Percentages are everywhere: exam results, discounts, salary increases, interest rates and tax. The good news is that almost every percentage question uses one of three simple formulas. Here they are, with worked examples, plus a free calculator that does the maths for you.
Percentage of marks
percentage = marks you got ÷ total marks × 100
If you scored 437 out of 500: 437 ÷ 500 = 0.874, and 0.874 × 100 = 87.4%. For a single paper, 68 out of 75 is 68 ÷ 75 × 100 = 90.67%.
Percentage for several subjects
When subjects have different totals, add up all the marks first, then divide by the total of all the papers:
| Subject | Marks | Out of | Percentage |
|---|---|---|---|
| Maths | 78 | 100 | 78% |
| Science | 64 | 100 | 64% |
| English | 45 | 50 | 90% |
| Total | 187 | 250 | 74.8% |
Let the calculator do it
The Percentage Calculator has four small calculators. For marks, use “… is what % of …?”: type 437 in the first box and 500 in the second, and it shows 87.4%. The answer updates as you type.
Discounts and tax
- 20% off Rs. 4,500: 4,500 × 20 ÷ 100 = Rs. 900 off, so you pay Rs. 3,600. In the calculator, use the last box: 4,500 decreased by 20%.
- Adding 18% tax to Rs. 10,000: 10,000 × 18 ÷ 100 = Rs. 1,800, so the total is Rs. 11,800. Use 10,000 increased by 18%.
- Finding the price before a discount: if Rs. 3,600 is the price after 20% off, the original was 3,600 ÷ 0.8 = Rs. 4,500. Adding 20% back to 3,600 gives Rs. 4,320, which is wrong.
Percentage change: pay rises and price rises
percentage change = (new − old) ÷ old × 100
A salary that goes from Rs. 85,000 to Rs. 95,000 has risen by (95,000 − 85,000) ÷ 85,000 × 100 = 11.76%. A bus fare that drops from Rs. 250 to Rs. 200 has fallen by 20%. Use the “Change from … to …” box and the calculator shows ▲ for increases and ▼ for decreases.
Percent vs percentage points
If an interest rate goes from 10% to 12%, it has risen by 2 percentage points, but the rate itself is 20% higher (2 ÷ 10 × 100). News reports and loan offers mix these up all the time, so check which one is meant. For loans, our guide to calculating your monthly EMI shows what a rate change does to your payments.
Common questions
How do I find how many marks I need to pass?
Multiply the total by the pass percentage. If the pass mark is 40% of 150, you need 150 × 40 ÷ 100 = 60 marks.
How do I calculate 15% of 2,000?
2,000 × 15 ÷ 100 = 300. In the calculator, use 'What is 15 % of 2,000?'.
Why can't I just average my subject percentages?
Because papers with bigger totals should count for more. Add up all your marks and all the totals, then divide.
How do I write a percentage as a decimal?
Divide by 100: 87.4% is 0.874, and 5% is 0.05.