Reverse Percentage Calculator
This reverse percentage calculator works backwards from a price after a discount, VAT or markup to find the original figure.
Quick answer: To find the original price before a percentage change, divide the final price by 1 plus the rate for an increase, or by 1 minus the rate for a discount. A price of £120 after a 20% increase was £100 originally, because 120 ÷ 1.2 = 100. Taking 20% off £120 would give the wrong answer.
How do you use the Reverse Percentage Calculator?
- Enter the final price. Type the price you see after the increase or discount.
- Enter the percentage and direction. Choose whether it was an increase (such as VAT or a markup) or a discount, and enter the percentage.
- Press Find Original Value. Read the original price and the amount the change added or took off.
What is the formula, and what does a worked example look like?
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.
Worked examples for the Reverse Percentage Calculator
Each figure below was produced by the same code as the calculator, so you can enter the inputs and get the same result. Rates and thresholds are the ones on the official pages linked under “How it is calculated”.
£225 including 20% VAT: what was the net price?
The final price is 120% of the original.
- Original = £225 ÷ 1.20 = £187.50.
- VAT part: £225 − £187.50 = £37.50.
Result: £187.50 before VAT, of which £37.50 is VAT paid on top.
A coat is £180 after 25% off: what was the original price?
The sale price is 75% of the original.
- Original = £180 ÷ 0.75 = £240.00.
- The discount was £60.00.
Result: Original price £240.00. Taking 25% off £180 instead would wrongly give £135.
A $54.17 receipt including an example 8.25% sales tax
8.25% is an example rate; use the rate for your location.
- Pre-tax price = $54.17 ÷ 1.0825 = $50.04.
- Tax paid: $4.13.
Result: $50.04 before tax.
How is the Reverse Percentage Calculator calculated, and where do the rates come from?
A reverse percentage starts from the answer and recovers the original. After an increase of p%, the final value is the original × (1 + p ÷ 100), so original = final ÷ (1 + p ÷ 100). After a discount of p%, the final value is original × (1 − p ÷ 100), so original = final ÷ (1 − p ÷ 100). The calculator does exactly that division and shows the size of the change.
This is the reason you cannot simply subtract the percentage from the final figure: 20% of £120 is £24, but the VAT actually inside £120 is £20. The same logic recovers a pre-sale price, a pre-tax price, a price before a service charge or a salary before a rise.
UK VAT rates are published on GOV.UK (standard 20%, reduced 5%, zero 0%). US sales tax rates are set by states and localities, so enter the rate printed on your receipt or from your state's revenue department.
Always verify the answer by going forwards. If the calculator says the original price was £240, take 25% off £240 and you should land on the £180 you started with; if you add 20% to £187.50 you should reach £225. A mismatch means the percentage was applied to the wrong base or in the wrong direction. This forward check also protects against typing the percentage in as a decimal by mistake.
Real prices often combine steps, such as a sale discount followed by VAT or sales tax at the till. Work backwards one step at a time in the reverse order: remove the tax first to get the sale price, then reverse the discount to get the original. Doing the two in one go with the wrong order gives a different, wrong number because the percentages apply to different bases.
When the percentage applies to the original amount rather than to the final price, you are not doing a reverse percentage at all. Tips, service charges and commission are usually a percentage of the pre-charge bill, so use the percentage-increase mode on the bill, not this tool, to find what the total should be.
- GOV.UK – VAT rates – Standard rate 20%, reduced rate 5% and zero rate 0%, with examples of what each covers.
What are the common mistakes and edge cases?
- Subtracting the percentage from the final price. Always divide by the multiplier (1.2, 0.75 and so on).
- Using the wrong direction. A price after a discount needs the 'decrease' option; a price after VAT needs 'increase'.
- Reversing two stacked percentages as one. A 10% discount followed by a 10% coupon is not 20%; reverse them one at a time, last first.
- Rounding the multiplier. Use the exact percentage; 8.25% is 1.0825, not 1.08.
- Trying to reverse a 100% discount. The original price cannot be recovered from zero.
More in this category: Percentages & Pricing calculators.
How do you work 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.
How do you find 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 does reversing a percentage matter?
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.
Divide the sale price by (1 − discount ÷ 100). For £180 after 25% off, £180 ÷ 0.75 = £240.
Reverse the last discount first, then the earlier one. Each step divides by that step's multiplier.
For removing VAT it gives the same result. This tool works for any percentage, not only VAT.