Is PEMDAS the same as BODMAS?

Yes — they are the same rule with different names. BODMAS (used in the UK and many other countries) stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. “Orders” means exponents and roots, and “Brackets” means parentheses. The letters look different but the priority is identical, so PEMDAS and BODMAS always give the same answer.

Do you always multiply before dividing in PEMDAS?

No. Multiplication and division share the same rank, so you do not always do the M before the D. You work through them left to right in the order they appear. In 10 ÷ 2 × 3 the division comes first because it is further left: 10 ÷ 2 = 5, then 5 × 3 = 15. The same left-to-right rule applies to addition and subtraction.

What is the answer to 6 + 2 × 3?

It is 12, not 24. Multiplication is done before addition, so you first work out 2 × 3 = 6, then add the 6 in front: 6 + 6 = 12. Working strictly left to right (the wrong way) would give 8 × 3 = 24, which is the most common order-of-operations mistake.

Why do calculators disagree on 8 ÷ 2(2 + 2)?

Because the expression is deliberately ambiguous. By standard PEMDAS, the implied multiplication beside the bracket has the same rank as division, so you go left to right: 8 ÷ 2 = 4, then × 4 = 16. Some textbooks treat a number stuck to a bracket as binding more tightly, giving 8 ÷ (2 × 4) = 1. This calculator uses the standard left-to-right convention and returns 16. The real fix is to add brackets so the meaning is clear.

Does the negative sign or the exponent come first in −2²?

The exponent comes first. By convention, −2² means −(2²) = −4, because the power binds more tightly than a leading minus sign. If you actually want to square a negative number, write it with brackets: (−2)² = 4. This calculator follows the standard convention, so −2^2 evaluates to −4 and (−2)^2 evaluates to 4.

How do exponents fit into the order of operations?

Exponents are evaluated after parentheses but before any multiplication, division, addition, or subtraction. In 2 + 3², you square the 3 first to get 9, then add 2 for 11. A power only attaches to the number directly beneath it unless brackets group more, so 2 × 3² is 2 × 9 = 18, not (2 × 3)² = 36.

What happens to operations inside nested parentheses?

You work from the innermost brackets outward. For 2 × (3 + (4 − 1)), the inner (4 − 1) = 3 is resolved first, then (3 + 3) = 6, and finally 2 × 6 = 12. Each level of brackets is its own little expression that you fully simplify before using its value in the level above.

Arithmetic

Order of Operations Calculator

Type any arithmetic expression — with parentheses, exponents, ×÷, and +− — and evaluate it in correct PEMDAS / BODMAS order. The answer updates live, and every reduction step is shown so you can see exactly which operation happens when.

Evaluate an expression

PEMDAS

Your expression+ − × ÷ ^ ( )

Type * or × for multiply, / or ÷ for divide, ^ for powers. Brackets [ ] and work too.

Result

=−13

6 + 2 × 3 − (4 + 1) ^ 2

operations

exact value

whole number

Updates live

1
Multiplication (× and ÷ before + and −, left to right)
2 × 3 = 6
→ 6 + 6 − (4 + 1) ^ 2
2
Addition (+ and − last, left to right)
6 + 6 = 12
→ 12 − (4 + 1) ^ 2
3
Addition (+ and − last, left to right)
4 + 1 = 5
→ 12 − 5 ^ 2
4
Exponents come before × ÷ and + −
5 ^ 2 = 25
→ 12 − 25
5
Subtraction (+ and − last, left to right)
12 − 25 = −13
→ −13

Try a classic trap

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The basics

What is the order of operations?

The order of operations is the agreed-upon rule for which calculation to do first when an expression mixes several operations. Without it, 6 + 2 × 3 could mean either 24 or 12 — the rule guarantees everyone, and every calculator, lands on the same answer. It is summed up by the acronyms PEMDAS and BODMAS.

P E M D A S

A priority list, not a strict line

The letters rank the operations. Higher-priority work is done first, no matter where it sits in the line — so the multiply beats the add even though the add is written first.

6 + 2 × 3 → 6 + 6 = 12

left → right

Equal ranks go left to right

When two operations share a rank — multiply with divide, or add with subtract — neither wins automatically. You take them in reading order, left to right.

10 − 4 ÷ 2 → 10 − 2 = 8

Method

How to evaluate an expression by hand

Work down the priority list one rank at a time, always resolving the left-most operation within the current rank before moving right.

1
Parentheses first
Simplify everything inside brackets, working from the innermost pair outward. A bracketed group is its own little expression — finish it completely before using its value.
(4 + 1) → 5
2
Then exponents
Evaluate any powers and roots — the exponent calculator shows the expansion. An exponent attaches only to the number directly beneath it unless brackets group more.
5^2 → 25
3
Multiply and divide
Handle × and ÷ next. They share a rank, so sweep left to right — do not save all the multiplying for last.
2 × 3 → 6
4
Add and subtract
Finish with + and −, again left to right. Whatever is left is now a simple running total.
12 − 25 → −13

Worked examples

The classic traps, solved step by step

Each of these is a question people get wrong by reading left to right. Tab through to see the PEMDAS reductions the calculator performs.

