"Percent" means per hundred, so 15% is the same as 15/100 or 0.15. Almost every percentage problem is one of three questions about the same relationship, part = percent × whole: you know the percent and the whole and want the part; you know the part and the whole and want the percent; or you know the part and the percent and want the whole. This percentage calculator answers all three, shows the arithmetic and then checks the answer by running it backwards.
For increases and decreases between two values, use the percent change calculator. For prices, the discount calculator and tip calculator handle the money details, and teachers turning points into scores can use the test grade calculator.
How to use the percentage calculator
- Pick the question that matches your problem from the menu.
- Enter A and B. In "What is A% of B?", A is the percentage and B is the whole.
- In "A is what percent of B?", A is the part and B is the whole.
- In "A is B% of what?", A is the part you know and B is its percentage; the answer is the whole.
- Read the answer, then the check line, which reverses the calculation to confirm it.
Formula
All three are rearrangements of the same equation. OpenStax Prealgebra teaches them as translating "what is 15% of 80?" into the equation n = 0.15 × 80.
Worked example
- What is 15% of 80? 15 ÷ 100 × 80 = 0.15 × 80 = 12.
- 12 is what percent of 80? 12 ÷ 80 × 100 = 15%.
- 12 is 15% of what? 12 ÷ 0.15 = 80.
The same three numbers appear in each question; only the unknown moves. Another example: a class has 28 students and 21 passed, so 21 ÷ 28 × 100 = 75% passed.
Converting between percents, decimals and fractions
To turn a percent into a decimal, divide by 100 (move the decimal point two places left): 7.5% = 0.075. To go back, multiply by 100. A fraction becomes a percent by dividing top by bottom and multiplying by 100: 3/8 = 0.375 = 37.5%. The fraction calculator simplifies fractions if you need the reverse.
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33⅓% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1 | 1 |
Mental-math shortcuts
10% of a number is the number with the decimal point moved one place left, so 10% of 64 is 6.4. From there, 5% is half of that (3.2), 20% is double (12.8) and 15% is 10% plus 5% (9.6). Percentages are also reversible: 8% of 50 equals 50% of 8, which is 4. Swapping the numbers often turns a hard calculation into an easy one.
Percentages above 100 are normal when the part is larger than the reference: 150% of 40 is 60. Percentage points are different from percent: a rate going from 4% to 6% rose by 2 percentage points, which is a 50% increase in the rate.
Caveats and assumptions
- Results are rounded for display to four decimal places (two for large numbers).
- The whole cannot be zero when you are solving for a percent, and the percent cannot be zero when you are solving for the whole.
- Percentage points and percent change are different measures; see the extra section above.
- Negative values are allowed and follow the same algebra.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 80: 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 12 out of 80 is 12 ÷ 80 × 100 = 15%.
How do I find the original number from a percentage?
Divide the part by the percentage written as a decimal. If 12 is 15% of a number, the number is 12 ÷ 0.15 = 80.
Can a percentage be more than 100%?
Yes. It means the part is bigger than the reference amount; 150% of 40 is 60.
Is 20% of 50 the same as 50% of 20?
Yes. Both are 0.2 × 50 = 0.5 × 20 = 10, because multiplication can be done in either order.
Sources
- OpenStax Prealgebra 2e — 6.1 Understand Percent — definition of percent and conversions
- OpenStax Prealgebra 2e — 6.2 Solve General Applications of Percent — translating percent questions into equations
- OpenStax Prealgebra 2e — 6.5 Solve Proportions and their Applications — percent proportion method
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