Percentage change compares a difference with the original value. Identifying that base is the key step, especially when comparing a rise with a later fall.
The formula
Percentage change equals (new value minus original value) divided by original value, multiplied by 100. A move from 80 to 100 is a 25% increase because the $20 difference is divided by 80.
Why reversing is different
If 80 rises to 100, returning to 80 is a $20 decrease divided by 100, or 20%. The bases differ, so the percentages are not mirror images.
Use the right mode
Use a percentage-of calculation for a portion, percentage change for a before-and-after comparison, and reverse percentage when the final value and rate are known. Keep full precision until the final display.
A worked example
Worked example: changing from 80 to 100 is a 25% increase because the $20 difference is divided by 80. Changing from 100 back to 80 is a 20% decrease because the base is now 100.
Write the original value above the fraction before entering numbers. If the original value is zero, report the absolute change or another meaningful comparison instead.
When reporting a change, name both values and the base in words. That small habit makes a percentage claim auditable and prevents readers from confusing percentage points with percent change.
Most percentage mistakes come from choosing the wrong base, not from the arithmetic itself.
COMMON QUESTIONS
Frequently asked questions
Can percentage change be negative?
Yes. A negative result represents a decrease from the original value.
What if the original value is zero?
Percentage change is undefined because division by zero is not valid. Use an absolute difference or another comparison.