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Invoicing, margin & GST calculators
Reverse Discount Calculator — Find the Discount % or Original Price
A reverse discount works backwards from what you paid to what the deal really was. Given the original price and the sale price, the discount is d% = (price − sale) / price. Paid $40 on a $50 item? That is (50 − 40) / 50 = 20% off. And if you only know the sale price and the discount, you can recover the original with original = sale / (1 − d%): a $40 price after 20% off came from 40 / 0.80 = $50. This mode handles both directions — find the effective discount from an original-and-sale pair, or find the original price behind an advertised "X% off" — so you can check whether a "was $50, now $40" claim is honest. Free, no login.
Find the discount %: d% = (price − sale) / price
- Find the original price: original = sale / (1 − d%)
- Worked example — original $50, sale $40: d% = (50 − 40)/50 = 20% off
- Worked example — sale $40 after 20% off: original = 40 / 0.80 = $50
- Worked example — original $80, sale $60: d% = (80 − 60)/80 = 25% off
- Amount saved = price − sale (the dollar figure behind the percentage)
- Guard: if the sale price exceeds the original, the "discount" is negative (a markup) — flagged, not shown as a %
Frequently asked questions
How do I find the discount percentage from the original and sale price?
Subtract the sale price from the original, then divide by the original: d% = (price − sale) / price. If a $50 item sold for $40, the discount is (50 − 40) / 50 = 10 / 50 = 20%. The dollar saving is simply price − sale = $10. This is the reverse of a forward discount: instead of applying a known percentage to get the sale price, you infer the percentage from the two prices — useful for checking whether an advertised discount matches the actual price cut.
How do I find the original price from the sale price and discount?
Divide the sale price by (1 − discount). A $40 price after a 20% discount came from 40 / (1 − 0.20) = 40 / 0.80 = $50. A $60 price after 25% off came from 60 / 0.75 = $80. Do not add the discount percentage back to the sale price — that under-recovers the original, because the percentage was taken off the larger original, not the smaller sale price. The correct operation is always to divide by the surviving fraction.
What if the sale price is higher than the original price?
Then there is no discount — the price went up, which is a markup rather than a markdown. The formula d% = (price − sale) / price returns a negative number in that case, and this calculator flags it as a price increase rather than displaying a nonsensical "negative discount". This can happen when comparing a current price against an older, lower reference price, or when a "sale" price is actually above a previous everyday price — a reason to verify reference prices before trusting a discount claim.