Percentage Points vs Percentage Increase

One move, two true descriptions

A savings rate goes from 5% to 7%. The gap is 7 − 5 = 2, so the rate rose by 2 percentage points. That subtraction does not care how large the starting rate was. A move from 90% to 92% is also 2 percentage points.

The percentage increase asks a second question: how big is that gap compared with the rate you had before? For the savings rate, 2 / 5 × 100 = 40%. The rate is 40% larger than it was. For the move from 90% to 92%, the same 2-point gap is only 2 / 90 × 100, about 2.2222%. The points match. The relative increases do not.

Where the mix-up changes a decision

A test average that moves from 70% to 77% improved by 7 percentage points. Relative to 70, the increase is 10%. Saying “scores increased 7%” is ambiguous, and many readers will hear “7 percent of the old score,” which would have landed on 74.9, not 77.

Mortgage quotes, unemployment rates, and fee schedules run into the same wording. “Up 1%” might mean one percentage point or a 1% relative bump. Write “1 percentage point, from 6% to 7%” when you mean the subtraction. Write “a 10% increase, from 6% to 6.6%” when you mean the formula.

Run 5 to 7 in the calculator and you will see the relative increase, 40%. The percentage-point gap is the plain subtraction, 2.

Points are not the percentage difference either

Percentage difference would compare 5 and 7 against their average of 6, giving about 33.3333%. That third number is useful when the two rates are peers. It is still not “2 percent,” and it is still not the increase from the earlier rate. Pick the baseline on purpose: the old rate, the average, or a simple point gap.