Reverse Percentage Calculator
Find an original value when you know the final value and the percentage that was added, removed, increased, or discounted. This calculator is useful when you know the result after a percentage change but need to work backward to find the starting value.
Enter the final value and the percentage it increased by to find the original value.
How to Reverse a Percentage
It's tempting to simply add or subtract the percentage from the final value to find the original — but that gives the wrong answer, because the percentage was calculated from the original value, not the final one.
Example: reducing $100 by 20% gives $80 (a 20% ). But if you try to reverse it by simply adding 20% back to $80, you get $80 + $16 = $96 — not the original $100. The correct way is to divide instead: $80 ÷ (1 − 0.20) = $80 ÷ 0.80 = $100.
Reverse Percentage Formula
For an increase: Original = Final ÷ (1 + Percentage ÷ 100)
For a decrease: Original = Final ÷ (1 − Percentage ÷ 100)
Reverse a Discount
A discount is just a percentage decrease applied to a price, so reversing it uses the same decrease formula: divide the sale price by (1 − discount percentage ÷ 100). This is useful when you know what you paid after a and want to find the item's original price before the markdown.
Examples
Example 1: A value increased by 20% to reach 120. Original = 120 ÷ (1 + 0.20) = 120 ÷ 1.20 = 100.
Example 2: A value decreased by 20% to reach 80. Original = 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = 100.
Example 3: A sale price of $80 followed a 20% discount. Original price = 80 ÷ 0.80 = $100.