A 50 % Rise Is Undone by a 33 % Fall
Published 10/5/2026 · 3 min read · Everyday calculators
Lena Hoffmann — Science & education writer at OneKitly
Mathematics · Physics
Checked against 2 sources
A percentage change is the difference divided by where you started, so the starting point decides the answer. From 50 to 75 the difference is 25 and the base is 50: +50 %. From 75 back to 50 the difference is still 25, but the base is now 75, so it is −33.3 %. Nothing about the movement changed; only what it was measured against did. The general rule follows from that: a rise of p is undone by a fall of p ÷ (1 + p), so +25 % needs −20 %, +50 % needs −33.3 % and +100 % needs −50 %. This is why a share that halves must double to recover, and why a headline pairing a percentage rise with a percentage fall is comparing two numbers that were never on the same scale.
Going from 50 to 75 is +50 %. Coming back from 75 to 50 is −33.3 %. The move is the same 25 units both times; the base is not.
Two rises in a row do not add
Ten per cent followed by another ten per cent is not twenty: the second is measured on a base that the first already raised, so 100 becomes 110 and then 121, an increase of 21 %. The gap grows with the size of the steps — three rises of 20 % give 72.8 %, not 60 %. The reliable method is to multiply the factors rather than add the percentages: 1.10 × 1.10 = 1.21, and 1.20³ = 1.728. Anyone summing a column of monthly percentage changes to get an annual one is producing a number that is always wrong and always in the same direction.
A rise from zero has no percentage
Dividing by the starting value fails when the starting value is zero, and no convention rescues it: going from 0 to 5 is not an infinite increase, it is a change for which relative change is undefined. The same problem arrives quietly when the base is merely small — a move from 1 to 5 is +400 %, and a report that mixes such lines with normal ones invites the reader to treat the largest percentage as the most important change. Where a base can be zero or near it, report the absolute difference and leave the percentage column empty rather than filling it with a symbol.
| Rise | Fall needed to return |
|---|---|
| +25 % | −20.0 % |
| +50 % | −33.3 % |
| +100 % | −50.0 % |
| +300 % | −75.0 % |
Worked with our own calculator
Percentage increase calculator
Given
- Original value
- 50
- New value
- 75
Result
- Increase
- 50%
- Absolute change
- 25
These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.
Run it on your own figures →Frequently asked questions
- Is "three times more" the same as "three times as much"?
- Read literally they differ by one whole unit of the original — three times more than 10 would be 40, while three times as much is 30 — but in ordinary use most writers mean the second and most readers understand the second. The phrase is therefore ambiguous rather than wrong, and the cure is not to argue about it but to avoid it: write "rose from 10 to 30" and no interpretation is needed. The same applies to "a 200 % increase", which means tripling and is regularly written when doubling was meant.
- Why do two sources report different increases for the same event?
- Almost always because they chose different bases. Comparing this month with last month, with the same month a year ago, or with the average of the preceding twelve gives three legitimate and quite different percentages from one set of figures, and each of them can be quoted honestly. The way to compare two reports is to ignore the percentages entirely at first, find the two raw numbers each is built on, and only then decide which comparison answers the question you actually have.
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