Quick answer: X% of Y = (X ÷ 100) × Y. X as a percentage of Y = (X ÷ Y) × 100. Percentage change = ((New − Old) ÷ Old) × 100. To increase Y by X%, multiply by (1 + X/100); to decrease, multiply by (1 − X/100).
Percentages are everywhere — shop discounts, exam scores, salary rises, loan interest and growth reports. Here are the four formulas you will use most, with simple examples. Want the answer instantly? Use the free Percentage Calculator.
1. What is X% of Y?
Formula: (X ÷ 100) × Y
Example: 15% of 200 = 0.15 × 200 = 30.
2. X is what percent of Y?
Formula: (X ÷ Y) × 100
Example: You scored 45 out of 60. 45 ÷ 60 × 100 = 75%.
3. Percentage change (increase or decrease)
Formula: ((New − Old) ÷ Old) × 100
Example: Website visitors went from 800 to 1,000. (1000 − 800) ÷ 800 × 100 = +25%.
4. Increase or decrease a number by a percentage
Increase: Y × (1 + X ÷ 100) — Decrease: Y × (1 − X ÷ 100)
Example: A 500 item with a 20% discount costs 500 × 0.8 = 400.
Common percentage mistakes
- Percentage points vs percent: an interest rate rising from 4% to 5% is a 1 percentage-point rise, but a 25% increase.
- Reversing a percentage: a 20% rise followed by a 20% fall does not get you back to the start (100 → 120 → 96).
- Using the wrong base: always divide by the original (old) value when calculating change.
Percentages and loans
Loan interest is quoted as a yearly percentage, but you pay monthly. The Loan EMI Calculator converts the yearly rate into your exact monthly instalment and shows the total interest you will pay.
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More worked examples
- Percentage change: a price rises from 80 to 100. Change = (100 − 80) ÷ 80 × 100 = 25% increase. Going back from 100 to 80 is a 20% decrease — the starting value is different, so the percentage is too.
- Reverse percentage: a jacket costs 400 after a 20% discount. The sale price is 80% of the original, so the original = 400 ÷ 0.80 = 500.
- Two discounts in a row: 20% off and then a further 10% off is not 30% off. 100 × 0.80 × 0.90 = 72, so the total discount is 28%.
- Tax-inclusive price: a bill of 1,180 includes 18% tax. The price before tax = 1,180 ÷ 1.18 = 1,000, and the tax is 180.
- Exam marks: 42 out of 60 = 42 ÷ 60 × 100 = 70%.
Check any of these with the Percentage Calculator, the Discount Calculator or the GST & Tax Calculator.
Percent vs percentage points
If an interest rate goes from 10% to 12%, it rose by 2 percentage points, but by 20 percent (because 2 is 20% of 10). News reports and bank offers mix these up often, so check which one is meant.
Mental-math shortcuts
- 10% of a number: move the decimal point one place left (10% of 250 = 25).
- 5% is half of 10%; 1% is a tenth of 10%.
- x% of y equals y% of x: 8% of 50 is the same as 50% of 8, which is 4.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 240 = 240 × 15 ÷ 100 = 36.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.
Can a percentage be more than 100%?
Yes, when comparing growth. If sales go from 50 to 150, they increased by 200%. A part of a whole, however, cannot be more than 100% of it.
How do I add a percentage to a price?
Multiply by 1 plus the rate. Adding 18% to 500 gives 500 × 1.18 = 590.
Keep reading: related guides
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