A percentage calculator handles three everyday questions: finding a percentage of a number, working out what percent one number is of another, and measuring how much a value has changed. Each mode uses the same idea, a percentage is a fraction out of 100, but the formula runs in a different direction depending on what you already know.
Percentage Change vs Percentage Points
Percent of a number
(Percent ÷ 100) × Number. Example: 20% of 150 = (20 ÷ 100) × 150 = 30
What percent one number is of another
(Part ÷ Whole) × 100. Example: 30 is what percent of 150 = (30 ÷ 150) × 100 = 20%
Percentage change
((New − Old) ÷ Old) × 100. Example: a price moving from 80 to 100 is ((100 − 80) ÷ 80) × 100 = +25%
A rate moving from 40% to 45% is a rise of 5 percentage points, but as a percentage change it is ((45 − 40) ÷ 40) × 100 = 12.5%. Percentage points and percent change describe the same move differently, so keep them separate when comparing rates.
Common Mistakes with Percentages
- xMixing up percentage points and percent. Going from a 40% rate to a 45% rate is a 5 percentage point rise, not a 5% rise. The percentage change (12.5%) is a different, larger number.
- xApplying a percentage to the wrong base (reverse percentage confusion). If a discounted price of 80 already reflects a 20% discount, the original price is not 80 plus 20% of 80 (96). Divide instead: 80 ÷ (1 − 0.20) = 100. Reversing a percentage means dividing by the adjusted factor, not adding the percentage back.