Math · 1 min read
How to calculate percentage change
Percentage change compares a new value with an old one. Subtract, divide by the old value, then multiply by 100.
Last updated November 5, 2026
The formula
Percentage change formula
percentage change = (new value − old value) ÷ old value × 100
- new value
- the value after the change
- old value
- the starting value, which is always the base
A positive result is an increase and a negative result is a decrease.
Worked example: an increase
Worked example
A price rises from 80 to 100
| Step | Calculation | Value |
|---|---|---|
| Change | 100 − 80 | 20 |
| Divide by the old value | 20 ÷ 80 | 0.25 |
Result: up 25%
Worked example: a decrease
Worked example
A price falls from 100 to 80
| Step | Calculation | Value |
|---|---|---|
| Change | 80 − 100 | −20 |
| Divide by the old value | −20 ÷ 100 | −0.20 |
Result: down 20%
Why the two directions differ
Going from 80 to 100 is +25%, but going back from 100 to 80 is −20%. The base changes, so the percentages are not mirror images. This is why a 20% drop needs a 25% rise to get back to where you started.
Common mistakes
Common mistake
- Dividing by the new value instead of the old one.
- Mixing up percentage change with percentage points: a rate moving from 4% to 5% is up 1 percentage point, but up 25% in relative terms.
- Using a starting value of zero. The change is undefined because you cannot divide by zero.