Percentage change tells you how much a value has shifted relative to its starting point. The formula is (new − old) ÷ old · 100, and the sign shows an increase or a decrease. Worked example: from 200 to 250 is +25%. Suitable for Grade 7 / Year 8.
Percentage change is the difference between the new and old value, divided by the old value, times 100: (new − old) ÷ old · 100. A positive result is an increase, a negative one a decrease. Example: from 200 to 250 → (250 − 200) ÷ 200 · 100 = +25%.
At a glance
Summary of this tutorial
Example
(250 − 200) ÷ 200 · 100
Method
Difference ÷ old value · 100
Steps
4
Result
+25%
Sign
positive = increase, negative = decrease
Grade level
Grade 7 (ages 12–13)
Worked example: 200 → 250
EXAMPLE
(250 − 200) ÷ 200 · 100
The old value is 200, the new value 250. We take the difference and relate it to the old value.
The steps to find a percentage change
These four steps work for any old and new value.
1
Step 1 · Start
200 → 250
Old value 200, new value 250.
2
Step 2 · Formula
(250 − 200) ÷ 200 · 100
Difference over the old value, then times 100.
3
Step 3 · Difference
50 ÷ 200 · 100
New minus old gives 50.
4
Step 4 · Result
= +25%
Positive sign: an increase of 25%.
Why the formula works
Percent means "per hundred". You are asking: how big is the change compared with the old value, if that value equals 100%? That is why you divide the difference (new − old) by the old value and multiply by 100. The old value is the reference point — dividing by the new value would give a different answer.
We only use technically necessary storage. Optionally, anonymous statistics (Google Analytics) help us improve the site — these are loaded only after you agree. More in the privacy policy