PEMDAS Calculator

Type any expression and see it solved in the correct order of operations — PEMDAS / BODMAS — one step at a time, with parentheses, exponents and roots.

Use + − × ÷ ^ and parentheses. You can type * / and sqrt( ) too.

Result —

Order of Operations, Step by Step

The same rules every time, from the inside out.

1

Parentheses first

Anything inside brackets is resolved before it can be used elsewhere. Nested brackets work from the innermost pair outward.

2

Then exponents and roots

Powers and square roots come next, before any multiplying or dividing. Powers stack right to left, so 2^3^2 is 2^(3^2) = 512.

3

Multiply/divide, then add/subtract

Multiplication and division share a level and run left to right; addition and subtraction do the same afterwards. Need banker-safe figures at the end? Send the result to the Rounding Calculator.

Frequently Asked Questions

What does PEMDAS stand for?
PEMDAS is the order of operations: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction. You work left to right within each level. A common memory aid is "Please Excuse My Dear Aunt Sally". The key subtlety is that multiplication and division share one level, and addition and subtraction share another, so you do not do all multiplication before all division — you take them in the order they appear. This calculator applies exactly that order and shows each step so you can follow the reasoning.
Is PEMDAS the same as BODMAS?
Yes, they describe the same rules with different names. BODMAS stands for Brackets, Orders (powers and roots), Division and Multiplication, Addition and Subtraction, and is taught in the UK and many other countries, while PEMDAS is common in the US. "Brackets" and "Parentheses" mean the same thing, and "Orders" and "Exponents" both refer to powers. Division and multiplication still share a level, as do addition and subtraction, so the two give identical answers. You can type any expression here and it follows both conventions.
What is the answer to 8 ÷ 2(2 + 2)?
Under the standard order of operations the answer is 16. You resolve the parentheses first (2 + 2 = 4), then work left to right through the division and multiplication: 8 ÷ 2 = 4, then 4 × 4 = 16. The expression goes viral because the implied multiplication next to the parentheses tempts people to do 2 × 4 first and get 1. That interpretation is not standard; implicit multiplication has the same priority as explicit multiplication. This calculator treats 2(2 + 2) as 2 × (2 + 2) and returns 16.
Does multiplication always come before division?
No. Multiplication and division have equal priority, so you carry them out in the order they appear from left to right, not multiplication first. For example, 12 ÷ 3 × 2 is 8, because you do 12 ÷ 3 = 4 first and then 4 × 2 = 8, not 3 × 2 first. The same applies to addition and subtraction, which also share a level. The "MD" and "AS" in PEMDAS are each a single step, and this calculator follows that left-to-right rule and shows it in the steps.