How to calculate percentages: discounts, increases and change
A percentage is a fraction out of 100: 20% means 20 out of every 100, or 0.20. Nearly every everyday calculation comes from one idea: multiply the amount by the percentage written as a decimal.
The most common calculations
| Question | Math | Example |
|---|---|---|
| What is 20% of $80? | 80 × 0.20 | $16.00 |
| Price after a 20% discount | 80 × 0.80 | $64.00 |
| Price after a 20% increase | 80 × 1.20 | $96.00 |
| $64 is what percent of $80? | 64 ÷ 80 | 80% |
| Change from $80 to $96 | (96 − 80) ÷ 80 | +20% |
| Price before a 20% discount if you paid $64 | 64 ÷ 0.80 | $80.00 |
The way back is a different percentage
After a 20% discount, the item is worth 80% of the original. To get back, it must rise 1 ÷ 0.80 − 1 = 25%. The bigger the drop, the bigger the gap: a 50% loss needs a 100% gain to recover.
Successive percentages multiply
A 10% increase followed by another 10% is not 20%, but 1.10 × 1.10 − 1 = 21%. Likewise, a 10% rise and a 10% fall leave the value 1% below where it started. Rent increases, monthly inflation and investment returns all follow this rule.
Percent vs percentage points
When a rate moves from 10% to 12%, it rose 2 percentage points, but 20% in relative terms. News about interest or unemployment rates uses percentage points; price changes use percentages.