Percentage increase vs decrease, explained
Percentage changes look simple until you try to undo one. Here is how the two directions work.
Calculating an increase or decrease
Both use the same idea: take the difference between the new and the original value, divide by the original, and multiply by 100.
- From 80 to 60: (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
- From 60 to 80: (80 − 60) ÷ 60 × 100 = 33.3%, a 33.3% increase.
The same 20-unit gap gives different percentages because the starting value is different.
Why they do not cancel
A 20% decrease on 100 leaves 80. Increasing 80 by 20% gives 96, not 100. To get back to 100 you need a 25% increase, because the increase is applied to a smaller base.
Working backwards
If a price is 120 after a 20% increase, the original is 120 ÷ 1.20 = 100. If a sale price is 80 after a 20% discount, the original is 80 ÷ 0.80 = 100. Subtracting 20% from the final value is the classic error.
Percent vs percentage points
If an interest rate moves from 10% to 8%, it fell by 2 percentage points, but that is a 20% decrease relative to the old rate. Be clear about which one you mean.
Use the percentage increase calculator or the percentage decrease calculator for the change itself, the percentage difference calculator when neither value is the starting point and the backwards percentage calculator to find the original value.