How to Calculate Percentages: 5 Methods With Examples
Percent of a number, percent change, reverse percentages and the common traps, explained step by step with everyday examples.
Percentages appear everywhere: discounts, tips, tax, interest rates, test scores, statistics in the news. Almost every percentage problem falls into one of five patterns. Learn these and you can handle nearly any of them, with or without a calculator.
1. Find a percentage of a number
Convert the percentage to a decimal by dividing by 100, then multiply.
25% of 80 = 0.25 × 80 = 20
Mental shortcut: 10% means moving the decimal one place left. 10% of 80 is 8, so 5% is 4, 20% is 16 and 25% is 20.
2. What percentage is one number of another?
Divide the part by the whole and multiply by 100.
18 out of 24 = 18 ÷ 24 × 100 = 75%
This is how test scores, survey results and market shares are calculated.
3. Percentage change
Subtract the old value from the new one, divide by the old value and multiply by 100.
From $50 to $65: (65 − 50) ÷ 50 × 100 = +30%
A negative result is a decrease. From $65 back to $50 is (50 − 65) ÷ 65 = −23.1%. Notice the asymmetry: a 30% rise followed by a 23.1% fall gets you back to the start. This catches many people out with investments: a 50% loss needs a 100% gain to recover.
4. Increase or decrease by a percentage
Multiply by (1 + rate) to increase or (1 − rate) to decrease.
$80 + 15% = 80 × 1.15 = $92 $80 − 15% = 80 × 0.85 = $68
This one-step method is faster and less error-prone than calculating the percentage and then adding or subtracting.
5. Reverse percentages: find the original
If you know the value after a percentage change, divide by the multiplier to get back to the original. Do not subtract the percentage from the final number.
Price after 20% discount is $64 → original = 64 ÷ 0.80 = $80
Price including 8% tax is $54 → before tax = 54 ÷ 1.08 = $50
Subtracting 20% of $64 would give $51.20, which is wrong, because the 20% was taken from $80, not from $64.
Common traps
- Stacked discounts: 20% off then 10% off is 28% off in total, not 30%: 0.8 × 0.9 = 0.72.
- Percent vs percentage points: an interest rate rising from 2% to 3% is a 1 percentage point rise but a 50% increase.
- Base matters: "prices rose 10%" means nothing without knowing compared to when.
- Percentages of percentages: 40% of voters, of whom 25% said yes, is 10% of all voters.
Practice with real tools
The percentage calculator handles all five problem types and shows the formula used. For shopping, the discount calculator handles stacked discounts and tax, and the sales tax calculator handles reverse tax calculations.