How to calculate percentages
A percentage is just a fraction out of 100. The three boxes above cover the questions people ask most, each with its own simple formula.
The three formulas
X% of Y = Y × X ÷ 100 · X is what % of Y = X ÷ Y × 100 · Change = (New − Old) ÷ Old × 100
Worked examples
- What is 20% of 150? → 150 × 20 ÷ 100 = 30
- 30 is what % of 150? → 30 ÷ 150 × 100 = 20%
- From 120 to 150? → (150 − 120) ÷ 120 × 100 = +25%
A percentage trap to know
A 25% increase isn't undone by a 25% decrease, because each percentage applies to a different starting number. Go up 25% from 100 and you get 125; drop 25% from 125 and you land on about 94 — not 100. The same idea explains why a 50% loss needs a 100% gain to break even.
Everyday uses
Percentages show up everywhere: discounts while shopping, tips at restaurants, interest on savings, tax, exam scores, and price changes. A quick calculator saves time and avoids mistakes.
Common mistakes to avoid
Dividing by the new value instead of the old one when finding percentage change. Adding and subtracting the same percentage and expecting to return to the start. Confusing "percent" with "percentage points" (a rate going from 5% to 6% is a 1 percentage-point rise, but a 20% increase).
Frequently asked questions
What is 20% of 150?
150 × 20 ÷ 100 = 30.
How do I find what percent one number is of another?
Divide the first by the second and multiply by 100. 30 ÷ 150 × 100 = 20%.
How do I add a percentage to a number?
Find the percentage, then add it. A 10% increase on 200: 200 + (200 × 10 ÷ 100) = 220.
Why doesn't +25% then −25% return to the start?
Each percentage applies to a different base, so you land slightly below where you began.
What's the difference between percent and percentage points?
Going from 5% to 6% is +1 percentage point, but a 20% relative increase.
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