Compare percentages and percentage points
Name the denominator and distinguish a change in a rate from a relative change.
Follow the method ↓
The answer in 30 seconds
Percentage points describe the difference between two percentages. A relative percentage change compares that difference with the starting value. The two answers can be numerically very different.
For a rate rising from 20% to 25%, the change is 5 percentage points. Relative to the initial 20%, it is a 25% increase: (25 − 20) ÷ 20 × 100. State the measure, population and dates alongside either figure.
Examples to adapt
A support rate moving from 20% to 25% rose by five points, not five percent relative.
Check the original price and whether successive discounts use different bases.
Inspect the axis and denominators before repeating a stated change.
Try your own values
Percentage points and relative change
Enter two rates between 0 and 100%. The calculation distinguishes their difference in percentage points from their relative change.
Calculated in your browser without sending or saving values. Results rounded to four decimals; very small differences may appear as zero.
Combine two groups without averaging their percentages
A combined rate uses the total number of cases divided by the total population. Both groups must use the same definition and period, and must not overlap.
| Group | Cases / population | Rate |
|---|---|---|
| A | 10 / 20 | 50 % |
| B | 90 / 100 | 90 % |
| Combined | 100 / 120 | 83.33 % |
The simple average (50 + 90) ÷ 2 = 70% gives equal weight to the two groups. The combined rate gives equal weight to each observation: (10 + 90) ÷ (20 + 100) × 100 ≈ 83.33%.
Calculated only in this browser. No entries are sent or saved. Rounding to two decimals does not measure uncertainty; this tool does not validate group comparability.
Follow the method
- 1Identify the quantities
Record the original rate, new rate, population and period.
- 2Calculate point difference
Subtract the original percentage from the new percentage.
- 3Calculate relative change
Divide the difference by the original percentage, when it is non-zero, then multiply by 100.
- 4Label the result
Write either percentage points or percent relative change and show the denominator.
A closer look
One change, two ways to measure it
Fictional example: in two groups of 100 responses each, favourable responses rise from 20% to 25%. Group size is held constant in this exercise.
| Question | Calculation | Correct interpretation |
|---|---|---|
| Difference between the rates? | 25 − 20 = 5 | +5 percentage points |
| Increase relative to the starting rate? | (25 − 20) ÷ 20 × 100 = 25 | +25% relative change |
| Decrease needed to return from 25% to 20%? | (20 − 25) ÷ 25 × 100 = −20 | −20%, using 25 as the new base |
Combine group counts when calculating a pooled proportion. Ten favourable responses out of twenty and ninety out of one hundred give 100 out of 120, approximately 83.3%. The simple average of the two rates, 70%, answers a different question.
Do a 10% increase and a 10% decrease cancel out?
No: 100 becomes 110 and then 99. The second change uses 110 as its base. Multiply successive change factors: 1.10 × 0.90 = 0.99.
A checklist to keep
Use these checks to record what you found. The grid supports a decision; it does not make one for you.
| Check | What to examine | Action |
|---|---|---|
| Start | What is the original rate? | Record |
| End | What is the new rate? | Record |
| Points | End minus start? | Subtract |
| Relative | Difference divided by start? | Calculate |
| Base | Same population and period? | Check |
Read the checklist directly in the table.
What to check
A change in population can make rates less comparable.
Relative change from zero needs a different description; division by zero is undefined.
Rounded input rates can make a derived relative change approximate.
Common questions
Is 20% to 25% a 5% increase?
It is a five-percentage-point increase, or a 25% increase relative to the starting 20%.
Why name the denominator?
Because the same count can represent a different percentage when the group size changes.
Sources and documentation
Documentation consulted on . Examples are illustrative; interfaces and results may change.