What is a percentage?
Per cent means “per hundred”. 25% is 25 out of every 100, or 25 ÷ 100 = 0.25. Percentages make it easy to compare amounts of different sizes — marks, discounts, interest, price rises and growth.
Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 200 = 0.15 × 200 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 45 out of 60 = 45 ÷ 60 × 100 = 75% |
| % change from X to Y | (Y − X) ÷ X × 100 | 80 → 100 = 20 ÷ 80 × 100 = 25% increase |
| Y increased by X% | Y × (1 + X ÷ 100) | 500 + 18% = 500 × 1.18 = 590 |
| Y decreased by X% | Y × (1 − X ÷ 100) | 500 − 20% = 500 × 0.8 = 400 |
How to calculate percentage of marks
Percentage = (Marks obtained ÷ Total marks) × 100
Example: 432 out of 500 → 432 ÷ 500 × 100 = 86.4%. Use the second calculator above (“X is what percent of Y”) with X = 432 and Y = 500.
Percentage increase and decrease
Percentage change is always measured against the starting value. If a price goes from ₹80 to ₹100 it rises by 25%, but if it falls from ₹100 back to ₹80 it drops by only 20% — the base is different.
Percentage points vs percent: if a loan rate goes from 8% to 10%, it rose by 2 percentage points, which is a 25% increase in the rate itself.
Quick mental tricks
- 10% — move the decimal point one place left: 10% of 450 = 45.
- 5% — half of 10%: 5% of 450 = 22.5.
- 1% — move the decimal two places: 1% of 450 = 4.5.
- X% of Y = Y% of X — 8% of 50 is the same as 50% of 8 = 4.
- Reverse a percentage — if ₹590 includes 18%, the original is 590 ÷ 1.18 = ₹500 (not 590 − 18%).
Percentage in daily life
- Marks: 432 out of 500 = 86.4%.
- Salary hike: ₹40,000 with a 12% raise = ₹44,800.
- GST: 18% of ₹2,000 = ₹360.
- Discount: 25% off ₹1,600 = ₹1,200 to pay.
- Interest: 7% of ₹1 lakh = ₹7,000 a year.
- Price change: petrol from ₹95 to ₹100 = a 5.26% increase.
Frequently asked questions
How do I calculate the percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 200 = 200 × 15 ÷ 100 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 45 out of 60 is 45 ÷ 60 × 100 = 75%.
How is percentage increase calculated?
Percentage increase = (new value − old value) ÷ old value × 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
Why is a 20% fall not undone by a 20% rise?
Because each is measured on a different base. ₹100 falling 20% is ₹80; 20% of ₹80 is only ₹16, so it rises to ₹96, not ₹100.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100: 3/8 = 0.375 × 100 = 37.5%.