Order of Operations Calculator
Enter any expression with +, −, ×, ÷, ^ and parentheses to see it solved one PEMDAS step at a time.
Use + − * / ^ and parentheses. ^ means exponent (2^3 = 8).
What Is the Order of Operations?
The order of operations is the fixed sequence every expression is evaluated in, so that the same expression always gives the same answer no matter who solves it. PEMDAS spells out that sequence: Parentheses first, then Exponents, then Multiplication and Division together (left to right), then Addition and Subtraction together (left to right).
The common mix-up is treating PEMDAS as six separate, ranked steps instead of four tiers. Multiplication doesn't outrank division, and addition doesn't outrank subtraction — within each of those two pairs, whichever operation appears first, reading left to right, happens first.
Worked example
Solve 3 + 4 × (2 − 1)² using PEMDAS.
1. Parentheses: (2 − 1) = 1, so the expression becomes 3 + 4 × 1².
2. Exponent: 1² = 1, so the expression becomes 3 + 4 × 1.
3. Multiplication: 4 × 1 = 4, so the expression becomes 3 + 4.
4. Addition: 3 + 4 = 7
Common mistake
Solving 20 − 4 × 3 as (20 − 4) × 3 = 48, working strictly left to right through every operator regardless of type. Multiplication outranks subtraction, so the 4 × 3 = 12 has to happen first: 20 − 12 = 8. Left-to-right order only applies within a single tier (multiplication/division together, or addition/subtraction together), never across tiers.
Keep going
- PEMDAS handles a single exponent as one step among several; the exponent calculator isolates just that base-and-power calculation on its own. Exponent Calculator
- A full expression often ends with add/subtract/multiply/divide steps on fractions; the fraction calculator carries out that arithmetic once PEMDAS has trimmed the expression down. Fraction Calculator
Frequently Asked Questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). It's the order every standard calculator and every math class uses to make sure an expression like 3 + 4 × 2 has exactly one correct answer.
Do you always multiply before you divide?
No — multiplication and division are the same priority tier and are done left to right in the order they appear, not multiplication first. 8 / 2 * 2 = 8, not 2: it's (8 / 2) * 2, because division comes first reading left to right. The same rule applies to addition and subtraction.
Why does 6 / 2(1 + 2) cause arguments online?
Because it's genuinely ambiguous notation, not a PEMDAS trick. Strict left-to-right PEMDAS reads it as (6 / 2) × 3 = 9. But some people treat "2(1+2)" as implicit multiplication with higher priority than the division, giving 6 / (2×3) = 1. This calculator follows strict left-to-right PEMDAS, so enter 6 / (2*(1+2)) or 6 / 2 * (1+2) depending on which meaning you actually intend — the parentheses remove the ambiguity either way.
How are repeated exponents evaluated, like 2^3^2?
This calculator evaluates repeated exponents left to right (2^3^2 → 8^2 = 64), the convention most basic and scientific calculators use. Some higher-level math systems instead evaluate exponents right to left (2^(3^2) = 512). If your course specifies one convention, add parentheses to make it explicit rather than relying on either default.
Does a negative sign count as subtraction or part of the number?
Both readings give the same answer as long as you're consistent, and this calculator treats a minus sign at the very start of the expression, or right after another operator or an open parenthesis, as part of the number that follows (so -3 + 4 = 1, and 5 * -2 = -10).
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