The three percentage formulas
Almost every everyday percentage question is one of three calculations. Here they are side by side:
percent of: result = ( P ÷ 100 ) × number
X is what % of Y: percent = ( X ÷ Y ) × 100
percent change: change = ( ( new − old ) ÷ old ) × 100
The trick to all percentages is remembering that “percent” literally means “per hundred,” so a percent is just a fraction with 100 on the bottom. 25% is 25/100 = 0.25.
Worked examples
20% of 150? (20 ÷ 100) × 150 = 0.20 × 150 = 30.
30 is what % of 150? (30 ÷ 150) × 100 = 20%.
From 80 to 100? ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase.
From 100 to 80? ((80 − 100) ÷ 100) × 100 = −20% (a decrease).
Percentage points vs percent change
These two are constantly confused. A percentage point is the plain difference between two percentages; a percent change is relative to the starting value. If an interest rate rises from 10% to 12%, that is a jump of 2 percentage points — but a 20% relative increase (because 2 is 20% of 10). News headlines often mix these up, which can make a change sound bigger or smaller than it is.
Quick check: when comparing two percentages, ask whether you want the gap between them (points) or how much one grew relative to the other (percent change). They are rarely the same number.