Distinguish a percentage of a number from a percentage change.
Use the Percentage Calculator alongside this illustrative example.
A practical example
A rise from 80 to 100 is a 25% increase because the increase of 20 is divided by the starting value of 80. Returning from 100 to 80 is a 20% decrease. The same two values therefore produce different percentages depending on the direction.
Check the result
Write the starting value first and name the quantity being compared. For a discount, compare the reduction with the original price, not the final price. Check that a zero starting value does not produce a meaningful percentage-change claim.
Try a comparison
Compare a 20% increase followed by a 20% decrease starting from 100. The sequence gives 120 and then 96, not 100. The second percentage uses a different base, which also explains why percentage changes cannot simply be added and cancelled.
What this does not establish
Percentage points are different again: a rate rising from 10% to 12% increases by two percentage points, or 20% relative to the original rate.
Try the tools from this guide
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