, then multiplication and division at equal priority, then addition and subtraction at equal priority.
Why does 8 ÷ 2 × (2 + 2) equal 16?
First reduce the brackets to 4. Then 8 ÷ 2 = 4, followed by 4 × 4 = 16. Multiplication and division run left to right.
Why is implied multiplication ambiguous?
Some textbooks bind an implied product more tightly than division. This calculator uses equal priority, read left to right. Add brackets to specify which interpretation you intend.
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