Percentage changes are always anchored to a starting value. That detail explains why an increase and an equal-looking decrease do not return a number to where it began.
Always name the starting value
The formula is (new − old) ÷ old × 100. Calling out the old value makes the comparison honest. A move from 80 to 100 is a 25% increase because the gain of 20 is one quarter of 80.
Equal percentages use different bases
If 100 rises by 50%, it becomes 150. A 50% decrease from 150 removes 75, leaving 75. To return from 150 to 100 requires a 33.33% decrease, not 50%.
Percentage points are different
If a rate moves from 12% to 15%, it rises by three percentage points. Its relative percentage increase is 25%, because the three-point gain is one quarter of the original 12%.
Be careful when the start is zero
A conventional percentage change from zero is undefined because there is no non-zero base. Report the absolute change instead, or provide another meaningful reference value.
A calculator is often the quickest way to check your mental math. The important part is using the right starting value.
Open a calculator →Common questions
Can percentage change be negative?
Yes. A negative result means the new value is lower than the old value.
What decrease reverses a 25% increase?
A value of 100 becomes 125; returning to 100 requires a 20% decrease.
Should I use the larger number as the base?
Use the original or reference value, even when it is smaller.
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