Introduction
The Order of Operations Calculator solves math problems in the right order and shows you every step. Type an expression like (3 + 4) × 2² − 6 ÷ 3, press Calculate, and you get the answer plus each step listed in order.
Order of operations is the rule that tells you what to do first in a math problem. Most people learn it as PEMDAS or BODMAS: parentheses (or brackets) first, then exponents (or orders), then multiplication and division from left to right, then addition and subtraction from left to right. If you skip this rule, you get the wrong answer.
This tool works with plus, minus, times, divide, powers, square roots, nth roots, percents, and all three bracket types: ( ), [ ], and { }. It also spots implicit multiplication, so 3(2+1) works just fine. Each step is labeled, so you can see exactly which rule was used and why.
You can also pick a practice level, load an example problem, and use the "Check Your Answer" box to test your own work first. The number line at the end shows where your answer sits, which helps with negative numbers and decimals. Students can check homework with it, and teachers can put the steps on screen.
How to use our Order of Operations Calculator
Type a math problem into the box, press Calculate, and the tool shows the final answer plus every PEMDAS step in order.
Math expression: Type your problem in the big box. You can use + − × ÷ ^ for powers, √ for square roots, r for other roots, % for percent, and ( ) [ ] { } for groups. Writing 3(2+1) works too. The "Expression interpreted as" line shows how the calculator reads your problem, so you can spot mistakes early.
Math keypad: Click the keys to add numbers, operators, roots, powers, and brackets without typing. Use "Full Pad" for all keys, "Compact Pad" for fewer, and Hide Keypad to close it. ⌫ deletes one character and AC clears everything.
Practice type: Pick how hard you want the math to be, from simple two-step problems to multi-step problems with parentheses and exponents. This changes the list of sample problems below it.
Try an example: Click any sample problem to drop it straight into the input box. Click "Show More Examples" to see the rest.
Calculate button: Press it (or hit Enter) to solve. You get the final answer, a step-by-step PEMDAS solution with each operation highlighted, and a number line that plots the result. Press Reset to start over with the default problem.
Your answer (Check Your Answer): Type the answer you got on your own, then click Check. Whole numbers, decimals, negatives, fractions like 3/4, and percents like 25% all work. The tool tells you if you are right or gives you the correct answer.
What Is the Order of Operations?
The order of operations is a set of rules that tells you which part of a math problem to solve first. Without these rules, one expression could give many different answers. With them, everyone who solves 3 + 4 × 2 gets the same answer: 11, not 14.
PEMDAS and BODMAS
Most students learn the rules with a short word. In the United States it is PEMDAS. In many other countries it is BODMAS or BIDMAS. They all mean the same thing.
- P / B (Parentheses or Brackets): solve anything inside ( ), [ ], or { } first. Start with the innermost group.
- E / O / I (Exponents, Orders, or Indices): powers and roots come next, like 2³ or √16.
- MD (Multiplication and Division): do these together, moving from left to right.
- AS (Addition and Subtraction): do these last, also from left to right.
Left to Right Matters
Multiplication does not beat division, and addition does not beat subtraction. They are equal partners. When you see both, work from left to right. For example, 12 ÷ 3 × 2 equals 8, because you divide first (it comes first), then multiply.
A Worked Example
Solve (3 + 4) × 2² − 6 ÷ 3:
- Parentheses: 3 + 4 = 7, so the problem is 7 × 2² − 6 ÷ 3
- Exponent: 2² = 4, so it becomes 7 × 4 − 6 ÷ 3
- Multiply and divide, left to right: 7 × 4 = 28 and 6 ÷ 3 = 2, giving 28 − 2
- Subtract: 28 − 2 = 26
Common Mistakes to Avoid
- Adding too soon. In 2 + 3 × 5, you must multiply first. The answer is 17, not 25.
- Doing all multiplication before all division. Work left to right instead.
- Forgetting hidden multiplication. 3(2 + 1) means 3 × (2 + 1).
- Missing a negative sign. −3² means −(3 × 3) = −9, while (−3)² = 9.
- Skipping the inner group. In [4 + {3 − 1} × 5], solve {3 − 1} before anything else.
Why It Is Useful
Order of operations shows up far past homework. It runs inside spreadsheets, computer code, calculators, science formulas, and money math like interest and discounts. Learning the steps now makes algebra much easier later, because equations follow the exact same rules.