Reverse discount: finding the price before the sale
A reverse discount works backward from the sale price to the original price. If you paid 80 after a 20 percent discount, the original was 100. You need division, not addition, because the percentage was taken from the larger number.
TL;DR
- When an item is discounted by a certain percentage, the remaining price represents a specific fraction of the original value
- Formula: Original Price = Sale Price ÷ (1 - (Discount Percentage ÷ 100))
- Example 1: Finding original cost of a jacket purchased for $75 at 25% off
How it works
When an item is discounted by a certain percentage, the remaining price represents a specific fraction of the original value. For example, if a jacket is on sale for 20% off, the price you pay represents exactly 80% of its original cost. Reconstructing the original price requires dividing the sale price by this remaining percentage factor.
The math
To find the original price, subtract the discount rate from 100 to find the remaining price percentage. Convert this percentage into a decimal factor, and divide the sale price by this decimal factor.
First convert the discount rate into a decimal. Subtract this decimal from 1 to find the remaining percentage factor. Finally, divide the sale price by this factor to find the original pre-discount price.
Examples
Example 1: Finding original cost of a jacket purchased for $75 at 25% off
- Identify discounted sale price: $75.00
- Identify the applied discount rate: 25%
- Calculate remaining percentage: 100% - 25% = 75% (or 0.75 as a decimal)
- Divide sale price by factor: $75.00 ÷ 0.75 = $100.00
- The original price before the sale was $100.00.
Example 2: Reconstructing list price of a software subscription bought for $180 at 10% off
- Identify discounted sale price: $180.00
- Identify the applied discount rate: 10%
- Calculate remaining percentage: 100% - 10% = 90% (or 0.90 as a decimal)
- Divide sale price by factor: $180.00 ÷ 0.90 = $200.00
- The original price before the sale was $200.00.
When to use it
✦ Expense Report Auditing
Corporate finance teams use reverse discounting to verify travel and equipment expenses when receipts only show the final discounted amounts paid.
✦ Verifying Retail Promotions
Smart shoppers use reverse calculations during sales events to verify if the 'original price' printed on tags is correct, or if stores inflated prices before the sale.
✦ Historical Financial Reconstruction
Accountants and tax professionals use reverse discounting to reconstruct transactions when historical data is incomplete or has been aggregated.
⚠ Common mistakes
- Adding the Percentage Directly: The most common math error is trying to find the original price by adding the discount percentage directly to the sale price. For example, adding 20% directly to an $80 sale price results in $96 (which is incorrect!). The correct original price was $100. You must always use division to reconstruct prices.
- Confusing Tax Rates with Discount Rates: Applying tax extraction formulas to discount rates will lead to incorrect calculations, as tax is added to the base while discounts are subtracted.
FAQ (7)
Why can't I just add the discount percentage to the sale price?
Because percentages are calculated relative to the original price, not the sale price. Since the sale price is smaller, adding the percentage to it will result in an original value that is too low.
Is reverse discounting useful for business bookkeeping?
Yes, it is highly useful for reconstructing business expenses, verifying vendor discounts, and filing accurate tax returns.
Does reverse discounting account for sales taxes?
No, reverse discounting should be performed on pre-tax amounts. If taxes are included, you should extract the tax first, then reconstruct the original price.
If I type my salary or prices here, do you store them?
No — and that's deliberate. Everything runs locally in your browser, nothing leaves your device. We don't see your net salary, your margins, or the VAT numbers you test. For a finance tool that matters: you can run a quick check on a payslip or an invoice while on public Wi-Fi and close the tab knowing no trace is kept server-side.
Can I use it on the train without signal to check an invoice?
Yes. Load the page once, then it works offline. VAT, discount and mortgage math are all pure JavaScript — no API call. I often test it in airplane mode: open the mortgage page, type 250,000 at 4.5% for 25 years, you get the schedule instantly, even in a tunnel.
Can I file taxes with these results?
Use it as a fast sanity check, not as the final filing. Formulas are standard (e.g. Net = Gross / 1+VAT) and verified against official sources listed at the bottom, but rates and thresholds change — Italy's 22% vs Germany's 19%, or IRPEF brackets. For the actual declaration, double-check with your accountant or Agenzia delle Entrate / HMRC / IRS.
How do I send a calculation to my accountant?
Hit 'Share Link' under the results. It encodes the inputs in the URL — e.g. ?price=1200&vat=22 — so your accountant opens the exact same view, no screenshot needed. You can also copy the result with one tap and paste it into an email.