Reverse percentage calculator
Removing a percentage is not the same as subtracting it. To undo a 20% increase you divide by 1.2, not multiply by 0.8.
%
Original value
100
- The amount added or removed
- 20
- What the wrong method would give
- 96
- How far wrong that would be
- -4
Show the working
- Value after the change = 120
- Percentage applied = 20
- It was = 1
- factor = 1 > 0 ? 1 + 20/100 : 1 - 20/100 = 1.2
- Original value = 1.2 != 0 ? 120 / 1.2 : 0 = 100
- The amount added or removed = abs(120 - 100) = 20
- What the wrong method would give = 1 > 0 ? 120 * (1 - 20/100) : 120 * (1 + 20/100) = 96
- How far wrong that would be = 96 - 100 = -4
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- original = final / (1 + p) when p was added
- original = final / (1 - p) when p was removed
The "wrong method" row is there because it is the single most common percentage mistake.