Percent change

Percent change is the amount that a quantity changes relative to its original value.

The percent change formula is as follows:

Old here refers to the value we start with, or the initial value, while new refers to the final value.

When we subtract the old from the new value, we can get a negative number, a positive number, or 0. A positive number would mean that the initial value increased. A negative number means that the initial value decreased. In order to get a 0 difference, the old and new number would have to be the same, meaning there was no change.


1. Given an initial value of 5, how much of a percentage increase will result in a new value of 12?

So, 12 is a 140% increase of 5.

2. What is the percent change between an initial value of 800 and a final value of 115?

So, 115 is an 85.625% decrease of 800.

3. What is the percent change between an initial value of -25 and a final value of 75?

So, 75 is a 400% increase of -25.

Are percent changes invertible?

Percent changes are not invertible. Referencing example 1 above, it may seem intuitive that since 12 is a 140% increase relative to 5, a 140% decrease relative to 12 should be 5. However, this is not true (a 140% decrease of 12 is actually -4.8). To confirm this, plug the numbers back into the percent change equation using 12 as the initial value and 5 as the final value:

So, 5 is a 58.3% decrease of 12, not a 140% decrease. This is because the percent change is relative to the initial value. Starting with a different initial value will therefore result in a different percent change, even if the same two numbers are used.