Order of Operations Calculator
Type an arithmetic expression and get the answer the way a mathematician (and a grader) would evaluate it: parentheses first, then exponents, then multiplication and division, then addition and subtraction.
Calculator
- Parentheses, exponents, ×, ÷, +, −
- Left-to-right associativity
- Right-associative exponents
- No eval — a safe parser
Result & calculation receipt
- Method
- PEMDAS/BODMAS — parentheses, exponents, then multiplication/division and addition/subtraction left to right
- Formula
Evaluate innermost parentheses → exponents → ×,÷ (left→right) → +,− (left→right)- Substitution
- 2 + 3 × 4 − 1 = 13
- Steps
- 3 × 4 = 12 (Multiplication/Division, left to right)
- 2 + 12 = 14 (Addition/Subtraction, left to right)
- 14 - 1 = 13 (Addition/Subtraction, left to right)
- Verification
- Re-evaluated with strict operator precedence; the reduction order above is the only valid PEMDAS order.
- Exact result
- 13
- Decimal result
- 13
- Engine
- math-solvers v1.4.0
How this calculator works
The calculator tokenizes your expression and evaluates it with a small recursive-descent parser — never with JavaScript eval — so the order of operations is enforced by the grammar itself. Multiplication and division bind more tightly than addition and subtraction, exponents bind tighter still and are right-associative, and a leading minus is treated as unary negation. Each reduction is recorded as a step with the rule that justified it.
Worked example
For 2 + 3 × 4 the calculator multiplies before adding: 3 × 4 = 12, then 2 + 12 = 14 — not 20. Add parentheses and (2 + 3) × 4 becomes 5 × 4 = 20, because the parentheses are evaluated first. The step panel shows both the operation and the PEMDAS rule that fired, so the answer is auditable.
Key insight
PEMDAS is a convention, not a law of nature, but it is universal: without it "2 + 3 × 4" would be ambiguous. The two rules people forget are that ×/÷ share a level (left to right) and that a bare minus sign in front of a power applies after the exponent, so −2² is −4 while (−2)² is 4.
Frequently asked questions
What does PEMDAS actually stand for?
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division share one level and are done left to right, as do addition and subtraction. BODMAS and GEMS are the same rules under different names.
Why is 2 + 3 × 4 equal to 14 and not 20?
Multiplication is done before addition, so 3 × 4 = 12 is computed first and then 2 is added, giving 14. You would only get 20 if you added first, which the order of operations does not allow without parentheses.
Is −2² equal to −4 or 4?
With standard precedence −2² is −4, because the exponent applies to 2 first and the minus sign negates the result. Only (−2)² with explicit parentheses gives 4. This calculator follows the standard convention and shows the grouping.
How are multiple exponents handled?
Exponentiation is right-associative, so 2^3^2 means 2^(3^2) = 2^9 = 512, not (2^3)^2 = 64. The steps make the grouping explicit.
Does this use eval to compute the answer?
No. The expression is parsed by a dedicated grammar and evaluated numerically. Nothing you type is executed as code, and division by zero is reported as an error rather than returning Infinity.
Methodology & verification
Expressions are tokenized and evaluated by a recursive-descent parser that encodes PEMDAS in its grammar: parentheses recurse, exponentiation is right-associative and binds tighter than unary minus, multiplication/division bind tighter than addition/subtraction, and equal-precedence operators are applied left to right. No eval or Function is used. Division by zero, unbalanced parentheses and malformed numbers return structured errors. Each reduction is recorded with the rule that produced it, and the final value is a reproducible calculation receipt.
Engine: math-solvers v1.4.0 · Last reviewed: · Every result is computed client-side and never sent to a server. See the verification methodology and the scientific calculator validation.