Order of Operations Calculator
Order of Operations Calculator (PEMDAS)
Related Tools
What is Order of Operations?
The order of operations is a set of rules that determines the sequence in which mathematical operations should be performed. Following these rules ensures that everyone arrives at the same answer when solving a math expression.
This calculator helps you solve complex expressions step-by-step, showing exactly how PEMDAS (or BODMAS) rules are applied. Whether you're a student learning these concepts or need to verify your calculations, this tool breaks down each step clearly.
Use our practice mode to test your understanding and build confidence in applying order of operations correctly!
Understanding PEMDAS
P - Parentheses
Solve expressions inside parentheses first, starting with the innermost set.
Example: 2 × (3 + 4) = 2 × 7 = 14
E - Exponents
Calculate powers and roots next.
Example: 2 + 3² = 2 + 9 = 11
M & D - Multiplication & Division
Perform from left to right. These operations have equal priority.
Example: 8 ÷ 4 × 2 = 2 × 2 = 4 (left to right)
A & S - Addition & Subtraction
Perform last, from left to right. These operations have equal priority.
Example: 5 - 3 + 2 = 2 + 2 = 4 (left to right)
Frequently Asked Questions
What is PEMDAS?
PEMDAS is a mnemonic that helps remember the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. In some countries, it's called BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
Why does multiplication come before addition?
Mathematically, multiplication and division represent repeated addition/subtraction and are considered "stronger" operations. Following a consistent order ensures everyone gets the same answer when evaluating expressions.
Do multiplication and division have the same priority?
Yes! Multiplication and division are performed left to right at the same priority level. The same applies to addition and subtraction. PEMDAS can be misleading - think of it as P-E-MD-AS.
How do I solve nested parentheses?
Start with the innermost parentheses and work outward. For example: 2 × ((3 + 4) × 2) - first solve 3 + 4 = 7, then 7 × 2 = 14, finally 2 × 14 = 28.
Common Examples
Basic Examples
2 + 3 × 4 = 2 + 12 = 14
10 - 4 ÷ 2 = 10 - 2 = 8
(5 + 3) × 2 = 8 × 2 = 16
3² + 4 = 9 + 4 = 13
Complex Examples
2 × (3 + 4) - 5 = 2 × 7 - 5 = 9
12 ÷ 4 × 3 + 2 = 3 × 3 + 2 = 11
2³ + 4 × 2 = 8 + 8 = 16
(2 + 3)² - 10 = 25 - 10 = 15
Tips for Success
- When in doubt, use parentheses to make your intention clear
- Remember that × and ÷ are done left to right, not × before ÷
- Same for + and - : they're done left to right together
- Write out intermediate steps to avoid mistakes
- Double-check by working backwards from your answer
- Use our practice mode to build confidence!