How to calculate percentages
A percentage expresses a part of a whole as if out of one hundred. We use it every day for discounts, taxes, grades, profits and growth rates. This calculator covers the six most common percentage problems and shows the answer as soon as you type.
Formulas with examples
1. What is X% of Y?
Formula: result = (X ÷ 100) × Y. Example: 20% of 150 = 0.2 × 150 = 30.
2. X is what percent of Y?
Formula: percent = (X ÷ Y) × 100. Example: 30 out of 120 on a test = 30 ÷ 120 × 100 = 25%.
3. Percent change (increase or decrease)
Formula: change = ((new − old) ÷ old) × 100. Example: a price rising from 80 to 100 is a 20 ÷ 80 × 100 = 25% increase. A negative result is a decrease.
4. Add a percentage
Formula: Y × (1 + X ÷ 100). Example: a salary of 200 with a 15% raise becomes 230.
5. Subtract a percentage
Formula: Y × (1 − X ÷ 100). Example: 200 with 15% off becomes 170.
6. Find the whole from a part
Formula: whole = part ÷ (percent ÷ 100). Example: if 45 is 30% of an amount, the amount is 45 ÷ 0.3 = 150.
Common percentage mistakes
- Up then down by the same percent doesn't return to the start: 100 + 10% = 110, then 110 − 10% = 99.
- Percentage points vs percent: an interest rate going from 4% to 5% is a one-point rise but a 25% increase.
- Stacked discounts don't add up: 20% then 10% off equals 28%, not 30%. Use the Discount Calculator to get it right.
Frequently Asked Questions
How do I calculate a percentage on a calculator?
Divide the part by the whole and multiply by 100. For 45 out of 60: 45 ÷ 60 = 0.75 × 100 = 75%.
How do I find the discount percentage?
Subtract the new price from the old one, divide by the old price and multiply by 100.
How do I calculate my exam percentage?
Divide your score by the maximum score and multiply by 100 — or use the second calculator above.
Can a percentage exceed 100%?
Yes — when the part is larger than the base, e.g. sales growing from 100 to 250 is a 150% increase.
Does it accept decimals?
Yes, decimals and even Arabic-Indic digits are understood automatically.
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