Quick brief
What to know before you calculate
A short read on the assumptions, trade-offs and definitions that shape the answer.
- Percentage change compares the difference with the original value.
- A 20 percent fall followed by a 20 percent rise does not return to the starting value.
- Reverse percentages work backwards from the final value to the original value.
The percentage change formula
Percentage change equals the new value minus the original value, divided by the original value, multiplied by 100. The original value is the anchor. If the original value changes, the percentage change changes too.
Increase and decrease are not symmetrical
A fall from 100 to 80 is a 20 percent decrease. A rise from 80 back to 100 is a 25 percent increase because the new comparison starts from 80. This is a common reason percentage changes feel counter-intuitive in prices, discounts and performance reports.
Reverse percentage questions
A reverse percentage starts with the final value after a percentage has been added or removed. If a price after 20 percent VAT is 120, the original value is 120 divided by 1.20, which equals 100. The multiplier changes depending on whether the percentage was added or deducted.
How to avoid mistakes
Write down the original value, the new value and the question being asked before calculating. Most percentage errors come from using the wrong base, mixing up percentage points and percentages, or treating a decrease and an increase as if they cancel out.
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