# What is the percentage increase?

Increases a number by a percentage, or finds the percentage increase from one number to another, or the original number.

- Page: https://www.acalculator.org/math/percentage-increase-calculator
- JSON spec: https://www.acalculator.org/math/percentage-increase-calculator.json
- Version: 2c19b9b86a0c

## Default answer

Example with the default inputs (Original value 80, Percentage increase 15%): 80 increased by 15% is 92.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Original value | The value A before the increase. Not 0. |
| to | New value | The value B after the increase. |
| change | Percentage increase | The increase from A to B as a percent of \|A\|. A negative increase is a decrease. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| from | Original value | The value A before the increase. Not 0. |
| to | New value | The value B after the increase. |
| change | Percentage increase | The increase from A to B as a percent of \|A\|. A negative increase is a decrease. |
| direction | Increase or decrease | Whether the value went up, went down, or stayed the same. |
| increase | Amount of increase | The new value minus the original value, B − A, when the new value is at least the original. |
| decrease | Amount of decrease | The original value minus the new value, A − B, when the new value is smaller. |
| verdict | In words | The change in words: increased by p%, or decreased by the size of a negative p. |

## Method

B = A + |A| × p ÷ 100, so p = (B − A) ÷ |A| × 100, where A is the original value and B the new value.

## Assumptions

- The increase is measured against the size of the original value, |A|; for a positive A, B = A × (1 + p ÷ 100).
- A negative percentage increase is a decrease.
- There is no percentage increase from 0: the original value must not be 0.
- Finding the original value from the new value and the increase can give two answers, one positive and one negative: both are shown.

## Worked examples

1. from = 80, change = 15% gives to = 92, increase = 12, direction = Increase, verdict = increased by 15%. Source: hand calculation in content.mdx: 15% of 80 is 12, and 80 + 12 = 92.
2. from = 50, to = 65 gives change = 30%, increase = 15. Source: hand calculation in content.mdx: (65 − 50) ÷ 50 × 100 = 30%.
3. to = 92, change = 15% gives from = 80. Source: hand calculation in content.mdx: 92 ÷ 1.15 = 80.
4. from = 200, to = 150 gives change = -25%, decrease = 50, direction = Decrease, verdict = decreased by 25%. Source: hand calculation in content.mdx: (150 − 200) ÷ 200 × 100 = −25%, a decrease.
5. from = 0.5, change = 300% gives to = 2. Source: hand calculation in content.mdx: 0.5 × (1 + 3) = 2.

## FAQ

### How do I increase a number by a percentage?

Multiply the number by 1 plus the percentage as a decimal. To increase 80 by 15%, work out 80 × 1.15 = 92. You can also find 15% of 80 (12) and add it on: 80 + 12 = 92.

### How do I calculate the percentage increase between two numbers?

Subtract the original number from the new one, divide by the original, and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.

### How do I find the original number before a percentage increase?

Divide the new number by 1 plus the increase as a decimal. If a price is 92 after a 15% increase, the original was 92 ÷ 1.15 = 80. Taking 15% off 92 would give 78.20, which is wrong, because the 15% was worked out on 80, not on 92.

### What does a negative percentage increase mean?

A decrease. From 200 to 150 is an increase of −25%, which is the same as a 25% decrease. For decreases on their own terms, the percentage change calculator reports the direction too.

### Can a percentage increase be more than 100%?

Yes. An increase of 100% doubles a number, 200% triples it, and 300% makes it four times as big: 0.5 increased by 300% is 0.5 × 4 = 2.

### Is a 10% increase followed by a 10% increase the same as a 20% increase?

No, it is a 21% increase, because the second 10% is worked out on the bigger number. 100 becomes 110, and 110 becomes 121. Repeated increases multiply: 1.1 × 1.1 = 1.21.

## Sources

- OpenStax, Elementary Algebra 2e, section 3.2 Solve Percent Applications (percent increase and percent decrease): https://openstax.org/books/elementary-algebra-2e/pages/3-2-solve-percent-applications