Percentage points measure the gap between two percentages; percentage change compares the change with the starting value. From 40% to 50%, the increase is 10 percentage points, or 25% relative to the starting rate. Identify what the question asks before choosing a calculation.
Read the unit before you calculate
Imagine a fictional school survey: 40% of respondents chose a science club in one year, and 50% chose it the next year. Two students describe the same change:
- Mika says the share rose by 10 percentage points.
- Ren says the share rose by 25% relative to the original share.
Both are correct. They are answering different questions. The first describes the gap on a percentage scale; the second compares that gap with the starting rate.
Eurostat uses “percentage point” to distinguish a difference between percentages. Its separate percentage-change definition compares the later value with the earlier value. These definitions underpin the calculations below; all survey and practice examples in this guide are original illustrations, not official entrance-exam questions.
Keep two calculations on your scratch paper
| What the question asks | Calculation | How to label the answer |
|---|---|---|
| The difference between two percentages | New percentage minus original percentage | Percentage points |
| The increase or decrease relative to the starting value | (New value minus original value) ÷ original value × 100 | Percent increase or decrease |
| The extra number of items | New count minus original count | The original unit, such as questions or students |
For percentage change, the original value must be nonzero. When the starting value is positive, a negative result indicates a decrease. In ordinary school exercises, you can write either “−20% change” or “20% decrease”; avoid writing “−20% decrease,” which mixes two signals for direction.
Worked example 1: the same survey, two valid answers
The science-club share rises from 40% to 50%.
Question A: By how many percentage points did it rise?
Subtract the percentages: 50 − 40 = 10 percentage points.
Question B: What was the percentage increase in the share?
Compare the change with the original share: (50 − 40) ÷ 40 × 100 = 25%.
Check the second answer by working forward: 40% × 1.25 = 50%. If you instead increased 40% by 10% of itself, you would get 40% × 1.10 = 44%, which does not match the question.
Notice what this example does not tell you: the number of students who chose the club. The two survey totals might differ. A larger percentage alone does not prove a larger count.
Worked example 2: question counts are not percentage points
You finish 24 practice questions on Saturday and 30 on Sunday.
The difference is 30 − 24 = 6 questions. Relative to Saturday, you completed 6 ÷ 24 × 100 = 25% more questions.
Calling this “6 percentage points” would be incorrect: the given values are counts, not percentages. You would need a stated total for each day before comparing completion percentages.
For example, if each day’s target was 40 questions, the completion rates would be 24 ÷ 40 × 100 = 60% and 30 ÷ 40 × 100 = 75%. That is a 15-percentage-point rise in completion rate. Always name what you are comparing.
Worked example 3: the reverse trip uses a different starting value
Suppose a fictional survey share later falls from 50% back to 40%.
The drop is 10 percentage points. The relative decrease is (50 − 40) ÷ 50 × 100 = 20%.
Why not 25%, like the earlier rise? Because the starting rate is now 50%, not 40%. An increase and the reverse decrease can cover the same gap while having different percentage-change magnitudes.
A quick check is 50% × 0.80 = 40%.
Four checks before you pick an answer
- Circle the requested unit. Is it percentage points, percent change, or a count?
- Underline the starting value. “From A to B” means A is the baseline.
- Write the units beside your arithmetic. For example: “12 percentage points,” not an unlabeled “12.”
- Check the result against the ending value. Apply your increase or decrease to the starting value and see whether you arrive at the stated result.
If the prompt only says “What is the increase?” and supplies percentage values, the wording may be ambiguous. In your own notes, state both interpretations and label each. On a practice item, inspect its exact wording and explanation rather than assuming that every subtraction deserves a percent sign.
Try this four-question self-check
Cover the answers below and write both a number and its unit.
- A fictional survey share rises from 32% to 40%. Give the percentage-point increase and the relative percentage increase.
- Your completed-question count falls from 45 to 36. What is the percentage decrease?
- A rate of 60% increases by 5% of its starting value. What is the new rate, and how many percentage points did it rise?
- In group A, 18 of 30 students choose an activity. In group B, 28 of 40 choose it. What is the percentage-point difference between the groups’ shares?
Answers and reasoning
- 8 percentage points; 25% increase. Subtract 40 − 32 = 8, then divide the gap by the original 32: 8 ÷ 32 × 100 = 25%.
- 20% decrease. The drop is 9 questions; 9 ÷ 45 × 100 = 20%. Dividing by 36 would use the wrong baseline.
- 63%; 3 percentage points. Five percent of 60 is 3, so 60% × 1.05 = 63%. A rise of 5 percentage points would have produced 65% instead.
- 10 percentage points, with group B higher. Group A’s share is 18 ÷ 30 = 60%; group B’s is 28 ÷ 40 = 70%. Compare the percentages, not just the counts of 18 and 28. These are different groups, so describe a difference rather than implying a change over time.
If you missed a question, record the reason in your entrance-exam mistake log: wrong unit, wrong denominator, or skipped conversion. Then invent a fresh pair of numbers and explain the method without looking. The 20-minute active-recall routine can give that check a place in your next session.
Put the distinction into practice
Try the free PasadoPH diagnostic, and pay attention to the wording of any percentage question you encounter. All current exams, regular explanations and progress tools are free during launch; Premium AI coaching is optional. This guide does not predict the questions or scoring rules of a particular university’s exam.
Common questions
Is an increase from 40% to 50% a 10% increase?
It is a 10-percentage-point increase. Relative to the starting 40%, the increase is 10 divided by 40, or 25%. A 10% relative increase from 40% would instead give 44%.
Can I use percentage points when the values are counts?
Not directly. A change from 40 questions to 50 questions is 10 questions, or a 25% increase. Percentage points describe differences between percentages, so first convert counts to percentages of clearly specified totals if the question requires that comparison.
Which value goes in the denominator for percentage change?
Use the original value. For a change from 50 to 40, the signed percentage change is (40 minus 50) divided by 50, multiplied by 100, giving minus 20%, or a 20% decrease.
What if the starting value is zero?
The usual percentage-change formula is undefined because it would divide by zero. If a rate goes from 0% to 8%, you can report an increase of 8 percentage points, but not a finite relative percentage increase using that formula.
Sources & further reading
Sources checked for this guide on November 3, 2026. Admissions requirements can change; confirm your application cycle with the university.
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