How to find a percentage of a number
Percent means “per hundred”: the % sign stands for the number 0.01 (NIST Guide to the SI, chapter 7). So 15% of 80 is 80 × 15 ÷ 100 = 12. To do it in your head, find 10% by moving the decimal point one place left (8) and scale from there: 5% is half of that and 15% is the two added together.
How to find what percent one number is of another
Divide the part by the whole and multiply by 100: 18 ÷ 75 × 100 = 24%. For example, 18 correct answers out of 75 is a score of 24%.
How to calculate percent increase or decrease
Percent change = (new − old) ÷ old × 100
From 40 to 50 is (50 − 40) ÷ 40 × 100 = 25%. Going back is not the same percentage: from 50 down to 40 is -20%, because the change is measured against a larger starting value.
Percent vs percentage points. When a rate moves from 4% to 5%, it rises by 1 percentage point, which is a 25% increase in the rate. Saying it “rose 1%” is ambiguous, so say which you mean.
Percent difference compares two values without a direction, against their average: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50 that is 22.2222%.
How to calculate percent off
Multiply the price by 1 minus the discount as a decimal: $120.00 × (1 − 0.25) = $90.00, a saving of $30.00.
Discounts in a row multiply rather than add: 25% off and then another 10% off is $81.00, 32.5% off in total, not 35%. Sales tax, if any, is usually charged on the discounted price.
Common percentages
Percent of common numbers
| Percent | of 20 | of 50 | of 80 | of 100 | of 250 | of 1,000 |
|---|---|---|---|---|---|---|
| 5% | 1 | 2.5 | 4 | 5 | 12.5 | 50 |
| 10% | 2 | 5 | 8 | 10 | 25 | 100 |
| 15% | 3 | 7.5 | 12 | 15 | 37.5 | 150 |
| 20% | 4 | 10 | 16 | 20 | 50 | 200 |
| 25% | 5 | 12.5 | 20 | 25 | 62.5 | 250 |
| 30% | 6 | 15 | 24 | 30 | 75 | 300 |
| 50% | 10 | 25 | 40 | 50 | 125 | 500 |
| 75% | 15 | 37.5 | 60 | 75 | 187.5 | 750 |
Methodology and testing
Results are shown to up to four decimal places. Automated tests check hand-worked examples, that finding a percentage and then asking what percent it is gives the starting percentage back, that a change and its reverse bring a value back to where it started, and that stacked discounts multiply. How we build and test calculators.
Sources
- NIST Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities, National Institute of Standards and Technology. The symbol % represents simply the number 0.01, so a statement like "differ by 0.05 %" is ambiguous and should be written to show what the percentage is of.
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