# How do I work out a percentage?

Computes a percentage of a number, what percent one number is of another, or the whole number from a part and a percent.

- Page: https://www.acalculator.org/math/percentage-calculator
- JSON spec: https://www.acalculator.org/math/percentage-calculator.json
- Version: aac729e624c1

## Default answer

Example with the default inputs (Percent 18%, Of 240): 18% of 240 is 43.2.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| percentage | Percent | The percentage, in percent points (18 means 18%). |
| value | Of | The whole number the percentage is taken of. |
| result | Is | The part: the percentage of the whole number. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| percent | Percent | The percentage, in percent points (18 means 18%). |
| value | Of | The whole number the percentage is taken of. |
| result | Is | The part: the percentage of the whole number. |
| plus | The number plus the percent | The whole number increased by the percentage: V + R. |
| minus | The number minus the percent | The whole number decreased by the percentage: V − R. |

## Method

R = P ÷ 100 × V: the part R is P percent of the whole number V.

## Assumptions

- Percentages are in percent points: 18 means 18%.
- Solving for the percent or the whole number divides by the other one, so there is no answer when it is 0.

## Worked examples

1. percentage = 18%, value = 240 gives result = 43.2, plus = 283.2, minus = 196.8. Source: OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent. https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent.
2. result = 43.2, value = 240 gives percentage = 18%. Source: OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent. https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent.
3. percentage = 25%, result = 15 gives value = 60. Source: OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent. https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent.

## FAQ

### How do I calculate a percentage?

To calculate a percentage, divide the part by the whole and multiply by 100. For example, if you have 25 out of 100, the percentage is (25 ÷ 100) × 100 = 25%. The formula is: Percentage = (Part ÷ Whole) × 100.

### How do I calculate percentage increase?

To calculate percentage increase, subtract the original value from the new value, divide by the original value, and multiply by 100. Formula: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a price increases from $100 to $120, the percentage increase is ((120 - 100) ÷ 100) × 100 = 20%.

### How do I calculate percentage decrease?

To calculate percentage decrease, subtract the new value from the original value, divide by the original value, and multiply by 100. Formula: ((Original Value - New Value) ÷ Original Value) × 100. For example, if a price decreases from $100 to $80, the percentage decrease is ((100 - 80) ÷ 100) × 100 = 20%.

### What is the difference between percentage and percentage points?

A percentage is a ratio expressed as a fraction of 100. Percentage points are the difference between two percentages. For example, if interest rates increase from 5% to 7%, that's a 2 percentage point increase, or a 40% increase relative to the original rate. Percentage points are absolute differences, while percentages can be relative changes.

### How do I convert a decimal to a percentage?

To convert a decimal to a percentage, multiply by 100. For example, 0.25 becomes 25%, 0.75 becomes 75%, and 1.5 becomes 150%. You can also move the decimal point two places to the right and add the % symbol.

### How do I convert a percentage to a decimal?

To convert a percentage to a decimal, divide by 100. For example, 25% becomes 0.25, 75% becomes 0.75, and 150% becomes 1.5. You can also move the decimal point two places to the left and remove the % symbol.

### How do I calculate what percentage one number is of another?

To find what percentage one number is of another, divide the first number by the second number and multiply by 100. For example, if 15 is what percentage of 60, the calculation is (15 ÷ 60) × 100 = 25%. So 15 is 25% of 60.

### How do I add or subtract percentages?

To add or subtract percentages, first convert them to decimals, perform the calculation, then convert back to a percentage. For example, 25% + 15% = 0.25 + 0.15 = 0.40 = 40%. However, be careful with percentage changes - a 10% increase followed by a 10% decrease doesn't return to the original value.

### What is compound percentage growth?

Compound percentage growth occurs when a percentage change is applied repeatedly to the new value each time. For example, if an investment grows 10% each year, after 2 years it grows by 21% (not 20%) because the second year's 10% is calculated on the new higher value.

### How do I calculate percentage of total?

To calculate the percentage of total, divide the specific value by the total value and multiply by 100. For example, if you spent $30 out of a $100 budget, the percentage of total is (30 ÷ 100) × 100 = 30%. This shows what portion of the total the specific value represents.

### Why doesn’t a 25% rise and then a 25% fall get me back?

Because the fall is taken from the bigger number. 240 up 25% is 300, and 300 down 25% is 225. To get back to 240 from 300 you need a 20% fall.

## Sources

- OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent. https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent