Math · 1 min read
How to calculate percentages
Most percentage questions come down to three formulas. Learn which one fits your question, then check the answer with the calculator.
Last updated November 3, 2026
What a percentage means
A percentage is a fraction of 100. "30 percent" means 30 out of every 100, or 0.30 as a decimal. Converting between the two is the first step in every percentage problem: divide by 100 to get the decimal, multiply by 100 to get back to a percentage.
Percent of a number
To find a percentage of a number, multiply the number by the percentage as a decimal.
result = number × (percent ÷ 100)
20% of 150
Result: 150 × 0.20 = 30
What percent is one number of another
To express a part as a percentage of a whole, divide the part by the whole and multiply by 100.
percent = (part ÷ whole) × 100
Scoring 18 out of 60
Result: (18 ÷ 60) × 100 = 30%
Percent change
Percent change compares a new value with the old one, and the old value is always the base.
change = ((new − old) ÷ old) × 100
A price that rises and falls between 80 and 100
| Move | Old | New | Calculation | Change |
|---|---|---|---|---|
| Rise | 80 | 100 | (20 ÷ 80) × 100 | +25% |
| Fall | 100 | 80 | (20 ÷ 100) × 100 | −20% |
The two results differ because the base differs. This is why a 25% rise needs only a 20% fall to return to the start.
Common mistakes
Common mistake
- Dividing by the new value instead of the old value when finding percent change.
- Adding percentages that apply to different bases, such as a 10% discount followed by another 10% discount (the total is 19%, not 20%).
- Forgetting to convert the percentage to a decimal before multiplying.