Percentage Formula

One relationship covers every basic percentage problem: part = percent ÷ 100 × whole.

The formula and its rearrangements

part = (P ÷ 100) × whole

P = (part ÷ whole) × 100

whole = part ÷ (P ÷ 100)

P is the percentage. Dividing by 100 turns it into a decimal (35% → 0.35) or you can think of it as a fraction over 100.

Examples

35% of 240

  1. 0.35 × 240

84

84 out of 240 as a percentage

  1. 84 ÷ 240 = 0.35
  2. 0.35 × 100

35%

84 is 35% of what?

  1. 84 ÷ 0.35

240

Common mistakes

  • Dividing by the wrong whole: “what percent of the class are girls” uses the whole class, not the number of boys.
  • Adding percentages of different wholes: 10% of A plus 10% of B is not 20% of anything in particular.
  • Confusing percent with percentage points when comparing two rates.

Try it

Use the percentage calculator to solve all three forms with the working shown.