Order of Operations Calculator (PEMDAS/BODMAS)
Solve arithmetic expressions with a strict hierarchy visualization. See how PEMDAS determines the sequence of calculation steps.
About
Mathematics relies on a strict hierarchy of operations to ensure every expression yields a single unique result. This calculator implements the PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) ruleset to solve arithmetic problems. It is designed for students and professionals verifying complex calculations where the order of execution is not immediately obvious. The tool provides a hierarchical view of the solution process. It breaks down the expression step-by-step to demonstrate exactly which operation takes precedence at any given stage.
Formulas
The calculator uses a precedence ranking system. Operators are assigned weights.
When two operators share the same rank (e.g., multiplication and division), they are evaluated from left to right. Parentheses force the evaluation of the expression inside them before anything outside.
Reference Data
| Precedence | Operation | Symbol | Associativity |
|---|---|---|---|
| 1 (Highest) | Parentheses | ( ) | Inside to Out |
| 2 | Exponents / Roots | ^, √ | Right to Left |
| 3 | Multiplication / Division | ×, ÷ | Left to Right |
| 4 (Lowest) | Addition / Subtraction | +, − | Left to Right |
| Example | 2 + 3 × 4 = 14 (Not 20) | ||