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, nold is the old value and nnew 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 |nold| means the absolute value of nold
(ignore the − sign if nold is negative).

2

Substitute the numbers into the formula. In our example, nold = 20 and nnew = 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%.

Percentage Increase, Percentage Decrease

In the example above, the number increased from 20 to 25. The percentage change was positive. This is a percentage increase.

A percentage decrease happens when the number gets smaller. The percentage change will be negative.

The slider below gives another example of how to find a percentage change. This time, it is a percentage decrease.

Open the slider in a new tab

See Also

What is a percentage change? What is a percentage?