Order of Operations Calculator (PEMDAS)

The Order of Operations Calculator evaluates an arithmetic expression using standard PEMDAS precedence — Parentheses, Exponents, Multiplication/Division, Addition/Subtraction — and shows a numbered, step-by-step breakdown of exactly which operation is resolved at each stage.

It's built for students learning the order of operations, teachers preparing worked examples, and anyone who wants to double-check an expression by hand.

How to use it

1. Enter an expression using +, -, *, /, ^ (power), and parentheses — e.g. 3 + 4 * 2 / (1 - 5)^2.
2. Adjust Decimal places if you want more or fewer digits after the decimal point (default 6).
3. Read Result for the final answer, Whole Number? to see if it's an integer, and Step-by-Step Solution for the full breakdown.

Results update automatically as you type. For example, 3 + 4 * 2 / (1 - 5)^2 evaluates to 3.5, with steps showing the parenthesized subtraction first, then the exponent, then the multiplication, then the division, then the final addition.

What is PEMDAS?

PEMDAS (also taught as GEMDAS or BODMAS in some regions) is a mnemonic for the order in which arithmetic operations should be performed:

1. Parentheses — evaluate everything inside (...) first, innermost first.
2. Exponents — powers, like 2^3.
3. Multiplication and Division — evaluated left to right, whichever comes first.
4. Addition and Subtraction — evaluated left to right, whichever comes first.

Without this convention, an expression like 3 + 4 * 2 would be ambiguous — PEMDAS says the multiplication happens first (4 * 2 = 8), giving 3 + 8 = 11, not (3 + 4) * 2 = 14.

How is a negative sign in front of an exponent handled?

This calculator follows the same convention used by most programming languages and calculators: a leading minus sign binds looser than exponentiation on its own base, so -3^2 means -(3^2) = -9, not (-3)^2 = 9. If you want the base itself to be negative, wrap it in parentheses: (-3)^2 = 9. An exponent can carry its own sign too — 2^-2 evaluates to 0.25.

Need to check a root on its own instead of a full expression? Try the Nth Root Calculator or Square Root Calculator.

Privacy

This calculator runs entirely in your browser. Your expression is never uploaded, logged, or stored — the computation happens locally on your device.