PEMDAS / Order of Operations Calculator

Evaluate numerical expressions following the correct order of operations: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.

Concept Overview

In mathematics, the order of operations is a set of rules that dictates which procedures to perform first in a given mathematical expression. Without these rules, a single expression could result in multiple different answers depending on the order chosen.

1 Parentheses

Always solve anything inside parentheses or brackets first. If there are nested parentheses, start from the innermost pair and work your way out.

2 Exponents

Calculate any powers or roots (like squared numbers or square roots) after parentheses are cleared.

3 Mult & Div

Perform multiplication and division as they appear from left to right. Neither takes precedence over the other; they are equal in priority.

4 Add & Sub

Finally, perform addition and subtraction from left to right. Like multiplication and division, these share the same level of priority.

Step-by-Step Example

Solve: 3 + 6 * (5 + 4) / 3 - 7

  1. Parentheses: 5 + 4 = 9 → 3 + 6 * (9) / 3 - 7
  2. Exponents: None.
  3. Multiplication (Left): 6 * 9 = 54 → 3 + 54 / 3 - 7
  4. Division: 54 / 3 = 18 → 3 + 18 - 7
  5. Addition (Left): 3 + 18 = 21 → 21 - 7
  6. Subtraction: 21 - 7 = 14
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