Percentage points

An interest rate that goes from 2% to 3% rises by one percentage point, which is a 50% increase in the rate.

"The rate went up 1%" when it went from 2% to 3%

A savings rate goes from 2% to 3%, and someone says it went up 1%. It sounds right. It is not, at least not in the sense the word percent usually carries. The rate went up by one percentage point. Measured against the old rate it went up 50%, because 1 is half of 2. Two different numbers, both correct, for two different questions.

40% came last year, 50% this year

Last year 40% of a club's members came to the annual meeting. This year 50% came. Did attendance go up by 10% or by 25%? Both numbers describe the same change, and they answer different questions. The first is a subtraction: 50 − 40 = 10 percentage points. The second is a percent change: the share rose by 10 out of an original 40, and 10 ÷ 40 = 25%.

Merriam-Webster defines a percentage point as one hundredth of a whole and gives the example of interest rates rising one percentage point from 6.5 percent to 7.5 percent. A percentage point is the unit you use when you subtract one percent from another. The word percent, used for the change, should mean a percent change, worked out against the original, as in the previous unit.

The two bars show 40% (2 of 5) and 50% (1 of 2). The gap between them is 10 percentage points of the whole bar. Measured against the shorter bar, the gap is a quarter of it, so the second share is 25% bigger than the first.

Small starting percents stretch the gap

When the starting percent is small, the two descriptions drift far apart. A rate that goes from 2% to 3% rises by 1 percentage point, but by 50% of itself. A rate that goes from 0.5% to 1% rises by half a point, and doubles. A headline that says "a 50% rise" sounds dramatic; "up one point, from 2% to 3%" sounds mild. Both are true. A careful reader looks for the two actual percents before deciding which matters.

The mix-up also runs the other way. If a test pass rate was 60% and "rose 5%", the writer might mean 65% (5 points) or 63% (a 5% increase, 60 × 1.05). When you write, say "percentage points" for a subtraction and keep "percent" for a ratio of change, and the ambiguity disappears.

From 8% to 6%: 2 points, or a quarter

Going from a point change to a percent change: divide the point change by the original percent. From 8% to 6% is a fall of 2 points, and 2 ÷ 8 = 25%, so the rate fell by a quarter. Going the other way: a 30% rate that rises by 10% (a percent change) becomes 30 × 1.1 = 33%, a rise of 3 points.

A longer example. In a made-up survey, 45% of people said they cycle to work last year and 54% say so this year. The share rose by 54 − 45 = 9 percentage points. As a percent change, 9 ÷ 45 = 0.2, so the share of cyclists grew by 20%. If 2,000 people were asked both times, that is 900 people last year and 1,080 this year, and 1,080 ÷ 900 = 1.2 confirms the 20%. Counting people gives the same percent change as comparing the shares, as long as the group size stays the same.