Expression 6 + 2 × 3

2 × 3 = 6 → 6 + 6
6 + 6 = 12 → 12

6 + 2 × 3 = 12

Reading left to right gives 24. PEMDAS does the × first, so the answer is 12.

The tie-breaker

The left-to-right rule

The single most misunderstood part of PEMDAS: the M does not always beat the D, and the A does not always beat the S. Equal-rank operations are taken in reading order.

÷ then ×

Division can come before multiplication

Because they tie, the operation further left goes first. Doing the multiply first here would wrongly give 10 ÷ 6.

10 ÷ 2 × 3 = 15

− then +

Subtraction can come before addition

The same applies to the bottom rank. Saving the addition for last would wrongly give 8 − 5 = 3 instead of the correct 7.

8 − 3 + 2 = 7

Same rule, two names

PEMDAS vs. BODMAS

Different countries teach the rule under different acronyms, which makes people think there are two systems. There is only one — the letters just rename the same priorities.

Priority	PEMDAS (US)	BODMAS (UK)	Means
1st	Parentheses	Brackets	( ) [ ] { }
2nd	Exponents	Orders	powers & roots
3rd	Multiply / Divide	Divide / Multiply	× ÷ (left to right)
4th	Add / Subtract	Add / Subtract	+ − (left to right)

Note the apparent flip in the third row — BODMAS lists Division before Multiplication — but because they share a rank and run left to right, the answer never changes.

The internet argument

Why 8 ÷ 2(2 + 2) breaks the internet

This expression goes viral every few years because two reasonable readings of the same line give two different answers. The disagreement is about notation, not arithmetic.

standard PEMDAS

The answer 16

Treat the bracket-multiply as ordinary multiplication. It ties with division, so you go left to right: 8 ÷ 2 = 4, then × 4 = 16. This is the convention the calculator above uses.

8 ÷ 2 × 4 = 16

tight juxtaposition

The answer 1

Some texts read a number glued to a bracket — implied multiplication — as binding tighter than the ÷, grouping 2(2 + 2) first.

8 ÷ (2 × 4) = 1

The honest answer is that the expression is badly written. Adding one pair of brackets — (8 ÷ 2)(2 + 2) or 8 ÷ (2(2 + 2)) — removes all doubt. When in doubt, over-bracket.

Worth knowing

Common mistakes & pitfalls

Nearly every order-of-operations error comes from one of these. Knowing them is most of the battle.

left → right ≠ rank order

Plain left-to-right

The classic slip: evaluating the whole line in reading order and ignoring the ranks. That turns 6 + 2 × 3 into 24 instead of 12.

M before D

Always multiply first

Thinking the M in PEMDAS outranks the D. They tie — take whichever comes first reading left to right.

−a²

Squaring the sign

Reading −2² as (−2)². The power binds tighter than the minus, so −2² = −4. Use brackets if you mean to square a negative.

exponent spread

Over-applying a power

Letting an exponent cover more than its base. In 2 × 3² only the 3 is squared, giving 2 × 9 = 18 — not (2 × 3)² = 36.

dropped negatives

Losing a minus sign

Forgetting that a subtraction can leave a negative running total mid-expression, which then changes every step after it.

implied ×

Missing the hidden multiply

Not seeing the multiplication hiding in 2(3 + 4). A number beside a bracket means multiply: it is 2 × 7 = 14.

Reference

Operators this calculator accepts

Type symbols however you like — the calculator normalizes them. Powers use the caret, and any bracket style works.

Operation	Type any of	Rank	Example
Group	( ) [ ] { }	1st	(2 + 3) × 4 = 20
Power	^	2nd	2^3 = 8
Multiply	× · *	3rd	4 × 5 = 20
Divide	÷ /	3rd	20 ÷ 4 = 5
Add	+	4th	7 + 8 = 15
Subtract	− -	4th	9 − 4 = 5
Decimals	.	—	3.5 × 2 = 7
Negatives	− in front	—	−3 + 5 = 2

Where it shows up

Why the order matters

One shared convention so that a formula written by one person means the same thing to everyone — and every machine — that reads it.

spreadsheets

Formulas & code

Spreadsheets and programming languages follow the same precedence. Misreading the order is one of the most common formula bugs.

algebra

Algebra & beyond

Simplifying expressions, substituting values, and rearranging equations all rest on the order of operations being automatic — as does the percentage calculator and the “what is X% of Y” family.

exams

Tests & homework

It is a staple of school maths from late primary onward — and a reliable source of lost marks when the left-to-right rule is forgotten.

FAQ

Common questions

PEMDAS is the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. You work from left in that priority — anything in brackets first, then powers, then multiply and divide, and finally add and subtract. A common memory aid is “Please Excuse My Dear Aunt Sally.”

Keep going

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Guide

What is PEMDAS? The order of operations

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