Quick reference
What reverse percentage is
A percentage change is always calculated relative to the original (starting) value. When you know the final value and the percentage change, you can find the original value by undoing the percentage operation.
If a price increased by 20% to reach 120, the original price was 100 because 100 x 1,20 = 120. Reverse: 120 / 1,20 = 100.
If a price decreased by 20% to reach 80, the original price was 100 because 100 x 0,80 = 80. Reverse: 80 / 0,80 = 100.
The critical insight: 20% of the original is not the same as 20% of the final. The percentage was applied to the original. To undo it, you must divide by the multiplier that was applied — not add or subtract a percentage of the final value.
The reverse percentage formula
Why adding the percentage back gives the wrong answer
The most common error in reverse percentage calculations is to add the percentage back to the final value. This always gives a wrong answer because you are applying the percentage to the wrong base.
Example: a price is 80 after a 20% discount. What was the original?
Wrong method: 80 + 20% of 80 = 80 + 16 = 96. This is wrong. Correct method: 80 / (1 - 0,20) = 80 / 0,80 = 100.
Why is the wrong method wrong? A 20% discount means the sale price is 80% of the original. If the original was 100, the 20% discount is 20. But if you add 20% of the sale price (80) back, you are adding 16, not 20. You are adding 20% of the wrong number.
The original price is always the correct base for the percentage. The sale price is smaller, so 20% of the sale price is also smaller than 20% of the original. You need to divide the sale price by 0,80 to get back to the original, not add 20% of the sale price.
Worked examples
Original = 75 / (1 - 0,25) = 75 / 0,75 = 100. Verification: 100 x (1 - 0,25) = 100 x 0,75 = 75. Correct. The wrong method: 75 + 25% of 75 = 75 + 18,75 = 93,75. This would imply the original was 93,75. But 25% of 93,75 is 23,44, and 93,75 - 23,44 = 70,31, not 75. The wrong method does not even verify correctly.
Original = 2.530 / (1 + 0,15) = 2.530 / 1,15 = 2.200. Verification: 2.200 x 1,15 = 2.530. Correct. If someone's salary is 2.530 after a 15% rise, subtracting 15% from 2.530 gives 2.530 x 0,85 = 2.150,50, which is wrong. The percentage must be undone by dividing by the multiplier, not by subtracting a percentage of the new value.
Work backwards through each discount. After 25% discount: 54 / 0,75 = 72. After 10% discount: 72 / 0,90 = 80. Alternatively, the combined multiplier is 0,90 x 0,75 = 0,675. Original = 54 / 0,675 = 80. Two sequential discounts of 10% and 25% are equivalent to one discount of 32,5%, not 35%. Percentage discounts are multiplicative, not additive.
Calculate the original value
Enter the final value and percentage change to find the original price before the percentage was applied.
Extracting VAT from a tax-inclusive price
When a price includes VAT, extracting the VAT amount requires a reverse percentage calculation. The common error is to calculate VAT rate percent of the inclusive price.
For a 21% VAT rate on an inclusive price of 121:
Wrong method: 21% of 121 = 25,41 VAT. This implies the pre-tax price is 121 - 25,41 = 95,59, which is wrong.
Correct method: the inclusive price of 121 is 121% of the pre-tax price (100% pre-tax + 21% VAT). Pre-tax price = 121 / 1,21 = 100. VAT = 121 - 100 = 21.
Alternatively, use the fraction method: VAT = inclusive price x (VAT rate / (100 + VAT rate)) = 121 x (21 / 121) = 121 x 0,1736 = 21.
At the Netherlands standard VAT rate of 21%: divide the inclusive price by 1,21 to get the pre-tax price. At the reduced rate of 9% (food, medicine): divide by 1,09. At 0% (exports, some services): no VAT to extract.
VAT extraction — Netherlands rates
| VAT Rate | Divide inclusive price by | VAT fraction to apply | Examples |
|---|---|---|---|
| 21% | 1,21 | 21/121 = 0,1736 | Most goods and services |
| 9% | 1,09 | 9/109 = 0,0826 | Food, books, medicine |
| 0% | 1,00 | 0 | Exports, international services |
Common mistakes
Methodology
Reverse percentage uses the algebraic inverse of the percentage change formula. If final = original x (1 +/- rate), then original = final / (1 +/- rate). VAT extraction uses the same principle. All formulas use exact arithmetic with rounding applied only to final displayed results.
VAT rates used are Netherlands standard rates as of May 2026. Rates vary by country and product category. Always verify current rates with your local tax authority.
Calculate the original value now
Enter the final value and the percentage change to find the original price before the percentage was applied.
Frequently asked questions
Formula based on standard mathematical and financial methods. Results are for informational purposes. Last reviewed May 2026. Version 1.