How to Calculate Percentages
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." There are three core percentage calculations you will encounter in everyday life — this guide covers all three with simple formulas and worked examples.
Use the free calculator below to try each method as you read through this guide, or work through Khan Academy’s free percentages lessons for additional practice.
Method 1 – Find X% of a number
Question: What is 15% of 80?
Formula: Result = (Percentage ÷ 100) × Number
- Divide the percentage by 100: 15 ÷ 100 = 0.15
- Multiply by the number: 0.15 × 80 = 12
Examples
| Question | Calculation | Answer |
|---|---|---|
| What is 10% of 200? | 0.10 × 200 | 20 |
| What is 25% of 360? | 0.25 × 360 | 90 |
| What is 7.5% of 400? | 0.075 × 400 | 30 |
| What is 20% of 55? | 0.20 × 55 | 11 |
Common uses: calculating tips, discounts, tax amounts, commission.
Use the Percentage Calculator to do this instantly.
Method 2 – What percent is X of Y?
Question: 30 is what percent of 120?
Formula: Percentage = (X ÷ Y) × 100
- Divide X by Y: 30 ÷ 120 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
Examples
| Question | Calculation | Answer |
|---|---|---|
| 45 is what % of 180? | (45 ÷ 180) × 100 | 25% |
| 17 is what % of 68? | (17 ÷ 68) × 100 | 25% |
| 7 is what % of 20? | (7 ÷ 20) × 100 | 35% |
| 12 is what % of 50? | (12 ÷ 50) × 100 | 24% |
Common uses: test scores, survey results, budget proportions, market share.
Method 3 – Percentage change (increase or decrease)
Question: What is the percentage change from 80 to 100?
Formula: Change = ((New − Old) ÷ Old) × 100
- Subtract: 100 − 80 = 20
- Divide by old value: 20 ÷ 80 = 0.25
- Multiply by 100: 0.25 × 100 = +25%
Examples
| From | To | Calculation | Change |
|---|---|---|---|
| $50 | $75 | (25 ÷ 50) × 100 | +50% |
| 200 | 150 | (−50 ÷ 200) × 100 | −25% |
| 1,000 | 1,200 | (200 ÷ 1,000) × 100 | +20% |
| 90 kg | 81 kg | (−9 ÷ 90) × 100 | −10% |
Common uses: price changes, salary increases, investment returns, weight tracking.
Use the Percentage Change Calculator to do this instantly.
Mental shortcuts for common percentages
| Percentage | Shortcut | Example (of 200) |
|---|---|---|
| 50% | Divide by 2 | 100 |
| 25% | Divide by 4 | 50 |
| 10% | Move decimal one place left | 20 |
| 5% | Half of 10% | 10 |
| 1% | Move decimal two places left | 2 |
| 20% | Divide by 5 | 40 |
| 75% | Subtract 25% from the total | 150 |
Common mistakes to avoid
- Confusing percentage and percentage points. If a rate rises from 4% to 6%, that is a 2 percentage point increase, but a 50% relative increase.
- Adding percentages of different bases. A 10% rise followed by a 10% fall does not return to the original value. 10% rise on $100 = $110. 10% fall on $110 = $99.
- Reversing increase and decrease. A 25% increase requires a 20% decrease to undo (not 25%), because the base has changed.
Free percentage calculators
- Percentage Calculator — find X% of Y, or what percent X is of Y
- Percentage Change Calculator — measure increase or decrease between two values
- Discount Calculator — find the sale price after any percentage off
- Tip Calculator — calculate a tip for any bill
- VAT Calculator — add or remove VAT from any price
- Percentage Of Calculator — find what X% of any number is
- Fraction to Percentage — convert any fraction to a percentage
FAQ
What is a percentage?
A percentage is a number expressed as a fraction of 100. 45% means 45 out of every 100, or 0.45 as a decimal.
How do I convert a percentage to a decimal?
Divide by 100. 75% = 75 ÷ 100 = 0.75. Move the decimal point two places to the left.
How do I convert a decimal to a percentage?
Multiply by 100. 0.35 × 100 = 35%. Move the decimal point two places to the right.
How do I calculate percentage without a calculator?
Use the mental shortcuts above. For 15%, find 10% (move decimal left) then add half of that. Example: 15% of 80 = 8 + 4 = 12.
How do I calculate percentage on a phone?
Most phone calculators have a % button. Enter the number, press ×, enter the percentage, then press %. Or use the free calculator at the top of this page on any device.
How do I add a percentage to a number?
Multiply the number by (1 + percentage/100). To add 20% to $50: $50 × 1.20 = $60. This is useful for adding VAT, tips, or markup to a price.
How do I subtract a percentage from a number?
Multiply the number by (1 − percentage/100). To subtract 15% from $80: $80 × 0.85 = $68. Use this for calculating discounts or tax removal.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/4 = 3 ÷ 4 = 0.75 × 100 = 75%. Use the Fraction to Percentage Calculator for instant results.