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A club's attendance rate rises from 20% to 30%. One announcement celebrates a 50% increase; another reports a ten-point increase. There is no disagreement in the arithmetic. The comparison has changed.
Start with an invented attendance example before working with abstract percentages. Of 100 invited members, 20 attended the first event and 30 attended the second. Keep the group size fixed for this first calculation.
The short answer
Subtract for points, divide for relative change.
Percentage-point change = new percentage minus starting percentage. Relative percent change = (new percentage minus starting percentage) divided by starting percentage, then multiplied by 100. From 20% to 30%, the results are +10 percentage points and +50%. Use the same units in both parts of the division, and name the starting value.
The method
Calculate both versions.
These calculations use invented attendance figures, not results from a real study or Cadence.
01
Write the two rates
The first event has 20 attendees out of 100 invited, or 20%. The second has 30 out of 100, or 30%. Label which is the starting value before doing anything else.
02
Subtract for percentage points
30% minus 20% equals 10 percentage points. This describes the distance between the rates. It does not say that attendance increased by only 10% relative to where it started.
03
Divide for relative change
The increase is 10, and the starting rate is 20. Divide 10 by 20 to get 0.5, then multiply by 100 to get 50%. In this fixed-size example, ten additional attendees are half of the original twenty.
04
Report the before and after
Write: attendance rose from 20% to 30%, a rise of 10 percentage points, or 50% relative to the starting rate. Often the before-and-after figures are the clearest part of the sentence.
The terminology
Two labels for two comparisons.
The European Union's data-visualization guidance distinguishes the arithmetic difference between percentages from a relative percentage change. Using percentage points for the former prevents a reader from having to guess which calculation you meant.
Two percentage points and two percent give different answers.
Start with an invented attendance rate of 40%. If it rises by 2 percentage points, the new rate is 42%: add 2 to 40. If it rises by 2%, the new rate is 40.8%: calculate 2% of 40, which is 0.8, then add that to 40. The first change is a 5% relative increase; the second is a 0.8 percentage-point increase.
At the same starting rate, a rise of 20 percentage points produces 60%. A rise of 20% produces 48%, because 20% of 40 is 8. You cannot exchange the labels just because both contain the word percentage.
Use this sentence pattern: the rate moved from [old]% to [new]%, a change of [new minus old] percentage points. Add the relative percent change when it answers the reader's question. If someone says only that a rate rose by two points, confirm that they mean percentage points rather than points on some other scale.
The common trap
The return trip uses a different starting value.
Now attendance falls from 30% back to 20%. The fall is still 10 percentage points. But the relative fall is 10 divided by 30, about 33.3%. It is not a 50% decrease because the starting value is now 30.
Unequal groups
More attendees can still mean a lower attendance rate.
Keep the invented first event at 20 attendees out of 100 invited, or 20%. Now compare it with a second event where 30 of 200 invited members attend, or 15%. The attendee count rose by 10, a 50% increase relative to 20. The attendance rate fell by 5 percentage points, a 25% decrease relative to 20%.
Both descriptions are true. They answer different questions: how many people came, and what share of invited people came? A report saying attendance rose by 50% would be incomplete if the reader needs to understand participation among everyone invited.
Write the count and rate together when the group sizes differ. These calculations describe the two events; they do not establish why attendance changed or whether either event was better. Check that the groups and measurement periods are comparable before drawing that conclusion.
Try it first
Check three claims before reading the answers.
These are invented arithmetic exercises. For each rate change, write the change in percentage points and the relative percent change. Then rewrite the announcement so it names the starting and ending values.
A rate rises from 4% to 5%. An announcement calls this a 1% increase. Is the label correct?
A rate falls from 50% to 40%. An announcement calls this a 10% decrease. What are the two correct descriptions?
An event had zero attendees last time and five this time. Can you report an ordinary relative percentage increase?
Check your work
Answers and the calculation behind each.
First: 5 minus 4 equals 1 percentage point. Then 1 divided by 4, multiplied by 100, equals 25%. Write: the rate rose from 4% to 5%, up 1 percentage point or 25% relative to the starting rate. A 1% relative increase from 4% would instead produce 4.04%.
Second: 40 minus 50 equals minus 10 percentage points. Then minus 10 divided by 50, multiplied by 100, equals minus 20%. Write: the rate fell from 50% to 40%, down 10 percentage points or 20% relative to its starting value.
Third: the absolute increase is five attendees. Dividing by the starting count of zero is undefined, so the ordinary relative percentage increase is not available. Report the before-and-after counts. If you also know how many people were invited each time, you can calculate the attendance rates and their percentage-point difference.
For your next chart or report, write the baseline beside every percentage change. If someone could mistake a count change for a rate change, include both the count and its denominator. Correct arithmetic is the beginning of interpreting a result, not proof that the change matters.
From the publisher
Keep following the question.
We make Cadence. This arithmetic is useful when reading any product's claims, including ours. Keep the starting value, group size and time period in view before deciding whether a reported change matters.
Put it into practice
Start it today, one lesson at a time.
If you want to keep going, Cadence turns what brought you here into a course with practice and saved progress. Learn at your own pace. Cadence is our app.
Not usually. A percentage point is a fixed step, such as a rate moving from 4% to 5%. A percent change is measured against the starting value, so that same move is a 25% increase. One percent of 4% would be only 0.04 percentage points.
Is 20% to 30% a ten percent increase?
It is a ten percentage point increase. Relative to the starting 20%, it is a 50% increase.
Why is the percentage decrease different on the way back?
The denominator changes. The fall from 30 to 20 is measured against 30, while the rise from 20 to 30 is measured against 20.
What if the starting value is zero?
Report the absolute change. The usual relative-change calculation requires dividing by the starting value and cannot be used when that value is zero.
Which version belongs in a headline?
Prefer an explicit before-and-after comparison. If you use a relative increase, include enough context for readers to identify the starting value.
See it in concrete terms
Explore example courses for your goal.
If the difference finally landed, these courses build the rest of the arithmetic around it.
