How to calculate percentage: formulas and examples
Almost every percentage question is one of six types. Here is the formula for each, with a worked example.
Percent means "per hundred". Almost every percentage question is one of six types. Here is the formula for each, with a worked example you can check on a phone calculator.
1. X% of a number
X% of Y = X ÷ 100 × Y
15% of Rs 2,500 = 15 ÷ 100 × 2,500 = Rs 375. Shortcut: 10% is the number with the decimal moved one place left, so 10% of 2,500 is 250, and 5% is half that, 125. Add them for 15%.
2. What percent is X of Y?
Percentage = X ÷ Y × 100
You scored 42 out of 60: 42 ÷ 60 × 100 = 70%. This is the formula behind exam marks. See our Matric and Inter percentage guide for board results.
3. Percentage increase or decrease
Percentage change = (new − old) ÷ old × 100
Rent goes from Rs 40,000 to Rs 46,000: (46,000 − 40,000) ÷ 40,000 × 100 = 15% increase. A price falling from Rs 1,800 to Rs 1,350: (1,350 − 1,800) ÷ 1,800 × 100 = −25%, a 25% decrease. Always divide by the old value.
4. Add or remove a percentage
After increase = value × (1 + X ÷ 100) After discount = value × (1 − X ÷ 100)
A salary of Rs 120,000 with a 12% raise: 120,000 × 1.12 = Rs 134,400. A Rs 8,000 item at 30% off: 8,000 × 0.70 = Rs 5,600.
5. Reverse percentage (finding the original)
Original = final value ÷ (1 ± X ÷ 100)
You paid Rs 5,600 after a 30% discount. The original price was 5,600 ÷ 0.70 = Rs 8,000. A common mistake is to add 30% of 5,600 back (giving Rs 7,280), which is wrong.
The same works for sales tax. A price of Rs 11,800 including 18% tax: 11,800 ÷ 1.18 = Rs 10,000 before tax, so the tax is Rs 1,800.
6. Successive percentages
Percentages applied one after another multiply, they do not add. A 20% discount followed by an extra 10% off is not 30% off:
Rs 10,000 × 0.80 × 0.90 = Rs 7,200, a total discount of 28%.
Likewise, a 50% fall followed by a 50% rise leaves you at 75% of where you started, not back at 100%.
Percent vs percentage points
If an interest rate rises from 10% to 12%, it has risen by 2 percentage points, but by 20 percent (2 ÷ 10 × 100). News reports and bank offers mix these up, so check which one is meant.
Quick reference
| Question | Formula | Example |
|---|---|---|
| X% of Y | X ÷ 100 × Y | 20% of 450 = 90 |
| X is what % of Y | X ÷ Y × 100 | 90 of 450 = 20% |
| % change | (new − old) ÷ old × 100 | 450 → 540 = +20% |
| Add X% | Y × (1 + X/100) | 450 + 20% = 540 |
| Remove X% | Y × (1 − X/100) | 450 − 20% = 360 |
| Original before X% added | final ÷ (1 + X/100) | 540 ÷ 1.2 = 450 |
Do any of these instantly with the percentage calculator.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 2,500 is 0.15 × 2,500 = 375.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100.
How do I find the original price before a discount?
Divide the price you paid by (1 − discount ÷ 100). After 30% off, divide by 0.70.
Are two discounts of 20% and 10% the same as 30%?
No. They multiply: 0.80 × 0.90 = 0.72, so the total discount is 28%.
What is the difference between percent and percentage points?
Percentage points are the simple difference between two percentages (10% to 12% is 2 points). Percent change is that difference relative to the starting value (20%).