Percentage point: distinguish a difference from a percent change

If a number was already a percentage, “it went up by ten percent” may leave a question about the intended calculation. Ask for the starting value, ending value and unit of change. We use invented puzzle-card counts, not outcomes from a real household or ADHD study.

From 40% to 50%: two ways to describe the change

Imagine that 40 of 100 puzzle cards in a shared collection had printed labels at one check. At a later check, 50 of the same 100 had labels. The labeled share changed from 40% to 50%.

Subtracting those percentages gives an increase of 10 percentage points. The relative increase from the starting share is 10 divided by 40, multiplied by 100: 25%.

“Up 10 percentage points” and “up 25% relative to the starting share” describe different calculations using the same invented values. Neither means twenty-five additional cards acquired labels. The count changed by ten cards.

A teen writing the collection note chooses the direct version: “Labeled cards increased from 40 of 100 to 50 of 100.” A parent can read the underlying counts without needing to guess which use of “percent” was intended.

Keep the starting point attached

Suppose a different fictional collection changes from 20% labeled to 30% labeled. That is also a ten-percentage-point increase, but the relative increase is 50%: 10 divided by 20, multiplied by 100.

The common percentage-point difference does not make the starting collections equivalent. Equally, a larger relative percentage does not reveal how many cards changed unless the collection sizes are known.

These simple examples keep the collection size fixed. Do not assume a real report uses the same people, objects or total at each measurement; look for that information.

A before-and-after wording card

What the percentage describes:
Starting percentage and its underlying count/total:
Ending percentage and its underlying count/total:
Difference in percentage points:
If reporting relative percent change, the starting value used:
Whether the group and time frames are comparable:
Plain sentence with both values visible:

If the starting percentage is zero, the relative-change calculation shown above would divide by zero. Do not report a finite relative percent change using that calculation. You can still state the starting and ending percentages and their percentage-point difference.

Explain the numbers without ranking people

A child can ask how many objects the percentage refers to. A partner can request the original values without having to reconstruct an entire chart. A grandparent might prefer the count-based sentence. None of these choices turns an arithmetic comparison into an assessment of a family member.

For a health headline, finding the correct unit is only a reading step. It does not establish a cause, the quality of the study or what a result means for a particular person's care.

Source

[1] Office for National Statistics. Percentages and percentage points. ONS Service Manual. Page-specific publication date not stated; accessed September 6, 2026. Percentage-point definition supports [1]. Puzzle-card examples and calculations are original; no ONS example is reproduced.

Related guides

• Relative risk

  : find the reference behind a ratio.

• Absolute risk

  : retain the underlying event chance and context.

• Sample size

  : identify which count supports the result.

• Causation

  : separate numerical change from an explanation.