ToolWrenType 2 + 3 × 4 into a cheap calculator and you might get 20. Type it into a good one and you get 14. The difference is the order of operations — the universal rulebook for which parts of a calculation happen first. Here it is, made simple.
BODMAS and PEMDAS are the same thing
Two acronyms, one rule. BODMAS (used in the UK) stands for Brackets, Orders, Division/Multiplication, Addition/Subtraction. PEMDAS (used in the US) stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. "Orders" and "Exponents" both mean powers and roots, and "Brackets" and "Parentheses" are the same. So the priority order is: brackets → powers → multiply/divide → add/subtract.
Why 2 + 3 × 4 = 14
Multiplication outranks addition, so you do 3 × 4 = 12 first, then 2 + 12 = 14. A calculator that just works left to right does 2 + 3 = 5 then 5 × 4 = 20 — which is wrong. Our online calculator parses the whole expression and applies the correct precedence, so it gives 14.
Multiply and divide rank equally (so do add and subtract)
A common misconception is that multiplication always comes before division, or addition before subtraction. It does not — within each pair they have equal priority and you work left to right. So 8 ÷ 2 × 4 is (8 ÷ 2) × 4 = 16, not 8 ÷ (2 × 4) = 1. The same applies to 10 − 3 + 2 = 9.
Use brackets to be unambiguous
When in doubt, add parentheses — they force the order and make your intent clear. (2 + 3) × 4 = 20, while 2 + (3 × 4) = 14. This matters in spreadsheets and code too, where a missing bracket can silently change a result. You can group freely in the calculator, and its scientific mode adds powers, roots and functions that slot into the same precedence rules.
Powers and a note for coders
Exponents come right after brackets, so 2 × 3² = 2 × 9 = 18. One subtlety: powers are right-associative, meaning 2^2^3 is 2^(2^3) = 256, not (2^2)^3. Programmers should also note that many languages give unary minus and exponent surprising precedence, so parentheses are your friend. For related number work, see the percentage calculator and the number base converter.