20% → 25%
The difference is 5 percentage points; the relative change in the rate is 25%. These expressions answer different questions.
DATA / CALCULATIONS
Calculate change, percentage points and a combined rate
Before writing “a 5% increase”, check what changed: a quantity, a rate or the composition of a population. An arithmetic result alone does not establish that two series are comparable.
These three tools separate operations that are often confused. Enter non-negative numbers up to 1 000 000 000 000, with no more than eight decimal places. Either a comma or a dot can be the decimal separator; spaces can group thousands. Prefilled values are calculation examples, not study data.
1. Change in a quantity
Compare values in the same unit, with compatible coverage and periods. Absolute difference keeps the original unit; relative change uses the initial value as its base.
Formula used
difference = final − initial; change (%) = 100 × (final − initial) / initial; index = 100 × final / initial
2. Difference between rates
Enter rates on a 0–100 scale: use 20 for 20%. Subtracting gives percentage points. Relative change expresses a proportional change in the rate.
Formula used
gap (points) = final rate − initial rate; relative change (%) = 100 × (final rate − initial rate) / initial rate
3. Combine two populations
Use whole counts: observed cases and the corresponding population. Combine only disjoint groups with the same definition and compatible periods. A person present in both groups would be counted twice.
Formula used
combined rate (%) = 100 × (cases A + cases B) / (population A + population B)
Four interpretation traps
100 → 120 → 100
The increase is 20%, followed by a decrease of 16.66666667%. The second operation uses 120 as its base, so the percentages cannot simply be added.
1/10 and 45/90
The rates are 10% and 50%. If the groups can be combined, the result is 46/100 = 46%, not the simple average of 30%.
Zero is not missing data
An observed zero can be a count; an unknown value must not be replaced with zero. Change from a zero base has no defined relative percentage.
A repeatable method
Define the objects
Record indicator, unit, population, dates, series code and version. Check definitions before calculating.
Keep original values
Retain numerators, denominators, source file, extraction date and transformations.
Calculate and review
Show the formula, result unit, rounding and what the figure does not establish.
Keep conclusions proportionate
A descriptive increase proves neither causation nor statistical significance.
Practical questions
Can two percentages be added?
Not to combine successive changes. Multiply the factors: +20% then +10% gives 1.2 × 1.1 = 1.32, or +32%.
Why is a negative base rejected?
Relative change with a negative base can be read in reverse. This calculator covers non-negative quantities; show a difference in units for balances that cross zero.
Can I average two rates?
Only when appropriate weights allow it. For a population rate, use numerators and denominators of comparable, non-overlapping groups.
Is the difference statistically significant?
The calculator performs arithmetic. It does not analyse sampling design, margins of error or confidence intervals.
Is a printed value of 20.0 exact?
No. Published rounding can conceal a range of values. Do not infer more precision than the original data support.