Order of Operations Calculator
Order of operations calculator — evaluate expressions with brackets, powers, × ÷ and + − in the right order. Free with steps and pyramid visual.
Same digits, different order, different answer. The pyramid ranks every operation — evaluate top-down and left-to-right within each row.
- Grade level
- 5–9
- Curriculum band
- Difficulty
- Intermediate
- For this topic
- Time to master
- 2 weeks
- With daily practice
- Tools on page
- 10 on page
- Calculator + practice
Calculator
Expression — evaluate in order
Allowed: digits, + − * / ^ ( ) decimals and spaces. ^ means power.
Evaluation Summary
Breakdown
| Property | Value |
|---|---|
| Expression | 2+3*4 |
| Power form (^ → **) | 2+3*4 |
| Value | 14 |
| Symbols check | allowed symbols only |
Results
Value
14
Correct precedence applied — brackets, then orders, then × ÷, then + −
2+3*4
As typed (^ means power)
2+3*4
^ rewritten as ** for evaluation
positive
Sign of the answer
Evaluation follows standard precedence (brackets, powers, × ÷ left to right, + − left to right) on whitelisted symbols only.
Statistics
Live readouts from your current expression — operands, operators and the answer move together.
Answer
14
2+3*4
Operands
3
Numbers found
Operators
2
+ − × ÷ ^ count
Sign
positive
Of the answer
Visualizations
Numbers inside the expression
Operands in order of appearance
Answer magnitude
The order pyramid — top first
Formula
Precedence ranks operations so every expression has exactly one correct value. Brackets override everything; within a level, go left to right.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| brackets | Grouping | symbols | ( ) evaluated inside-out first |
| powers | Exponents | symbols | ^ evaluated after brackets |
| × ÷ | Middle rank | symbols | Equal rank — left to right |
| + − | Lowest rank | symbols | Equal rank — left to right |
Explanation
Without precedence, 2 + 3 × 4 would be ambiguous; the ranking removes all ambiguity.
Derivation
Precedence mirrors how expressions are built: powers are repeated multiplication, products are repeated addition — so each level binds tighter than the one it is built from. Brackets exist precisely to override the default binding.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Read the whole expression and confirm every symbol is allowed.
First: innermost parentheses (compute inside-out).
Next: exponents — every ^ becomes ** and evaluates top-down.
Then: multiplication and division, strictly left to right.
Last: addition and subtraction, strictly left to right.
Sanity-check: estimate with rounded operands and confirm the magnitude.
Worked Examples
See how the calculator works with different scenarios.
Scenario
The classic precedence trap.
Inputs
Calculation
3 × 4 = 12 first, then 2 + 12
Result
14
Interpretation
Multiplication outranks addition.
Understanding Your Result
Your Result: Value: 14
Typical range: Mental two-step expressions first, then brackets, powers and multi-level chains.
What This Means
The headline value is the single correct result of your expression under standard precedence.
Why It Matters
Formulas in science, finance and code all assume this order — misreading it breaks spreadsheets and programs.
Professional Interpretation
When in doubt, add brackets — explicit grouping beats remembered rules.
Recommendations
- •Scan for brackets first
- •Handle powers before × ÷
- •Move left to right within a level
- •Bracket anything ambiguous
Learn — The Complete Guide
Arithmetic needs traffic rules: precedence decides which operation goes first when several share one expression.
The core concept
Four ranks — brackets, powers, × ÷, + − — evaluated top-down, left-to-right within ties. One rule, three famous names (PEMDAS, BODMAS, BIDMAS).
- Brackets first, inside-out
- Powers outrank × ÷
- × ÷ and + − tie-break left to right
Derivations — why the formulas work
Why × outranks +
- 13 × 4 means 4+4+4 — one grouped block
- 22 + 3×4 = 2 + (block) = 14
- 3Reading left-to-right would shred the block
- 4So products bind tighter than sums ✓
Why ties go left to right
- 1− and ÷ are not associative
- 2(10−2)+3 = 11 but 10−(2+3) = 5
- 3A fixed direction keeps notation unambiguous
- 4Convention chose left-to-right ✓
Where you meet this in real life
Learn this first — prerequisites in order
- 1Add, subtract, multiply, divide fluently
- 2Read powers as repeated multiplication
- 3Parse parentheses reliably
Careers that use this daily
- •Accountant — spreadsheet formulas
- •Programmer — expression evaluation
- •Engineer — formula substitution
- •Analyst — model arithmetic
Why it helps
- •Whitelist keeps evaluation safe
- •Pyramid visualises the ranks
- •Operand chart exposes structure
Best practices
- •Bracket first, always
- •Rewrite ^ chains carefully
- •Go left to right on ties
Limitations — what this tool does not do
- •Basic arithmetic operators only — no functions like sqrt
- •Results must be finite numbers
Curriculum map — where this topic lives in school
| Level | Grades | Standards | Skills |
|---|---|---|---|
| Upper Elementary | 4–5 | 5.OA | Two-step expressions · Brackets |
| Middle School | 6–8 | 6.EE | Powers · Multi-level chains |
| High School | 9+ | HSA-SSE | Nested brackets · Formula evaluation |
Timeline — how this idea grew up
1500s
Notation chaos
Expressions written in words; order argued case by case.
