Three percentage calculations in one place: a percentage of a value, one value as a share of another, and the percentage change between two values.
The three modes exist because "percent" describes three different operations and the German questions for them are distinct — wie viel Prozent sind, wie viel ist X Prozent von, and um wie viel Prozent. Percentage of multiplies; share divides; change subtracts first, then divides by the starting value. The base of a change is the original figure, always, which is why a rise and an equal-looking fall do not cancel out. Results are formatted for the language the page is being viewed in, so a German page shows a comma as the decimal separator.
Percentages that mislead
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The base of a change is the starting value:
from 200 to 250 is a rise of 25%; from 250 back to 200 is a fall of 20%. The same absolute step, two different percentages.
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Prozent and Prozentpunkte are different:
a rate moving from 5% to 7% has risen two percentage points, or forty per cent. Both are true and they are not interchangeable.
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A rise then an equal fall does not return to the start:
100 raised by 10% then reduced by 10% is 99, because the base changed in between.
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Percentages of different-sized groups cannot be averaged:
combine the underlying counts instead, or a rate from three cases will carry the same weight as one from three thousand.
One word, three genuinely different operations
"Percent" quietly covers three separate calculations, and the [msm_tool slug="prozentrechner"] keeps them as three distinct modes rather than one blended box: a percentage of a value, one value's share of another, and the percentage change between two values. Percentage-of multiplies, share divides, and change subtracts the two values first before dividing by the starting one — three different pieces of arithmetic that happen to share a single everyday word.
The base of a change is always the starting value
Going from 200 to 250 is a rise of 25%, and going back from 250 to 200 is a fall of 20% — the identical absolute step in opposite directions, expressed as two different percentages, because each one is measured against a different starting point. That asymmetry is built into what percentage change actually means, not an inconsistency in the calculation.
Prozent and Prozentpunkte answer different questions
A rate moving from 5% to 7% has risen two percentage points, which is also a forty per cent increase relative to where it started — both statements describe the same move correctly, and treating them as interchangeable is what makes a change look far larger or far smaller than it actually was.
Formatted for the page it is read on
Results follow the number formatting of the language the page is being viewed in, so a German page shows a comma as the decimal separator rather than a full stop, matching the convention readers of that page actually expect rather than a fixed international default.
Percentages cannot simply be averaged across different sample sizes
A fifty per cent rate from three cases and a fifty per cent rate from three thousand are not equally solid evidence, and averaging the two percentages directly gives the small sample exactly the same weight as the large one. Combining the underlying counts first, then taking the percentage of that combined total, is what actually reflects the full picture rather than treating every rate as equally trustworthy.