Percentage change uses a starting value. Percentage difference uses the average of two values. Choose change when asking how much a value rose or fell. Choose average-based difference when comparing two nonnegative values without treating either as the baseline.
The baseline is the amount you divide by. An absolute change of 20 units is a 25% increase from 80, but a 20% increase from 100. Always name the starting value when reporting a change.
Compare the denominators
| Question | Calculation |
|---|---|
| How much did a positive starting value A change to B? | (B − A) ÷ A × 100 |
| How far apart are A and B relative to their average? | |A − B| ÷ ((A + B) ÷ 2) × 100 |
| How far apart are two percentage rates? | Subtract the rates for percentage points |
Percentage change can be positive or negative. Average-based percentage difference uses an absolute difference, so the result is nonnegative and stays the same when the two values swap places.
Example: comparing 80 and 100
For average-based percentage difference, the gap is 20 and the average is 90:
For change from 80 to 100, use 80 as the starting value:
For change in the opposite direction, from 100 to 80, use 100 as the starting value:
These answers are compatible because they use different reference amounts. A 25% increase followed by a 20% decrease returns 80 to its starting value: 80 × 1.25 × 0.80 = 80.
Percentage points are a direct subtraction
If a rate moves from 20% to 25%, it rises by 5 percentage points. Relative to the original 20%, it has increased by 5 ÷ 20 × 100 = 25%. The average-based percentage difference is about 22.22%.
Label the result so readers know which comparison you made. Saying only “a difference of 5%” leaves the baseline unclear.
The debt-to-income calculator gives another ratio expressed as a percentage. When comparing two DTI results, use percentage points for the direct gap and percentage change for the relative change.
What happens with zero?
- Change from zero: undefined, because the starting value is the denominator. Moving from 0 to 10 is not a 100% increase.
- Change from a positive value to zero: −100%.
- Average-based difference between zero and a positive value: 200%.
- Difference between two zeros: undefined under this formula because the denominator is zero.
The average-based comparison described here applies to nonnegative values, and the percentage-change examples use a positive starting value. Negative baselines or averages can make the result misleading. Use the definition required by your subject when values are negative, and express both values in the same unit.
When percentage error is the right term
If you are comparing a measurement with an accepted reference value, your assignment may require percentage error instead. That calculation uses the reference value rather than the average. Check the definition required by the experiment or report.
References and method
- Clemson University: percentage error and percentage difference, for comparing measurements using their average.
- U.S. Bureau of Labor Statistics: calculating percent changes, for the starting-value method.
Examples are calculated independently using the formulas shown. Report a calculation issue.