Percentage Change
How much a number rose or fell between two points.
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Formula
How the calculation works
A percentage change is measured against the starting point, so the denominator is the old value and not the new one. Going from 250 to 310 is a move of 60, and 60 over 250 is 24%. Dividing the same 60 by the new 310 gives 19.4%, which is the most common slip in the whole topic. A fall carries a minus sign, so 250 down to 200 is -20%, and the starting value is used as a positive size whatever its sign.
The same absolute move is a different percentage depending on the base. Sixty is 24% of 250 but only 6% of 1,000, so a rise looks dramatic on a small base and modest on a large one. Two changes of the same size should never be compared without checking what they are a change of.
Percentage changes do not cancel. Up 25% and then down 25% leaves you 6.25% below where you started, because the fall is taken on the larger number: 250 becomes 312.50 and then 234.38. A 50% fall needs a 100% rise to recover. The tool stops when the starting value is zero, since there is no percentage change from nothing.
Common mistakes
- Dividing the difference by the new value instead of the old. A move from 250 to 310 read as 60 over 310 is 19.4%, but the true change is 24%.
- Adding successive changes. A rise of 25% followed by a fall of 25% is not back to the start; it leaves a net fall of 6.25%.
- Using percent change when what you want is one number's share of another. A move from 2 to 3 is a rise of 50%, but 3 is 150% of 2; that second question is the percentage-of tool.
When to use it
- Use it for any before-and-after pair: a price, a salary, a bill, a reading, to see how far it moved in proportional terms.
- It is the wrong tool when the starting figure is zero, where the code refuses because no percentage exists, and when you want a share of a whole rather than a change; use the percentage-of calculator for that.
Worked example
250 to 310 is a rise of 24%.
Common questions
If it rises 25% then falls 25%, are we back?
No. The percentage applies to the larger figure, so 25% of it is bigger. This is the commonest mistake in the whole topic.
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