# Percent of change (percentage change)

*Before learning about percent of change, please read the primer on percentages.*

Percent of change is also known as

- percent change
- percentage change

- percentage of change

It can be calculated using the **percent change formula**

An example

A gym introduces a new year offer of discounted annual membership.

*In the first year, 200 people take up the offer, then in the second year 250 people sign up.*

So the original quantity is 200 and the change in quantity is 250 - 200 = 50. To calculate percent change, apply these figures to the formula above

**% change**

**=**

**(250 - 200)/200 x 100 **

**= **

**50/200 x 100**

**=**

**0.25 x 100**

**=**

**25%**

Because the number of people taking up the new year offer has risen, you can say there's been a **percent of increase** of 25%.

## What if 300 people sign up in the 2nd year?

Here the original quantity is 200, the change in quantity is 300 - 200 = 100. Enter these numbers into the percentage change formula

**% change**

**=**

**(300 - 200)/200 x 100 **

**= **

**100/200 x 100**

**=**

**0.5 x 100**

**=**

**50%**

Again, the number of people taking the membership offer has gone up - in this case, a percent of increase of 50%.

## And if only 50 people sign up in the 2nd year?

Original quantity = 200, change in quantity = 50 - 200 = -150.

Therefore

**% change**

**=**

**(50 - 200)/200 x 100 **

**= **

**-150/200 x 100**

**=**

**-0.75 x 100**

**=**

**-75%**

Notice this time how the number of people taking up the offer has dropped, resulting in a **negative** percent change.

You could say there's been a percent of increase of -75%, but it's less awkward to say the equivalent - a **percent of decrease** of 75%.

## One more worked example!

*Now let's say 400 people take up the gym membership offer in the 1st year, and 250 sign up in the 2nd year.*

That's an original quantity of 400 and a change in quantity of 250 - 400 = -150.

Plugging these figures into the percent change formula gives

**% change**

**=**

**(250 - 400)/400 x 100 **

**= **

**-150/400 x 100**

**=**

**-0.375 x 100**

**=**

**-37.5%**

The percentage of change is a percent of increase of -37.5%, which is the same as a percent of decrease of 37.5%.

## Try some of your own percent of change calculations

Make up some figures of your own and apply them to the above scenario. Vary the number of people signing up to the gym during the first and second years. It's all good practice!

*And remember percent change may be **either** a percent of increase* *or a percent of decrease.*

For more on percentages click:

Calculate percentage

Percent to decimal

Decimal to percent

Percent to fraction

Fraction to percent

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Percent of change