# How to Find a Percentage Change

## Finding a Percentage Change

A percentage change tells you how a number has changed from one value to another value, expressed as a percentage.

Imagine you wanted to find the percentage change from 20 to 25.

## How to Find a Percentage Change

Finding a percentage change is easy. Find the difference between the numbers and express this a percentage of the original number.

This is 20% (said as "20 percent"). It means 20 parts out of 100.

## How to Find a Percentage Change

Finding a percentage change is easy. Find the difference between the numbers and express this a percentage of the original number.

### Question

What is the percentage change from 20 to 25?

### Step-by-Step:

# 1

Find the difference between the old and new number.

Subtract the old number from the new number. In our example, the old number is 20 and the new number is 25.

25 − 20 = 5

# 2

Divide the answer (5) by the old number (20).

5 ÷ 20 = 0.25

# 3

Multiply the answer (0.25) by 100%.

0.25 × 100% = 25%

### Answer:

The percentage change from 20 to 25 is 25%.

## How to Find a Percentage Change Using a Formula

A percentage change can be found using the formula below:

In this formula, n_{old} is the old value and n_{new} is the new value.

Let's use the formula to find the percentage change from 20 to 25.

### Question

What is the percentage change from 20 to 25?

### Step-by-Step:

# 1

Start with the formula:

Percentage change = ^{(nnew − nold)}⁄_{|nold| × 100%}

**Don't forget:** / means ÷ **and** |n_{old}| means the absolute value of n_{old}

(ignore the − sign if n_{old} is negative).

# 2

Substitute the numbers into the formula. In our example, n_{old} = 20 and n_{new} = 25.

Percentage change = ^{(25 − 20)}⁄_{|20|} × 100%

Percentage change = ^{(5)}⁄_{20} × 100%

Percentage change = 5 ÷ 20 × 100%

Percentage change = 0.25 × 100%

Percentage change = 25%

### Answer:

The percentage change from 20 to 25 is 25%.