The Lesson
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.
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.
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%.
Lesson Slides
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.
What Is a Percentage Change?
A percentage change is the change from one value to another value, expressed as a percentage.
What Does |nold| Mean in the Formula?
The vertical lines mean the
absolute value of n
old needs to be found.
This means that the value is always taken as positive, even if it is negative.
If the old number n
old equals 5, |n
old| also equals 5.
But if the old number n
old equals −5, |n
old| equals 5. You ignore the − sign.
Be Careful How You Talk About Percentage Changes
A percentage change expresses a change in values as a percentage.
You might say, "the share price has risen 5% today". This means the share price started the day at one value, $1, and ended it at a value that is 5% of $1 higher ($1.05).
It expresses the change between two numbers, values or quantities; not a change between percentages.
Sometimes people do refer to changes in percentages. For example, "the interest rate on my savings account has risen from 3% to 4%. The interest rate has risen by 1%".
This is not a percentage change in the sense we are using it. It is a difference in percentages (found by subtracting percentages).
Rather than saying "the interest rate has risen by 1%", you should say "the interest rate has risen by 1 percentage point".