How to Calculate Percentages: Marks, Discounts and Increases

A percentage is a number out of 100. The three formulas you need are: part ÷ whole × 100 to find a percentage, whole × percent ÷ 100 to find a part, and (new − old) ÷ old × 100 for a percentage change. Everything else, from exam marks to sale prices, is one of these.

1. What percentage is one number of another?

Divide the part by the whole and multiply by 100. If you scored 950 out of 1,100 in matric, your percentage is 950 ÷ 1,100 × 100 = 86.36%.

The same formula works for attendance (40 days present out of 46 = 87%) or how much of a goal you’ve finished.

2. Finding a percentage of a number

Multiply the number by the percentage and divide by 100. 15% of 8,000 is 8,000 × 15 ÷ 100 = 1,200. A quick mental trick: 10% is just moving the decimal one place (10% of 8,000 is 800), 5% is half of that, and 1% is moving it two places.

Percentages are reversible, too: 8% of 50 is the same as 50% of 8, which is 4. Swap them when one way is easier.

3. Discounts

To find a sale price, work out the discount and subtract it, or multiply directly by (100 − discount) ÷ 100. A 25% discount means you pay 75% of the price.

Two discounts don’t add up. “20% off, then an extra 10%” is 0.8 × 0.9 = 0.72 of the price, a 28% total discount, not 30%.

4. Percentage increase and decrease

Subtract the old value from the new one, divide by the old value, and multiply by 100. If a salary rises from Rs 80,000 to Rs 92,000, the increase is 12,000 ÷ 80,000 × 100 = 15%.

For a decrease the answer comes out negative. A bill falling from Rs 6,500 to Rs 5,200 is a change of (5,200 − 6,500) ÷ 6,500 × 100 = -20%, a 20% drop.

To increase a number by a percentage, multiply by (1 + percent ÷ 100). A Rs 50,000 rent going up 10% becomes 50,000 × 1.10 = Rs 55,000.

5. Reverse percentages: finding the original

This is the one people get wrong most often. If a jacket costs Rs 3,600 after a 20% discount, the original price is not 3,600 + 20%. You paid 80% of the original, so the original is 3,600 ÷ 0.80 = Rs 4,500.

Likewise, if your salary after a 15% raise is Rs 69,000, it was 69,000 ÷ 1.15 = Rs 60,000 before. The same trick removes sales tax from a price, explained in our post on adding or removing 18% sales tax.

Percentages in a spreadsheet

In Excel or Google Sheets, put the obtained marks in A2 and the total in B2, then use =A2/B2 and format the cell as a percentage. For a change, use =(B2-A2)/A2. To add 10% to a value, use =A2*1.1, and to find the original before a 20% discount, use =A2/0.8. Format cells as percentages rather than multiplying by 100, so later formulas stay correct.

Common mistakes

• Using the wrong base. A rise from 50 to 75 is 50%, but a fall from 75 back to 50 is only 33.3%. Always divide by the starting value.
• Adding percentages that don’t share a base. A 10% rise followed by a 10% fall leaves you at 99%, not 100%.
• Confusing percent with percentage points. A rate going from 10% to 12% rose by 2 percentage points, which is a 20% increase in the rate.
• Rounding too early. Keep decimals until the final step, then round.

Our percentage calculator covers all of these, including marks percentage and percentage change, and the tax calculator handles inclusive and exclusive tax. For loans, where interest compounds month by month, see how loan EMI is calculated.

Frequently asked questions