Type an arithmetic expression and get the answer with every step in PEMDAS order: brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Fractions and decimals stay exact, so 0.1 + 0.2 really is 0.3.
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Use + − × ÷ (or * /), ^ for powers, brackets ( ) [ ] { }, decimals and fractions like 3/4. A number next to a bracket means multiply.
Enter your values to see the result.
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How to use the Order of Operations Calculator
Type or paste the expression, for example 3 + 4 × 2 ÷ (1 − 5)^2. You can use * and / instead of × and ÷.
Pick the acronym you learned (PEMDAS, BODMAS or BIDMAS). It only changes the names of the steps, not the answer.
Choose fractions or decimals for numbers that are not whole.
Press Solve (the answer also updates as you type).
Read the steps: each line shows the operation done and the expression that remains, with the new value highlighted.
The order of operations rule
Step
PEMDAS
BODMAS
What you do
Example
1
Parentheses
Brackets
Work out the innermost brackets first, then the next layer out
2 × (3 + 4) = 2 × 7
2
Exponents
Orders
Powers and roots, from right to left when stacked
5 + 2^3 = 5 + 8
3
Multiplication & Division
Division & Multiplication
Equal priority: go from left to right
12 ÷ 3 × 2 = 4 × 2 = 8
4
Addition & Subtraction
Addition & Subtraction
Equal priority: go from left to right
10 − 4 + 3 = 6 + 3 = 9
A worked example: 3 + 4 × 2 ÷ (1 − 5)^2. The bracket comes first: 1 − 5 = −4. Then the exponent: (−4)^2 = 16. Multiplication and division go left to right: 4 × 2 = 8, then 8 ÷ 16 = 1/2. Finally the addition: 3 + 1/2 = 7/2 = 3.5.
Common mistakes the steps help you catch
Expression
Correct
Common wrong answer
Why
8 − 3 + 2
7
3
Subtraction is not done after addition; go left to right: 5 + 2
12 ÷ 4 × 3
9
1
Division and multiplication share a level; left to right: 3 × 3
−4^2
−16
16
The exponent applies to 4 only; write (−4)^2 to square −4
2^3^2
512
64
Stacked powers go right to left: 2^9
10 − (2 + 3)
5
11
The minus applies to the whole bracket: 10 − 5
1 ÷ 2 ÷ 2
1/4
1
Left to right: (1 ÷ 2) ÷ 2, not 1 ÷ (2 ÷ 2)
Tips for typing expressions
Use * or × for multiplication, / or ÷ for division and ^ or ** for powers.
Square brackets [ ] and braces { } work exactly like parentheses and make nested expressions easier to read.
A number written right next to a bracket, as in 4(2 + 1) or (1 + 1)(2 + 3), means multiply. The calculator tells you when it found one, because textbooks do not all agree on how strongly implied multiplication binds.
Square roots are powers: write √9 as 9^(1/2). Perfect roots stay exact, so 8^(2/3) = 4.
Write large numbers without commas (1500, not 1,500) and use a dot as the decimal point.
Frequently asked questions
What is the order of operations?
It is the agreed order for evaluating an expression: first anything inside parentheses or brackets, then exponents (powers and roots), then multiplication and division from left to right, and finally addition and subtraction from left to right. PEMDAS, BODMAS and BIDMAS are memory aids for the same rule.
Does multiplication come before division in PEMDAS?
No. Multiplication and division have the same priority and are done together from left to right, whichever comes first. The same goes for addition and subtraction. So 12 ÷ 3 × 2 = 4 × 2 = 8, not 12 ÷ 6 = 2.
What is the answer to 6 ÷ 2(1 + 2)?
Using the standard rule, where a number next to brackets is ordinary multiplication done left to right with division, the answer is 9: 6 ÷ 2 × 3 = 3 × 3 = 9. Some older texts treat implied multiplication as stronger and get 1. The expression is ambiguous, so it is better to write 6 ÷ (2(1 + 2)) or (6 ÷ 2)(1 + 2).
Why is −3^2 equal to −9?
Exponents are applied before the negative sign, so −3^2 means −(3^2) = −9. If you want to square negative three, put it in brackets: (−3)^2 = 9. This calculator follows that convention, which is the one used by math textbooks and most calculators.
How are stacked exponents like 2^3^2 evaluated?
Powers are evaluated from right to left (top down), so 2^3^2 = 2^(3^2) = 2^9 = 512, not (2^3)^2 = 64. Use brackets if you mean the second one.
Is PEMDAS the same as BODMAS?
Yes. PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is used in the US, BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) in the UK, India and Australia, and BIDMAS or BEDMAS in other places. All of them give the same answer.
Can I use fractions and decimals?
Yes. Write a fraction as 3/4. Because division is done in order, wrap a fraction in brackets when it follows a division or a power, for example 2 ÷ (3/4). The calculator keeps exact fractions internally, so there are no rounding errors, and shows the decimal value too.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.