What is a percentage?
"Per cent" means "out of one hundred". So 25% means 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25. Percentages make it easy to compare things of different sizes – for example, scoring 45 out of 60 and 72 out of 100 is easier to compare when you know they are 75% and 72%.
How to calculate percentages (with examples)
1. Finding X% of a number
Divide the percentage by 100 and multiply by the number. Example: 20% of 500 = (20 ÷ 100) × 500 = 100. This is useful for discounts, tips, GST and commissions.
Quick mental trick: 10% of any number is that number divided by 10. So 10% of 500 is 50, and 20% is double that: 100.
2. Finding what percent one number is of another
Divide the part by the whole and multiply by 100. Example: 45 is what % of 60? (45 ÷ 60) × 100 = 75%.
3. Percentage increase or decrease
Subtract the old value from the new value, divide by the old value and multiply by 100. Example: a price goes from ₹800 to ₹1,000. (1000 − 800) ÷ 800 × 100 = 25% increase. If the answer is negative, it is a decrease.
Note that a 25% increase followed by a 25% decrease does not bring you back to the start: ₹800 → ₹1,000 → ₹750. The percentage is always based on the starting value of each step.
4. Marks percentage
Add up the marks you got in all subjects, divide by the total maximum marks and multiply by 100. Example: 432 out of 500 = (432 ÷ 500) × 100 = 86.4%.
Some boards and universities convert CGPA to percentage with their own formula (for example, CBSE has used CGPA × 9.5). Always use the method given by your board or college.
Everyday uses of percentages
- Shopping: working out the final price after a 30% off sale.
- Money: understanding interest rates, GST (such as 5% or 18% – see our GST calculator) and salary hikes.
- Studies: exam results, attendance percentage and cut-off marks.
- Health: battery level, body fat percentage and nutrition labels.
Frequently asked questions
How do I calculate a percentage quickly?
Divide the part by the whole and multiply by 100. For example, 30 out of 40 is 30 ÷ 40 = 0.75, and 0.75 × 100 = 75%.
How do I add GST to a price?
Multiply the price by (1 + GST rate ÷ 100). For 18% GST on ₹1,000: 1,000 × 1.18 = ₹1,180.
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). If an item costs ₹700 after 30% off, the original price was 700 ÷ 0.7 = ₹1,000.
What is the difference between percent and percentage points?
If an interest rate rises from 8% to 10%, it has gone up by 2 percentage points, but by 25 percent (because 2 is 25% of 8).