Reverse percentage calculator
You know the final value and the percentage: get back the number you started from.
Original value
Original value: 100
- Amount added or removed
- 20
How it works
If a value was increased by P%, the final value is the original × (1 + P ÷ 100). Dividing the final value by that factor gives the original back.
For a decrease, the factor is (1 − P ÷ 100). A common mistake is to take P% off the final value instead: that gives the wrong answer because the percentage was applied to the original, not to the final value.
Formula
Original = final ÷ (1 + P ÷ 100) after an increase Original = final ÷ (1 − P ÷ 100) after a decrease
Worked example
A price of 120 after a 20% increase was 120 ÷ 1.2 = 100. A sale price of 60 after 25% off was 60 ÷ 0.75 = 80.
Questions people ask
Why not just subtract 20% from 120?
20% of 120 is 24, giving 96. But 96 plus 20% is 115.20, not 120. The 20% was added to the original, so you must divide.
How do I remove tax from a price?
Choose “Added”, enter the price including tax and the tax rate. The VAT and sales tax calculators do the same and also show the tax amount.