The percentage change formula
Percentage change compares a new value with an original value. Subtract the original from the new value, divide by the original, and multiply by 100. A positive result is an increase; a negative result is a decrease.
Choosing the correct base
The denominator is the original value. If a price rises from 80 to 100, the increase is 20 divided by 80, or 25%. Reversing the journey does not produce a 25% decrease: moving from 100 back to 80 is a 20% decrease because the base is now 100.
Percentage points are different
If an interest rate moves from 5% to 7%, it rises by 2 percentage points. Relative to 5%, the percentage increase is 40%. State clearly which measure you mean.
Common mistakes
- Dividing by the new value instead of the original.
- Treating percentage points and percent change as identical.
- Ignoring a negative sign.
- Calculating percentage change from an original value of zero, which is undefined.
- Rounding too early in a multi-step calculation.
A quick verification
After calculating, apply the percentage change to the original value. The adjusted result should return the new value, allowing for rounding. This simple reverse check catches many input errors.
Use enough decimal places for the decision you are making, and report both values alongside the percentage when context matters.