How to Calculate Percentages
Almost every percentage question comes down to one idea: a percentage is a number out of 100. This guide builds from that to discounts, changes and reverse percentages.
1. A percentage is a fraction of 100
35% means 35 out of 100, which is 35/100 or 0.35. Converting a percentage to a decimal — dividing by 100 — is the first step in nearly every calculation. Going the other way, multiply a decimal by 100: 0.075 is 7.5%.
2. Finding a percentage of a number
part = percentage ÷ 100 × whole
What is 15% of 80?
- 15% = 0.15
- 0.15 × 80 = 12
12
Mental method: find 10% by moving the decimal point one place left (8), then build the rest — 5% is half of that (4), so 15% is 8 + 4 = 12.
3. What percent is one number of another?
percentage = part ÷ whole × 100
You scored 42 out of 60
- 42 ÷ 60 = 0.7
- 0.7 × 100 = 70
70%
The key is identifying the whole — the number you are comparing against. It usually follows the words “of” or “out of”.
4. Percentage increase and decrease
change % = (new − old) ÷ old × 100
A price goes from 50 to 65
- Change: 65 − 50 = 15
- 15 ÷ 50 = 0.3
A 30% increase.
Always divide by the original value. Going back from 65 to 50 is a fall of 15 ÷ 65 ≈ 23.1%, not 30%. Increases and decreases of the same size are not symmetric.
5. Adding or removing a percentage
To increase a value by p%, multiply by (1 + p/100). To decrease it, multiply by (1 − p/100). This one-step method is faster and makes chains of changes easy.
| Change | Multiply by |
|---|---|
| +5% | 1.05 |
| +20% | 1.2 |
| +100% (double) | 2 |
| −10% | 0.9 |
| −25% | 0.75 |
| −50% (half) | 0.5 |
6. Reverse percentages
If you know the value after a change, divide by the multiplier to get the original.
A sale price of 68 after 15% off
- After 15% off you pay 85%, so the multiplier is 0.85
- 68 ÷ 0.85 = 80
The original price was 80.
The common mistake is adding 15% of 68 back on, which gives 78.20 — wrong, because the discount was 15% of the original price, not of the sale price.
7. Percentage points
If an interest rate goes from 2% to 3%, it has risen by 1 percentage point but by 50% in relative terms. News reports sometimes blur the two; being precise avoids confusion.
Check your work
- Is the answer sensible? 15% of 80 must be less than 80 and a bit more than 10% of it.
- Did you divide by the right whole?
- For chained changes, did you multiply the factors rather than add the percentages?
Ready to try it? The percentage calculator, percentage increase and discount calculators all show their working.