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.

Result

Steps

Left to right would give

605

Bracket pairs

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

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Keep this calculation as a scenario, change any input above, and the Now column shows how the result moves. Keep up to three, A to C; Open puts one back in the calculator.

How to use this calculator

Type your expression. + − × ÷ ^ and brackets all work, and so do*, / and x if they are easier to reach.
Read the answer at the top.
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.

What can I type in the expression box?

Expression — numbers with + − × ÷ ^ and brackets, up to 120 characters.*, /, x and : work as multiply and divide, square brackets work as brackets, and spaces and commas are ignored.
Implied multiplication and signs — 2(3 + 4) means multiply, a leading− makes a number negative, and −(2 + 3) works as0 − (2 + 3).
What is rejected — empty or incomplete expressions, unmatched brackets, other characters, division by zero and powers with no real value.

What do the results show?

Result — the value of the whole expression.
Steps — how many single operations it took to reduce the expression.
Left to right would give — the answer a basic calculator without precedence returns, or "the same" when it matches.
Bracket pairs and Highest stage used — how many brackets were opened, and the highest PEMDAS stage the expression reaches.
Order applied — the stages used, in the order they ran.
Working panel — one line per operation, with the expression as it stands afterwards.

How is an expression worked out?

The calculator reduces the expression one operation at a time, always taking the operation that ranks highest. Brackets are cleared from the innermost pair outwards, and every intermediate value is rounded to 12 significant digits to remove floating-point noise.

brackets → exponents → × and ÷ → + and −

Exponents run right to left, so 2^3^2 is 2^9
Multiplication and division share a rank and run left to right
Addition and subtraction share a rank and run left to right

The order of operations, in order

PEMDAS, BODMAS and BIDMAS are all this table
Stage	Symbols	Direction
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:

Brackets — 7 − 2 = 5, leaving8 + 3 × 5^2 ÷ 5.
Exponent — 5^2 = 25, leaving 8 + 3 × 25 ÷ 5.
Multiply — leftmost of the equal-ranked pair, 3 × 25 = 75.
Divide — 75 ÷ 5 = 15, leaving 8 + 15.
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
Expression	Common answer	Correct
8 ÷ 4 × 2	1	4
8 − 3 − 2	7	3
2 ^ 3 ^ 2	64	512
100 − 5^2 × 2	4,950	50
6 ÷ 2(1 + 2)	1	9

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.

Last updated 25 October 2026.

Order of Operations Calculator

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