1600s
Symbols settle
+ − × ÷ and brackets spread — precedence conventions follow.
1800s
Textbooks codify
PEMDAS-style rules enter school curricula.
A little history
- • Precedence grew from notation, not decree.
- • Brackets were invented to override defaults.
Exam-day checklist
- • Underline × ÷ islands first.
- • Work brackets inside-out.
- • Rewrite one rank per line.
Myths vs facts
Practical Tips
- •Find brackets before anything else
- •Do powers right after brackets
- •Tie? Go left to right
- •Add brackets when unsure
- •Estimate magnitude as a check
Common Mistakes
Assumptions
This calculator makes the following assumptions to provide estimates:
Limitations
Be aware of these limitations when using this calculator:
Frequently Asked Questions
Answers to common questions about this calculator.
What is the order of operations?
Why does 2 + 3 × 4 equal 14 and not 20?
What does the ^ symbol mean?
How are ties broken, e.g. 10 − 2 + 3?
Which characters can I type?
How do I use this calculator?
Related Calculators
Explore more calculators related to this topic.
Related Guides
Deepen your understanding with these educational resources.
Glossary
Technical terms used in mortgage calculations explained in plain language.
- Precedence
- The ranking that decides evaluation order.
- Brackets
- Parentheses — always first, inside-out.
- Exponent
- A power like 4^2 = 16.
- Left-to-right
- Tie-break within one rank.
- PEMDAS/BODMAS
- Regional names for the same rule.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
Diagrams & Illustrations
Visual intuition for every core idea. Select a card to enlarge it.
Did You Know?
Short intuition builders — great for class warm-ups.
PEMDAS vs BODMAS is just dialect
Americans say Parentheses/Exponents, Britons say Brackets/Orders — the mathematics is identical.
Left-to-right breaks calculators
Cheap calculators that ignore precedence answer 2+3×4 as 20 — this page refuses to make that mistake.
Brackets are the override button
Every programming language honours parentheses first, for exactly the same reason.
Orders once meant powers generally
BODMAS O covers squares, cubes and roots — anything that raises or lowers rank by levels.
Compare Side by Side
Same digits, different order, different answers — brackets and precedence decide.
| Expression | Correct value | Why |
|---|---|---|
| 2 + 3 × 4 | 14 | × before + |
| (2 + 3) × 4 | 20 | Brackets override everything |
| 2 + 3^2 | 11 | ^ before + |
| 10 − 2 × 3 | 4 | × before − |
Recent Calculations
Your last runs on this page — stored only in this browser, never uploaded.
2+3*4 = 14
Current inputs — live
Study Plan
A week-by-week path from prerequisites to mastery. Your checklist progress saves in this browser.
Prerequisites
- ▸All four operations fluently
- ▸Powers as repeated multiplication
- ▸Reading expressions left to right
Mastery progress — 0%
- I rank brackets, powers, × ÷, + −
- I break ties left to right
- I use brackets to override
- I estimate before trusting output
- 1
Week 1 · ~20 min/day
× ÷ before + −
Goals
- Spot the × ÷ islands first
- Evaluate two-step expressions
- Explain 2+3×4 = 14 aloud
Practice
Solve 10 mixed two-step expressions daily, underlining × ÷ first.
- 2
Week 2 · ~20 min/day
Brackets and powers
Goals
- Work brackets inside-out
- Evaluate small powers
- Combine all four ranks
Practice
Recompute each Try preset by hand, one rank per line.
- 3
Week 3 · ~15 min/day
Ties and traps
Goals
- Break × ÷ ties left to right
- Break + − ties left to right
- Add clarifying brackets
Practice
Invent one trap expression daily and spring it on a friend.
Exam tips
- •Underline × ÷ islands first.
- •Circle innermost brackets.
Practice Problems
0/5 solvedTry each problem first, peek at the hint only if stuck, then reveal the solution and mark it solved.
Evaluate 2 + 3 × 4.
Evaluate (2 + 3) × 4.
Evaluate 2 + 3^2.
Evaluate 12 ÷ 2 × 3.
Evaluate 10 + 2 × (5 − 3)^2.
Printable Worksheet
Generate a fresh problem set for class or homework. Print it, or copy the answer key separately.
- 1.18 × 47 =
- 2.8 ÷ 11 =
- 3.38 × 26 =
- 4.35 ÷ 4 =
- 5.21 − 16 =
- 6.2 + 26 =
- 7.14 ÷ 12 =
- 8.23 ÷ 3 =
- 9.49 ÷ 7 =
- 10.22 − 17 =
- 11.41 + 18 =
- 12.47 − 35 =
Formula Cheat Sheet
Every formula on this page in one printable table.
| Formula | Meaning | Example |
|---|---|---|
| ( ) first | Brackets override all | (2+3) × 4 = 20 |
| a^b next | Powers second | 3^2 = 9 |
| × ÷ left→right | Equal rank ties | 12 ÷ 2 × 3 = 18 |
| + − left→right | Lowest rank ties | 10 − 2 + 3 = 11 |
| 2+3×4 = 14 | Classic trap | × before + |
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Page Information
2026-09-29
3.1.0-math
Free to use for educational and professional purposes.