Key points
- Percentage change depends on the starting value.
- A percentage point is not the same as a percent change.
- Reversing a percentage increase takes a different calculation from adding the same percentage back.
Start with the base
Every percentage is relative to a base value. A rise from 50 to 60 is a 20 percent increase because the change is 10 and the base is 50. A fall from 60 to 50 is a 16.67 percent decrease because the base is now 60. The same absolute change can produce different percentage changes.
Percent and percentage points
If an interest rate moves from 3 percent to 4 percent, it has risen by 1 percentage point. Relative to the original 3 percent, it has risen by 33.33 percent. Mixing these terms can make small changes sound much bigger or smaller than they are.
Discounts do not reverse neatly
A 20 percent discount followed by a 20 percent increase does not return to the original price. If GBP 100 falls by 20 percent, it becomes GBP 80. Increasing GBP 80 by 20 percent gives GBP 96. To return from GBP 80 to GBP 100, the increase is 25 percent.
Use ratios when percentages feel unclear
Ratios can make comparisons easier when percentages become abstract. Saying 3 in 10, 30 out of 100 and 30 percent can describe the same proportion. Switching between fractions, ratios and percentages is often the quickest way to spot whether a result is sensible.
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Put the guide into practice
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