Order Operations Calculator

Accepts + - * / ^ ( ) as well as ×, ÷, − and superscripts such as 5².
Only changes the wording of the stages; all of these describe the same rule.
Result
3.5
Order of Operations Calculator (PEMDAS / BODMAS)
Unrounded result
3.5
Expression as parsed
3 + 4 * 2 / (1 - 5)^2
Number of operations
5
Mnemonic used
PEMDAS (US)
Worked out from NIST Digital Library of Mathematical Functions, §1.1 Notation (operator precedence) and 2 other sources.

How this is worked out

8 steps
  1. PEMDAS (US): Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
  2. Read as: 3 + 4 × 2 ÷ (1 - 5)^2
  3. 1. Parentheses → Subtraction: 1 - 5 = -4 → 3 + 4 × 2 ÷ (-4)^2
  4. 2. Exponent: (-4)^2 = 16 → 3 + 4 × 2 ÷ 16
  5. 3. Multiplication: 4 × 2 = 8 → 3 + 8 ÷ 16
  6. 4. Division: 8 ÷ 16 = 0.5 → 3 + 0.5
  7. 5. Addition: 3 + 0.5 = 3.5 → 3.5
  8. Result = 3.5
Step-by-step workingtable
1. Parentheses → Subtraction: 1 - 5 = -4 → 3 + 4 × 2 ÷ (-4)^2, 2. Exponent: (-4)^2 = 16 → 3 + 4 × 2 ÷ 16, 3. Multiplication: 4 × 2 = 8 → 3 + 8 ÷ 16, 4. Division: 8 ÷ 16 = 0.5 → 3 + 0.5, 5. Addition: 3 + 0.5 = 3.5 → 3.5
Rule appliedtable
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Results are general information, not financial, tax, legal, medical or engineering advice.