Percentage formulas
- X% of Y = X × Y ÷ 100 — e.g. 18% of 2,500 = 450.
- X is what % of Y = X ÷ Y × 100 — e.g. 450 of 1,800 = 25%.
- % change = (New − Old) ÷ Old × 100 — e.g. 1,200 → 1,500 = +25%.
- Increase by X% = Y × (1 + X/100).
- Decrease by X% = Y × (1 − X/100).
- Reverse percentage (find the whole) = Part × 100 ÷ %.
Everyday examples
- Shopping discounts: 30% off ₹2,000 → decrease 2,000 by 30% = ₹1,400.
- Salary hike: ₹40,000 → ₹46,000 is a 15% increase.
- Exam marks: 432 out of 500 = 86.4%.
- Business growth: leads from 80 to 120 = 50% growth.
Percentage vs percentage points
If a conversion rate rises from 2% to 3%, it increased by 1 percentage point but by 50% in relative terms. Marketers mix these up often — see our conversion rate calculator.
Percentage shortcuts you can do in your head
| To find | Do this | Example |
|---|---|---|
| 10% | Divide by 10 | 10% of 850 = 85 |
| 5% | Half of 10% | 5% of 850 = 42.5 |
| 1% | Divide by 100 | 1% of 850 = 8.5 |
| 25% | Divide by 4 | 25% of 800 = 200 |
| 50% | Divide by 2 | 50% of 850 = 425 |
A handy trick: X% of Y always equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
Marks and CGPA to percentage
Percentage = Marks obtained ÷ Total marks × 100
For a CGPA, CBSE’s commonly used indicative formula is CGPA × 9.5, so a CGPA of 8 is about 76%. Other boards and universities use their own conversion, so check your marksheet or institution’s rule.
Why a 50% rise and 50% fall do not cancel out
If ₹100 rises by 50%, you get ₹150. If ₹150 then falls by 50%, you get ₹75, not ₹100. That is because each percentage applies to a different starting number. The same logic applies to discounts on top of discounts: 20% off and then 10% off equals 28% off, not 30%.
Percentages in business
- GST: try our GST calculator for tax on any amount.
- Profit and discounts: see the profit margin calculator.
- Website results: use the conversion rate calculator.