Percentage formulas
"Per cent" means "per hundred", so 15% is 15/100 = 0.15. Every percentage problem is one of these:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 2,400 = 2,400 × 15 ÷ 100 = 360 |
| X is what % of Y? | X ÷ Y × 100 | 45 of 60 = 45 ÷ 60 × 100 = 75% |
| % change from X to Y | (Y − X) ÷ X × 100 | 80 → 100 = 20 ÷ 80 × 100 = +25% |
| Y after a change of X% | Y × (1 + X ÷ 100) | 1,000 − 20% = 1,000 × 0.8 = 800 |
Percentage change vs percentage points
If an interest rate goes from 4% to 5%, it rose by 1 percentage point, but by 25 per cent (1 ÷ 4). News reports mix these up all the time. Use "points" for the difference between two percentages, and "per cent" for the relative change.
Why +50% then −50% doesn't get you back
A price of 100 that rises 50% becomes 150. A 50% fall from 150 is 75, not 100, because the second percentage is taken of a bigger number. To undo a rise of X%, you need a fall of X ÷ (100 + X) × 100%: undoing +50% takes −33.3%.
Everyday uses
- Discounts: 30% off ₹2,499 → use "add or subtract" with −30 → ₹1,749.30.
- Exam marks: 412 out of 500 → "X is what percent of Y" → 82.4%.
- Salary hike: from 60,000 to 66,000 → "percentage change" → +10%.
- Tax: for GST or VAT, use the GST calculator or VAT calculator, which also remove tax from a tax-inclusive price.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20% of 350 is 350 × 20 ÷ 100 = 70.
How do I work out a percentage increase?
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% increase.
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). If something costs 720 after 20% off, the original price was 720 ÷ 0.8 = 900.
What is the difference between percentage and percentile?
A percentage is a share out of 100. A percentile is a rank: scoring in the 90th percentile means you did better than 90% of people, whatever your actual score was.
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