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Order of Operations Calculator

Type an expression and get the answer with every PEMDAS step shown — brackets, exponents, multiplication and division, then addition and subtraction.

Your expression

Use + − × ÷ ^ and brackets. * and / work too, and 2(3 + 4) means multiply.
Order applied
brackets, then exponents, then multiply and divide, then add and subtract
Expression
8 + 3 × (7 − 2)^2 ÷ 5
Result
23
Steps
5
Left to right would give
605
Bracket pairs
1
Highest stage used
Brackets
Brackets — Subtract: 7 − 2 = 5
8 + 3 × 5 ^ 2 ÷ 5
Exponent: 5 ^ 2 = 25
8 + 3 × 25 ÷ 5
Multiply: 3 × 25 = 75
8 + 75 ÷ 5
Divide: 75 ÷ 5 = 15
8 + 15
Add: 8 + 15 = 23
23

How to use this calculator

  1. Type your expression. + − × ÷ ^ and brackets all work, and so do*, / and x if they are easier to reach.
  2. Read the answer at the top.
  3. Open the working panel for the steps. Each line names the operation that ran and shows what the expression looked like afterwards, so you can follow it the way you would on paper.

The steps are the reason to use this rather than a plain calculator. If your own answer differs, the step list shows exactly which line you and it parted company on.

The order of operations, in order

PEMDAS, BODMAS and BIDMAS are all this table
StageSymbolsDirection
Brackets( ) and [ ]Innermost first
Exponents^Right to left
Multiply and divide× ÷Left to right, equal rank
Add and subtract+ −Left to right, equal rank

The two middle words in each acronym are the source of nearly every mistake. Multiplication and division sit on the same line, as do addition and subtraction — the acronym lists them in an order for pronunciation, not for precedence.

A worked example

Take 8 + 3 × (7 − 2)^2 ÷ 5. The stages run in this order:

  1. Brackets — 7 − 2 = 5, leaving8 + 3 × 5^2 ÷ 5.
  2. Exponent — 5^2 = 25, leaving 8 + 3 × 25 ÷ 5.
  3. Multiply — leftmost of the equal-ranked pair, 3 × 25 = 75.
  4. Divide — 75 ÷ 5 = 15, leaving 8 + 15.
  5. Add — 8 + 15 = 23.

Working straight through from left to right instead gives 605 — which is what a basic calculator with no precedence returns, and why the calculator shows that figure beside the correct one.

Expressions people get wrong

The common wrong answer against the correct one
ExpressionCommon answerCorrect
8 ÷ 4 × 214
8 − 3 − 273
2 ^ 3 ^ 264512
100 − 5^2 × 24,95050
6 ÷ 2(1 + 2)19

Each row has the same cause: treating one operator as outranking another of equal rank, or forgetting that exponents run right to left. Paste any of them in above and the steps show where the other answer comes from.

Frequently asked questions

What is the order of operations?

Brackets first, then exponents, then multiplication and division, then addition and subtraction. It is remembered as PEMDAS, BODMAS or BIDMAS depending on where you were taught, and all three describe the same rules.

Do multiplication and division not come before each other?

No — they share a rank and run left to right. That is why 8 ÷ 4 × 2 is 4, not 1: the division comes first because it is further left, not because division outranks multiplication. Addition and subtraction share a rank the same way.

Why is 2^3^2 equal to 512 rather than 64?

Because exponents run right to left. The 3^2 is evaluated first, giving 2^9 = 512. Every other operator runs left to right, and exponents are the single exception.

What is the answer to 6 ÷ 2(1 + 2)?

Nine. The bracket resolves to 3, then the expression is 6 ÷ 2 × 3, and left-to-right gives 3 × 3 = 9. The viral argument for 1 treats the implied multiplication as binding tighter than the division, a convention some older textbooks used but standard modern notation does not.

How do I enter an expression?

Use + − × ÷ ^ and brackets. Typing * for multiply and / for divide works, so does using x, and 2(3 + 4) is read as multiplication. A minus sign in front of a number makes it negative.

Does PEMDAS mean parentheses always come first?

It means whatever is inside them is worked out before it is used, which is not the same as being the first thing on the page. In 3 + 4 × (2 + 1), the bracket is evaluated first, but the multiplication still happens before the addition.