How to Calculate Percentage: Easy Formulas and Worked Examples
How to calculate a percentage: simple formulas for percent of a number, percentage change, reverse percentages and percentage points, with worked examples.
This guide is general information only, not professional financial, legal or technical advice. Menus and rules can vary by device and country.
To calculate a percentage of a number, divide the percent by 100 and multiply by the number: 15% of 80 is 0.15 × 80 = 12. To find what percent one number is of another, divide the part by the whole and multiply by 100: 18 out of 24 is 18 ÷ 24 × 100 = 75%.
"Percent" simply means "per 100", so 1% is one part in every hundred. Once you know the handful of formulas below, you can handle discounts, pay rises, test scores and news statistics with confidence.
Quick answer
- Percent of a number: (percent ÷ 100) × number
- What percent X is of Y: (X ÷ Y) × 100
- Percentage change: (new − old) ÷ old × 100
- Reverse percentage (find the original): final value ÷ (1 ± percent ÷ 100)
- Percentage points: new rate − old rate (used when comparing two percentages)
The Core Percentage Formulas
| What you want | Formula | Example | Answer |
|---|---|---|---|
| Percent of a number | (P ÷ 100) × N | 15% of 80 | 12 |
| What percent X is of Y | (X ÷ Y) × 100 | 18 out of 24 | 75% |
| Increase by a percent | N × (1 + P ÷ 100) | 80 increased by 15% | 92 |
| Decrease by a percent | N × (1 − P ÷ 100) | 80 decreased by 15% | 68 |
| Percentage change | (New − Old) ÷ Old × 100 | 50 to 65 | +30% |
| Reverse percentage | Final ÷ (1 ± P ÷ 100) | 96 after a 20% rise | 80 |
| Percentage-point change | New % − Old % | 4% to 6% | +2 percentage points |
Every example in this article was checked with a calculator.
How to Find a Percent of a Number
- Write the percent as a decimal by dividing it by 100. For example, 15% becomes 0.15.
- Multiply that decimal by the number.
- Check that the answer makes sense. A percent below 100% should give a smaller number than you started with.
Example: 15% of 80 = 0.15 × 80 = 12.
Shortcut: x% of y is always the same as y% of x. So 8% of 50 is the same as 50% of 8, which is easy: 4.
Real-life example: A meal costs 45 and you want to leave an 18% tip. 0.18 × 45 = 8.10.
How to Work Out What Percent One Number Is of Another
- Divide the part by the whole.
- Multiply by 100.
- Add the % sign.
Example: You scored 18 out of 24 on a quiz. 18 ÷ 24 = 0.75, and 0.75 × 100 = 75%.
How to Increase or Decrease a Number by a Percent
The fastest way is to use a multiplier.
- For an increase, add the percent to 100%. For a decrease, subtract it from 100%.
- Turn that into a decimal (divide by 100).
- Multiply the original number by it.
Example (increase): 80 increased by 15% → 100% + 15% = 115% → 80 × 1.15 = 92.
Example (decrease): an item priced 80 with 15% off → 100% − 15% = 85% → 80 × 0.85 = 68.
How to Calculate Percentage Change
Percentage change tells you how much something grew or shrank compared with where it started.
Formula: percentage change = (new value − old value) ÷ old value × 100
- Subtract the old value from the new value.
- Divide the result by the old value (always the starting number).
- Multiply by 100. A positive answer is an increase; a negative answer is a decrease.
Example (increase): rent goes from 50 to 65. (65 − 50) ÷ 50 × 100 = 15 ÷ 50 × 100 = +30%.
Example (decrease): a price drops from 80 to 60. (60 − 80) ÷ 80 × 100 = −20 ÷ 80 × 100 = −25%, a 25% decrease.
Watch the starting point. Going from 200 to 240 is a 20% increase, but going back from 240 to 200 is only a 16.67% decrease, because the second change is measured against 240.
This is also why a rise and a fall of the same percent do not cancel out. If 100 rises by 10%, you get 110. If 110 then falls by 10%, you lose 11 and end up at 99, not 100. The same idea explains how compound interest grows and how inflation adds up over time.
How to Calculate a Reverse Percentage
A reverse percentage finds the original number when you only know the value after a percentage change. A common use is finding the price before a discount or tax was applied.
- Work out what percent of the original you now have. Add the increase to 100%, or subtract the decrease from 100%.
- Turn that percent into a decimal.
- Divide the final value by that decimal.
Example (after an increase): a price is 96 after a 20% rise. 100% + 20% = 120% = 1.2. 96 ÷ 1.2 = 80.
Example (after a discount): a jacket costs 45 after 25% off. 100% − 25% = 75% = 0.75. 45 ÷ 0.75 = 60.
Example (bigger numbers): a car is worth 5,845 after losing 16.5% of its value. 100% − 16.5% = 83.5% = 0.835. 5,845 ÷ 0.835 = 7,000.
Common trap: do not take 20% off 96 to "undo" a 20% rise. That gives 96 × 0.8 = 76.80, which is wrong, because the 20% was a percentage of the original 80, not of 96.
Percent vs Percentage Points
When you compare two percentages, such as interest rates or survey results, there are two different ways to describe the change.
- Percentage points are a simple subtraction of the two rates.
- Percent change measures the change relative to the starting rate.
Example: an interest rate rises from 4% to 6%.
- Percentage points: 6 − 4 = 2 percentage points.
- Percent change: (6 − 4) ÷ 4 × 100 = 50%.
Both statements are true, but they mean very different things. Saying "the rate rose 2%" is ambiguous and often wrong; "the rate rose 2 percentage points" is clear. Look for this distinction when you compare savings accounts or loans while you make a budget.
Common Mistakes and How to Avoid Them
- Dividing by the wrong number. In percentage change, always divide by the old (starting) value, not the new one.
- Forgetting to adjust from 100%. For a 30% decrease, you have 70% left, so use 0.70, not 0.30.
- Undoing a percentage with the same percentage. A 10% rise followed by a 10% fall leaves you below where you started.
- Mixing up percent and percentage points. A move from 4% to 6% is 2 points but a 50% increase.
- Decimal slips. 5% is 0.05, not 0.5. Double-check by estimating: 10% of a number is just the number divided by 10.
- Rounding too early. Keep full decimals until the final step, then round.
Frequently Asked Questions
How do I calculate a percentage on a calculator?
To find 15% of 80, type 15 ÷ 100 × 80, or simply 0.15 × 80. To find what percent 18 is of 24, type 18 ÷ 24 × 100. Many calculators also have a % key, but its behaviour varies by model, so the decimal method is more reliable.
How do I calculate a percentage increase between two numbers?
Subtract the old number from the new number, divide by the old number and multiply by 100. For example, from 50 to 65 is (65 − 50) ÷ 50 × 100 = 30%.
How do I find the original price before a discount?
Divide the sale price by the percent you actually paid, as a decimal. If something costs 45 after 25% off, you paid 75% of the original, so 45 ÷ 0.75 = 60.
What is the easiest way to work out 10%, 5% or 1% in my head?
For 10%, divide by 10. For 5%, halve the 10% amount. For 1%, divide by 100. You can combine them: 15% is 10% plus 5%, which is handy for tips and discounts when you are trying to save money.
Can a percentage be more than 100%?
Yes. If a value more than doubles, the increase is over 100%. Going from 20 to 50 is a 150% increase, because the change (30) is one and a half times the starting value.