Math · 4 min read
Percentage points vs. percent change: SAT examples
Published October 29, 2026
The useful idea
A change from 10% to 15% is 5 percentage points. Relative to the original 10%, it is a 50% increase. The words “percentage points” and “percent increase” ask for different calculations.
Worked example
At a school, 10% of students joined a club last year and 15% joined this year. How much did the participation rate increase?
A tempting wrong move
Subtract 15 − 10 and answer “5%.”
The subtraction is useful, but the result is 5 percentage points. Calling it a 5% relative increase changes the unit of the answer.
- Read the requested unit. For percentage points, subtract the two rates: 15% − 10% = 5 percentage points.
- For percent increase in the rate, compare the change with the original rate: 5 ÷ 10 = 0.5.
- Convert 0.5 to 50%. Check the meaning: 15% is one and a half times 10%, so the rate rose by half of its original value.
A rule to reuse
Percentage-point change = new rate − old rate. Relative percent change = (new rate − old rate) ÷ old rate × 100%. Say which one you mean.
Try the idea
A survey response rate rises from 20% to 25%. What are the percentage-point change and the relative percent increase?
Show the reasoning
It rises 5 percentage points. Relative to 20%, the increase is 5 ÷ 20 = 25%.