How do I find a percentage of a percentage?
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Short answer
Convert both percentages to decimals and multiply them. 20% of 50% is 0.20 × 0.50 = 0.10, or 10%. To apply it to a number, multiply that too: 20% of 30% of 200 is 0.20 × 0.30 × 200 = 12. Percentages applied one after another multiply rather than add, which is why 20% off and then 25% off comes to 40% off, not 45%.
Step by step
Step 1: Convert to decimals
Divide each percentage by 100: 20% becomes 0.20 and 50% becomes 0.50.
Step 2: Multiply
0.20 × 0.50 = 0.10.
Step 3: Convert back
Multiply by 100: 0.10 is 10%.
Why don't stacked discounts add up?
The second discount applies to the price that's already reduced. After 20% off you pay 80% of the price, and after another 25% off you pay 75% of that: 0.80 × 0.75 = 0.60. You pay 60%, so the total discount is 40%.
To check each step on a real price, use this percentage calculator as a percent of percent calculator: run it on the first result, then on the second.
How do repeated increases and decreases work?
- Up 10%, then up 20%: 1.10 × 1.20 = 1.32, a 32% rise rather than 30%.
- Up 20%, then down 20%: 1.20 × 0.80 = 0.96, a 4% fall rather than no change.
- Down 50%, then up 50%: 0.50 × 1.50 = 0.75, still 25% below where you started.
What is the difference between percent and percentage points?
If a rate moves from 20% to 25%, it rose by 5 percentage points, which is a 25% increase in the rate itself (5 ÷ 20 = 0.25). News reports mix these up often, and the two figures can look very different.
Where does this come up in everyday life?
Survey results are a good example. If 30% of people surveyed own a car and 20% of those drive electric, then 0.30 × 0.20 = 0.06, or 6% of everyone surveyed. The same works for coupons, sales tax on a discounted price, and test sections worth a share of a final grade.