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How Order of Operations Works

This calculator evaluates every expression using the standard mathematical convention known as PEMDAS (or BODMAS outside the US): Parentheses first, then Exponents or Roots, then Multiplication and Division evaluated left to right, and finally Addition and Subtraction evaluated left to right. Operations at the same priority level are never reordered arbitrarily — they are always resolved left to right, which matters for expressions that mix division and multiplication.

Take 2 + 3 × 4. Multiplication happens before addition regardless of the order it was typed in, so the calculator computes 3 × 4 = 12 first, then adds 2, for a result of 14 — not 20, which is what a strict left-to-right reading with no precedence rules would give. Wrapping part of an expression in parentheses overrides the default order: (2 + 3) × 4 forces the addition to happen first, giving 5 × 4 = 20.

The same left-to-right rule applies within a single priority tier: 20 − 5 − 3 evaluates as (20 − 5) − 3 = 12, not 20 − (5 − 3) = 18, because subtraction chains resolve from the left. The identical logic governs chained division: 100 ÷ 5 ÷ 2 equals (100 ÷ 5) ÷ 2 = 10, not 100 ÷ (5 ÷ 2) = 40. This left-to-right rule for operators sharing the same priority is what keeps a calculator output predictable even in long chained expressions.

What You Should Know

Not every expression has one universally agreed answer. 6 ÷ 2(1 + 2) is a famous example that divides even professional mathematicians: solved strictly left to right under PEMDAS, since division and multiplication share equal priority, it comes to 6 ÷ 2 × 3 = 9. But many people read "2(1+2)" — implicit multiplication written without a × sign — as binding more tightly than an explicit division sign, which would give 6 ÷ (2×3) = 1 instead. This is not a bug or a calculator malfunction; it is genuine ambiguity in mathematical notation itself, specifically whether implicit multiplication (writing a number directly next to parentheses) should be treated as higher priority than explicit ×/÷ symbols. Different calculators and programming languages make different choices here — many scientific calculators and most programming languages such as Python and JavaScript treat all multiplication and division as equal priority evaluated left to right, while some other calculators and typesetting conventions give implicit multiplication higher priority. When an expression is ambiguous, the safest approach is always to add explicit parentheses so there is no room left for interpretation.