Order of operations: why 2 + 3 × 4 is 14

Last reviewed on 30 April 2026.

Type 2 + 3 × 4 into any modern calculator and the answer is 14. Compute it left to right by hand and you might get 20. The disagreement is not the calculator being clever — it is following a rule you may not have used since school. This page covers what that rule says, why it exists, the version everyone learns first, and the spots where it quietly bites.

The short version

Mathematicians agree on a fixed priority for arithmetic operations:

1. Anything inside parentheses, evaluated first from the inside out.
2. Exponents and roots.
3. Multiplication and division, evaluated left to right as equals.
4. Addition and subtraction, evaluated left to right as equals.

So 2 + 3 × 4 resolves the multiplication first (12), then the addition: 2 + 12 = 14. The calculator on this site applies these rules in the same order whether you type a short expression or a long one.

PEMDAS, BODMAS, BIDMAS — same idea, different names

School systems use different acronyms for the same rule. PEMDAS — Parentheses, Exponents, Multiplication, Division, Addition, Subtraction — is common in the United States. BODMAS uses Brackets, Orders, Division, Multiplication, Addition, Subtraction; BIDMAS swaps "Orders" for "Indices". The order of M and D, or A and S, in the acronym is misleading: multiplication and division share the same priority, and so do addition and subtraction. They are evaluated left to right when they appear together, not in the order of the letters.

That distinction is why 20 ÷ 5 × 2 equals 8, not 2. Read left to right: 20 ÷ 5 is 4, then 4 × 2 is 8. Treating the M as strictly before the D would give 20 ÷ 10 = 2, which is wrong by the standard convention.

Why we have a rule at all

Without an agreed priority, every formula would need parentheses everywhere. Writing the area of a circle as π × r × r requires no extra grouping because exponentiation already binds tighter than multiplication; πr² reads cleanly. Polynomials, physics formulas, and most algebra leans on the same convention to stay readable. The order of operations is best understood as a typographical convention that lets us drop parentheses without losing meaning, not a deep mathematical truth.

A worked example, step by step

Take a longer expression and resolve it the way the calculator does.

3 + 4 × 2 ^ 3 − (10 − 6) ÷ 2

1. Parentheses first: (10 − 6) becomes 4. Expression: 3 + 4 × 2 ^ 3 − 4 ÷ 2.
2. Exponent next: 2 ^ 3 is 8. Expression: 3 + 4 × 8 − 4 ÷ 2.
3. Multiplication and division, left to right: 4 × 8 is 32; 4 ÷ 2 is 2. Expression: 3 + 32 − 2.
4. Addition and subtraction, left to right: 3 + 32 is 35; 35 − 2 is 33.

Final answer: 33. Type the original line into the calculator and you will see the same number — that is the rule in action.

The traps people fall into

Implicit multiplication

Pen-and-paper notation lets you write 2(3 + 1) for "two times the quantity three plus one". Most calculators, including this one, require you to type the times sign: 2 × (3 + 1). Some interfaces also treat 2(3+1) and 2×(3+1) differently when they sit next to a division — a source of long-running internet arguments. The safe rule is to always insert the operator and use parentheses when the meaning could be debated.

Negative numbers and exponents

Is −3² equal to 9 or −9? By the standard convention, exponents bind tighter than the unary minus, so −3² is −(3²) = −9. To raise the negative number to a power, use parentheses: (−3)² = 9. Most calculators follow this convention; some scientific calculators with a dedicated +/− key behave differently when you press it. If a result surprises you, group the negative.

Division bars in handwritten formulas

A horizontal fraction bar groups everything above and below it as if there were parentheses. When you transcribe one to a calculator, those parentheses must be typed. The expression (a + b) ÷ (c + d) is not the same as a + b ÷ c + d. A common error is to translate a fraction directly without grouping the numerator or denominator.

Stacked exponents

Power towers associate to the right: 2 ^ 3 ^ 2 means 2 ^ (3 ^ 2) = 2⁹ = 512, not (2 ^ 3) ^ 2 = 64. The convention exists because the right-associative reading is the more useful one in algebra and combinatorics, but it does catch people. Use parentheses if you actually want the left-associated version.

The viral arithmetic problem

Posts of the form 8 ÷ 2(2 + 2) generate arguments because they mix implicit multiplication with division, and not every calculator resolves them the same way. The convention this site follows treats the implicit times as ordinary multiplication, so 8 ÷ 2(2 + 2) typed as 8 / 2 * (2 + 2) evaluates left to right and returns 16. If you mean the version where 2(2+2) sticks together as a denominator, write 8 / (2 * (2 + 2)) and you will see 1.

Decision checklist before pressing equals

• Are all numerators and denominators wrapped in parentheses?
• Have I typed an explicit operator between numbers and parentheses?
• If a negative is being raised to a power, is the negative grouped?
• Does the live preview match my mental estimate before I press equals?

Why the calculator might still seem wrong

If the answer here disagrees with another calculator, the cause is almost always one of three things: a different mode (degrees vs radians for trig), a different convention for the percent key, or different handling of stacked exponents. The first two are covered in degrees vs radians and using the % key; the third is best handled by adding parentheses.