These questions compare an old percentage with a new percentage and ask for one of two different measures. Decide whether the wording requests a percentage-point difference or a change relative to the old rate before you calculate.
Name the measure, then calculate
For percentage points, subtract the two rates directly. Use new rate - old rate for a signed change, or subtract the smaller from the larger when the direction is already stated. For example, a rise from 18% to 24% is 24 - 18 = 6 percentage points. The percent signs belong to the rates, while the difference is named in percentage points.
For relative percent change, first find the point difference, then divide it by the old rate and multiply by 100. With the same rise, 6 ÷ 18 × 100 = 33.3% to one decimal place. The old rate is the base because the question asks how large the change is compared with where it started. For a fall, use old rate - new rate in the numerator when reporting the size of the decrease.
| Requested measure | Form |
|---|---|
| Rise in percentage points | New rate - old rate |
| Fall in percentage points | Old rate - new rate |
| Relative percent rise | (new rate - old rate) ÷ old rate × 100 |
| Relative percent fall | (old rate - new rate) ÷ old rate × 100 |
The traps
| Tempting route | How to reject it |
|---|---|
| Attach a percent sign to the direct point gap | A direct subtraction measures percentage points. A relative percent requires one more step: divide that gap by the old rate. |
| Give the relative percent when percentage points are requested | Both measures can describe the same movement, but they answer different questions. Follow the named measure and use direct subtraction for points. |
| Report the new rate as the relative increase | The new rate includes the entire old rate as well as the growth. Relative increase describes only the extra part compared with the old rate. |
| Use the new rate itself as the size of the change | A final rate is a level, not a change. Find the difference between the new and old rates first. |
| Divide by the new rate | Relative change is measured from the starting point, so the denominator is always the old rate. |
Try it
Participation in a school club rises from 42% to 51%. By how many percentage points did it rise? Enter the number of percentage points.
A factory's defect rate falls from 8% to 6%. What is the relative percent decrease? Enter the number of percent.
Solar power's share of a site's energy rises from 12.5% to 15%. What is the rise in percentage points? Enter the number of percentage points.