Understand why subtracting two percentages gives percentage points, while relative percentage change compares their difference with the original percentage as its base.
Open Percentage Change CalculatorQuick answer
In short
- Percentage points: Subtract one percentage from the other. A change from 20% to 25% is an increase of 5 percentage points.
- Relative change: Divide the difference by the original percentage, then multiply by 100. The same move from 20% to 25% is a 25% relative increase.
- Calculate: For a signed relative change between a positive original value and a new value, use the Percentage Change Calculator.open Percentage Change Calculator
- Keep the formulas: Review the printable percentage formula sheet and its warnings about bases and undefined changes.open Percentage Formula Cheat Sheet
The same two rates can describe two different changes
A percentage is already a ratio on a scale of 100. If you subtract two percentages, the result is measured in percentage points. If you instead ask how large that change is relative to the original percentage, the result is a percentage change. The labels must not be interchanged, because they answer different questions.
This is a difference in percentage points, not a second percent-of-percent calculation. The sign indicates upward or downward movement.
25% − 20% = +5 percentage points. For relative change, (25 − 20) ÷ 20 × 100 = +25%. Both are correct, but a five-point increase and a 25% relative increase are not the same statement.
Relative change requires a defined starting base
For this expression the original rate must be nonzero. When the original rate is zero, the relative percent change is undefined; the percentage-point difference can still be reported.
The difference is 9% − 10% = −1 percentage point. The relative change is (9 − 10) ÷ 10 × 100 = −10%. A one-percentage-point fall is not the same as a one-percent relative fall.
A starting rate of zero needs different wording
Moving from 0% to 5% is an increase of five percentage points. You cannot calculate the relative percentage increase using the ordinary old-base formula, because dividing by the original zero is undefined. Report the point difference and the two observed rates rather than claiming an infinite or arbitrary percentage increase.
Percentage difference is another distinct comparison
An unsigned percentage difference between two nonnegative values often uses their arithmetic mean as a denominator. That symmetric measure differs from signed percentage change, which uses an explicitly named old value. Before reporting any result, identify whether the question is about two rates, a directional change, or a symmetric comparison.
Write “percentage points” after the direct subtraction of two rates, and “percent change” after a defined old-base division. Do not remove the minus sign when direction matters. The Percentage Change Calculator focuses on the signed old-base comparison, not percentage-point subtraction.
- Ask whether the inputs are percentages already, or ordinary measured amounts.
- For two reported rates, show both the percentage-point difference and the relative change when either could be misunderstood.
- Name the original rate before dividing; use the same percentage scale for both rates.
- If the old rate is zero, report the point difference and avoid an undefined relative-change number.
- Round after the calculation so closely spaced values are not distorted.
Next step: understand, calculate, or practise
Use the existing Understanding Percentages reference for the underlying percent-of-a-whole idea. Use the Percentage Calculator for arithmetic with a chosen base, the Percentage Change Calculator for signed old-to-new changes, and the printable Formula Cheat Sheet or Practice Worksheet for reusable learning and examples.
Percentage points and relative change
Is 20% to 25% a five-percent increase?
It is five percentage points higher, or 25% higher relative to the original 20%. Calling it simply “five percent higher” is ambiguous and usually misleading.
Can I calculate relative change from 0% to 5%?
Not with the standard old-base formula, because the original rate is zero. The increase is five percentage points.
Is percent difference the same as percent change?
Not necessarily. Directional change normally uses the original value as a base. Unsigned percent difference can use the mean of two nonnegative values instead.
When is a percentage-point comparison useful?
When comparing two quantities already expressed as percentages, such as two measured proportions, a point difference makes the absolute change in the rate explicit.
Reference check
Sources and references
These references provide background context for the topic. They do not replace professional advice or official documents.
- Percentages and percentage points
UK Office for National Statistics, content style guide
- 3.2 Solve Percent Applications
OpenStax, Rice University
The difference between two rates is measured in percentage points. Relative percentage change uses the starting rate as its denominator, so it answers a different question and is undefined when that base is zero.
Use the tool instead
Use the matching calculator when you want to plug in your own numbers and get a result faster.
Open Calculator