# Percentage change

A way to show how much something went up or down compared with where it started.

Maths (school) · Part 01: Number and ratio · Card 4 of 9 · Last updated 2026-10-19

## Analogy

Like measuring how much taller you grew compared with your old height.

## Example

**Price 40 to 50**

Change = 50 - 40 = 10
10 / 40 = 0.25
Increase of 25%

## In practice

Prices, population and phone battery levels are often reported as percentage changes.

## Practice

### Flashcards

- **A price goes from 40 to 50. What is the percentage increase?** 25%. The change is 10, and 10 / 40 = 0.25.

### Interview questions

**Explain how to work out the percentage increase when a price rises from 40 to 50, and why you divide by the original.**

- Work out the change: 50 - 40 = 10
- Divide the change by the original: 10 / 40 = 0.25
- Multiply by 100 to get 25%
- The original is the reference point

## Questions people ask

### What is the percentage change formula?

Work out the change (new minus old), divide it by the original value, then multiply by 100. For a price rising from 40 to 50, the change is 10, 10 / 40 = 0.25, so the increase is 25%. Always divide by the starting value.

### Why divide by the original amount and not the new one?

The percentage tells you how big the change is compared with where you started. The start is your reference point. Dividing by the new amount would give a different, wrong answer. A rise from 40 to 50 is 25%, not 20%.

## Related concepts

- [Percentage of an amount](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-3)
- [BIDMAS](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-1)
- [Adding fractions](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-2)
- [Laws of indices](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-7)

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