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.
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
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.