PEMDAS Calculator 2026 – Order of Operations Solver
Solve any expression step by step — parentheses, exponents, multiplication/division, addition/subtraction. This independent math tool performs the calculations directly in your browser and is designed for quick answers, homework checks, practice and understanding the order of operations.
PEMDAS Order of Operations Calculator
Type any expression and see every step. Calculations run in your browser.
The 2 most common wrong answers
What Is a PEMDAS Calculator?
How to Use This PEMDAS Calculator
The two things you can do
- Evaluate an expression step by step — type a full expression such as 6 + 2 × 3 or 8 ÷ 2(2+2) and see every intermediate step.
- Check why a "viral" answer is wrong — enter a debated expression and see the correct steps side by side with the two most common wrong answers and exactly where each one breaks the rules.
How it works
- Type your expression in the box (use (), ^ or ², × or *, ÷ or /, +, −).
- Click Solve step by step.
- Read the numbered steps — each shows the operation, the numbers combined, and the running expression.
- Compare your answer with the "common wrong answers" panel if your result surprised you.
What Is PEMDAS?
What is the order of operations?
The order of operations is the universal agreement about which part of a math expression gets calculated first. Without it, 6 + 2 × 3 could mean either 12 or 20, and every math book, exam, and calculator would disagree. PEMDAS is the mnemonic most US students learn:
| Letter | Meaning | Priority |
|---|---|---|
| P | Parentheses | 1 — first |
| E | Exponents | 2 — second |
| M | Multiplication | 3 — together, left to right |
| D | Division | 3 — together, left to right |
| A | Addition | 4 — together, left to right |
| S | Subtraction | 4 — together, left to right |
The letters are not the whole story: multiplication and division are one level, and addition and subtraction are one level. Within a level you work left to right — never add before subtracting just because A comes before S.
Worked examples (all hand-verified)
Example 1 — why multiplication beats addition
Step 1 (Multiplication): 2 × 3 = 6
Step 2 (Addition): 6 + 6 = 12
Example 2 — why parentheses win
Step 1 (Parentheses): (6 + 2) = 8
Step 2 (Multiplication): 8 × 3 = 24
Example 3 — the viral one
Step 1 (Parentheses): (2 + 2) = 4, leaving 8 ÷ 2 × 4
Step 2 (Division, left to right): 8 ÷ 2 = 4
Step 3 (Multiplication): 4 × 4 = 16
Example 4 — exponent plus left-to-right
Step 1 (Exponent): 4² = 16, leaving 33 − 12 + 16
Step 2 (Subtraction, left to right): 33 − 12 = 21
Step 3 (Addition): 21 + 16 = 37
Example 5 — all four levels at once
Step 1 (Parentheses): (2 + 2) = 4 → 2 + 4 × 3²
Step 2 (Exponent): 3² = 9 → 2 + 4 × 9
Step 3 (Multiplication): 4 × 9 = 36 → 2 + 36
Step 4 (Addition): 2 + 36 = 38
PEMDAS Step by Step
The rule you can memorize:
- Parentheses and brackets first — work from the innermost pair outward.
- Exponents next — squares, cubes, powers (3² = 9).
- Multiplication and division together, left to right — not all multiplications before all divisions.
- Addition and subtraction together, left to right — in 33 − 12 + 16, do not add 12 + 16 first.
Common Mistakes
Mistake #1: "8 ÷ 2(2+2) = 1"
The 1 answer comes from treating 2(2+2) as if it were glued together: solve the parentheses (4), then do 2 × 4 = 8, then 8 ÷ 8 = 1. The error is in step two — implied multiplication has no special precedence. Once the parentheses contain just the number 4, the expression is 8 ÷ 2 × 4, an ordinary division-followed-by-multiplication. Division comes first when you read left to right: 8 ÷ 2 = 4, then 4 × 4 = 16. Standard math texts, engineering calculators, and the ISO notation conventions all evaluate it as 16.
Mistake #2: "6 + 2 × 3 = 24"
The 24 answer comes from working strictly left to right, ignoring the priority levels: add first (6 + 2 = 8), then multiply (8 × 3 = 24). Multiplication is priority 3; addition is priority 4. 2 × 3 = 6 first, then 6 + 6 = 12. The deeper reason is that multiplication is repeated addition: 6 + 2 × 3 means 6 + 6, which can only be 12.
Benefits & Limitations
Benefits
- Ends every "16 vs 1" style argument with visible, checkable steps.
- Shows why an answer is wrong, not just the right number.
- Works for homework, test prep, and anyone relearning math basics.
- Free, no sign-up, works on phones and desktops.
Limitations
- Evaluates standard arithmetic expressions; not a full scientific calculator (no trig, logarithms, or calculus).
- Implicit multiplication like 2(3) is treated as ordinary multiplication — matching standard conventions, but some old textbooks disagreed on this one case.
- Very long expressions are still easiest to check in small pieces.
Quick Definitions
| Question | Direct Answer |
|---|---|
| What does PEMDAS stand for? | PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction — the US order-of-operations mnemonic. |
| What is the order of operations? | The universal rule for which operation to do first in a math expression. |
| What are BODMAS / BIDMAS? | The same rule under a different name (Brackets, Orders/Indices, Division, Multiplication, Addition, Subtraction), used in the UK, India, Australia and others. |
| What is implied multiplication? | Multiplication shown by juxtaposition, e.g. 2(4) — same precedence as any multiplication. |
| What is the left-to-right rule? | Within one precedence level (×/÷ or +/−), evaluate in reading order. |
Frequently Asked Questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction — the US mnemonic for the order of operations.
Is 8÷2(2+2) equal to 16 or 1?
16. Parentheses give 4, then the expression is 8 ÷ 2 × 4: division and multiplication share a level and go left to right, so 8 ÷ 2 = 4, then 4 × 4 = 16. The answer 1 only comes from wrongly giving implied multiplication special priority.
Are PEMDAS and BODMAS the same?
Yes — both describe the same priority levels (parentheses/brackets, exponents/orders, multiplication/division, addition/subtraction). The letters differ by country, not the math.
Why do multiplication and division share a level?
Because division is multiplication by a reciprocal: a ÷ b is a × (1/b). Neither operation outranks the other, so they are evaluated left to right.
Why can't I add before multiplying?
Multiplication is repeated addition, so it binds tighter: 6 + 2 × 3 means 6 plus three copies of 2, which is 12. Adding first breaks that structure.
Does the calculator show each step?
Yes. Type any expression and press "Solve step by step" to see every operation — parentheses, exponents, multiplication/division, addition/subtraction — in the order it was evaluated.
PEMDAS Calculator Methodology
The calculator parses the expression and evaluates it in this fixed precedence ladder, matching the conventions taught in US curricula and implemented by standard engineering calculators:
- Tokenize the expression into numbers, operators, and parentheses.
- Recursively evaluate the innermost parentheses first.
- Evaluate exponents (right-associative: 2^3^2 = 2^9 = 512).
- Evaluate multiplication and division left to right (equal precedence).
- Evaluate addition and subtraction left to right (equal precedence).
- Round display to a sensible precision; intermediate steps are never rounded.
Mathematical References
- Maths is Fun — Order of Operations (PEMDAS explained with worked examples).
- Khan Academy — Order of Operations unit (arithmetic course).
- Purplemath — Order of Operations (worked examples and practice).
- ISO 80000-1:2009 — general principles for quantities and units (symbol/notation conventions).
Stop arguing about 16 vs 1.
Type the expression into the free PEMDAS calculator above, see every step, and share the result — the steps settle the debate every time.
Use PEMDAS Calculator