Increase against what
Every percentage change needs a base, and reports go wrong when the base is left unstated. "Sales rose 50%" is only meaningful with the starting figure attached — a 50% rise on 20 units is not the same news as a 50% rise on 20,000.
Rises and falls are not symmetric
| Change | Reverse needed | | --- | --- | | +10% | −9.1% | | +25% | −20% | | +50% | −33.3% | | +100% | −50% |
A stock that falls 50% needs a 100% rise to recover. This asymmetry is not a quirk of the arithmetic; it is what percentages mean.
Use the multiplier when chaining
If you need to apply several changes in sequence, multiply the factors rather than adding the percentages. Three consecutive 10% rises are ×1.331, a 33.1% total — not 30%.
Questions
Why is reversing a rise not the same percentage?+
Because the base changes. Going from 100 to 150 is a 50% rise; going back from 150 to 100 is a 33.3% fall. The rise is measured against 100 and the fall against 150. This is the single most common percentage mistake in reporting.
What does the multiplier column mean?+
The number you multiply by to get from one value to the other — 1.5 for a 50% rise. Multipliers compose correctly where percentages do not: two 50% rises are ×1.5 × ×1.5 = ×2.25, a 125% total rise, not 100%.
Can the starting value be negative?+
Yes. The change is measured against the absolute size of the starting value, so a move from −200 to −100 reads as a 50% improvement rather than a sign-confused figure.
What if I start from zero?+
Then percentage change is undefined and a dash is shown. Any increase from nothing is infinite in percentage terms, which is why revenue growth charts starting at zero are meaningless.