Key takeaways
- X% of Y = Y × X ÷ 100.
- A as a percentage of B = A ÷ B × 100.
- Percentage change = (new − old) ÷ old × 100.
- Percentages of different bases do not simply add or cancel: up 50% then down 50% leaves you 25% lower.
The three formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 240 = 36 |
| A is what percent of B? | A ÷ B × 100 | 45 of 60 = 75% |
| Percentage change from old to new | (new − old) ÷ old × 100 | 80 → 100 = +25% |
The percentage calculator answers all three as you type.
Six everyday examples
1. A discount
A jacket costs 320 with 25% off. The discount is 320 × 25 ÷ 100 = 80, so you pay 240. Shortcut: multiply by 0.75. For stacked offers, use the discount calculator.
2. A restaurant tip
For 10% move the decimal point one place left (bill 86 → 8.60). For 15%, add half of that again (8.60 + 4.30 = 12.90). For 20%, double the 10%.
3. Exam marks
42 out of 56 is 42 ÷ 56 × 100 = 75%.
4. A salary rise
From 9,000 to 9,450 a month: (9,450 − 9,000) ÷ 9,000 × 100 = a 5% rise.
5. VAT
Adding 5% VAT to 1,200 gives 1,200 × 1.05 = 1,260. Removing it from a VAT-inclusive price means dividing by 1.05, not subtracting 5%. The VAT calculator does both.
6. Finding the original price
A phone costs 2,040 after a 15% discount. The original price is 2,040 ÷ 0.85 = 2,400. Dividing the new value by (1 − the percentage) reverses a decrease; dividing by (1 + the percentage) reverses an increase.
Mistakes to avoid
- Up and down are not symmetrical. A price rising 50% then falling 50% ends at 75% of where it started (100 → 150 → 75).
- Percent vs percentage points. An interest rate going from 4% to 5% rises by one percentage point, which is a 25% increase in the rate.
- Adding percentages of different totals. 20% off followed by 10% off is 28% off in total, not 30%.
Fact-checked against the sources above. We test every tool we mention. Editorial policy.
