Reverse Percentage Calculator
This reverse percentage calculator works backwards from a price after a discount, VAT or markup to find the original figure.
Formula & worked example
Formula: Original = final ÷ (1 + p ÷ 100) after an increase, or final ÷ (1 − p ÷ 100) after a discount.
Example: 80 after a 20% discount: 80 ÷ 0.80 = 100. 120 including 20% VAT: 120 ÷ 1.20 = 100.
Method & source: Inverse of the multiplier method: final ÷ (1 ± p ÷ 100). See how we test our calculators.
Next step: try adding and removing VAT or percentage increase and decrease or price per unit.
Working Backwards From a Percentage
This kind of tool works backwards from a final amount to the original one. If a jacket costs 80 after a 20% discount, or an invoice totals 120 after 20% VAT, this tool tells you the price before that change.
The common mistake is to take 20% off the final figure. That gives the wrong answer because the percentage was applied to the original amount, not the final one.
Finding the Original Value Before a Change
Enter the final value, the percentage and whether it was an increase (such as tax or markup) or a discount.
- After an increase: Original = final ÷ (1 + percent ÷ 100).
- After a discount: Original = final ÷ (1 − percent ÷ 100).
- Amount changed: The exact amount added or taken off.
- Working shown: The formula with your numbers so you can verify it.
- Proof check: The original is put through the percentage again to confirm the final value.
The proof line at the bottom makes it easy to trust the result before you use it in a quote or price list.
Why Reversing a Percentage Matters
Prices you see are often the finished figure, but decisions depend on the starting point.
- Find the price before VAT or sales tax was added.
- Discover the original price before a sale discount.
- Check whether a “70% off” offer is genuinely as good as it looks.
- Work out pre-raise salaries or pre-increase rents.
- Strip a service charge or markup out of a total.
With a reverse percentage calculator you can find the original price before an increase or discount without guessing or trial and error.
Worked walkthrough: a sale price
A television is on sale for 360 after a 25% discount. Because 360 is 75% of the original price, the original is 360 ÷ 0.75 = 480, and the discount saved 120. Taking 25% off 360 would wrongly give 270, which is why the divide-by-multiplier method matters. The same approach removes tax: a total of 120 that includes 20% VAT is 120 ÷ 1.20 = 100 before tax, with 20 of VAT. The calculator finishes with a proof line, multiplying the original by the multiplier to reproduce the final price.
Practical tips for Reverse Percentage calculations
- Choose “after a discount” when the price went down and “after an increase” for tax, markup or service charges added on top.
- For sales tax or VAT, enter the tax rate as the increase. The tool divides by 1 plus the rate to strip it out.
- If a price was reduced twice, work backwards one step at a time, starting with the last reduction.
- A discount of 100% or more cannot be reversed – the original would be undefined – so the tool asks you to check the figure.
- Use the proof line to double-check results before you put a number into a quote, receipt or spreadsheet.
Why you cannot just subtract the percentage
If something costs 80 after a 20% discount, the original was 100, not 96. The 20% was taken from the original price, not from 80. Adding 20% of 80 back gives 96, which is still 4 short. The correct route is division: final ÷ (1 − 0.20) = 80 ÷ 0.80 = 100.
After a discount or after an increase
The two cases differ only in the sign. After an increase of p%, original = final ÷ (1 + p ÷ 100). After a discount of p%, original = final ÷ (1 − p ÷ 100). A total of 120 that includes 20% is 120 ÷ 1.20 = 100 before the increase, and a price of 75 after 25% off was 75 ÷ 0.75 = 100 before.
The calculator also shows the amount that was added or removed, and a proof line that reapplies the percentage to the answer so you can check it.
Reverse percentage examples
The formula is original = final ÷ (1 + change), with the change written as a decimal: positive for an increase and negative for a discount.
| Situation | Working | Original value |
|---|---|---|
| A price of 150 after a 20% increase | 150 ÷ 1.20 | 125 |
| A price of 68 after a 15% discount | 68 ÷ 0.85 | 80 |
| A population of 52,500 after 5% growth | 52,500 ÷ 1.05 | 50,000 |
The calculator shows a currency sign for prices, but the arithmetic is the same for anything that grew or shrank by a percentage, such as a population, a salary or a score. To apply a discount to a known price instead, use the discount calculator.
Taking VAT or sales tax out of a total
A tax-inclusive price is an increase-type problem. With 7% sales tax, a receipt total of 53.50 was 53.50 ÷ 1.07 = 50.00 before tax. For UK VAT at 20%, divide by 1.2, or use the VAT calculator which adds the standard, reduced and zero rates and a custom rate.
Undoing more than one change
When a price was raised and later discounted, undo the steps in reverse order. A final price of 88 after a 10% rise and then 20% off was 88 ÷ 0.80 = 110 after the rise, and 110 ÷ 1.10 = 100 at the start. Run the calculator once per step and carry the result forward.
Checking a sale claim
Retailers often show a crossed-out price. Enter the sale price and the advertised discount to see what the original price must have been. A 30 sale price at “70% off” implies an original of 30 ÷ 0.30 = 100. If the shop’s crossed-out price is higher than that, the claim does not add up. To measure a change between two known prices instead, use the percentage change calculator.
A discount of 100% or more cannot be reversed, because the final price is zero or negative and no original can be recovered.
Frequently Asked Questions (FAQs)
Divide the sale price by (1 − discount ÷ 100). If a coat costs 80 after 20% off, 80 ÷ 0.8 = 100 was the original price.
Choose “Increase” and enter the tax rate. The calculator divides the total by 1 plus the rate, giving the price before tax and the tax amount.
Because the percentage was worked out on the original value, not on the final one. A price of 150 after a 20% increase was 125, but taking 20% off 150 gives 120, which is 5 too low. A price of 68 after 15% off was 80, while adding 15% to 68 gives only 78.20. Dividing by the multiplier is the only way to get back exactly.
The original price cannot be recovered from a final price of zero, so the calculator warns you that a discount of 100% or more cannot be reversed.
Yes. Both the final value and the percentage accept decimals, such as 12.5%.
Divide the sale price by 0.8, because you paid 80% of the original. £80 ÷ 0.8 = £100. For a price increase, divide by 1 plus the rate instead, for example by 1.2 for a 20% rise.
Divide the new price by 1 plus the increase as a decimal. After a 20% rise to £120, the price before was £100.
Yes. Enter the price you would pay and the advertised discount to see the price the shop is comparing against, then decide if the “was” price is realistic.