How to find the original price
before a discount -
the formula retailers don't explain.
You see a sale price. The tag says "X% off." But what was it actually worth before? And is that "was" price even real? One formula answers both questions instantly.
The reverse percentage formula
Most people know how to apply a discount: take the original price, knock off the percentage. But the reverse - working backwards from a sale price to find the original - trips almost everyone up.
The instinct is to just add the discount percentage back. If something is $80 after 20% off, people add 20% to $80 and get $96. That's wrong. The correct original is $100.
The reason: the discount was taken off the original price, not off the sale price. So adding 20% to the sale price adds 20% of the wrong base.
$80 + (20% of $80) = $80 + $16 = $96
This adds 20% of the sale price. But the discount was off a different (higher) base.
$80 ÷ (1 − 0.20) = $80 ÷ 0.80 = $100
Divides by 0.80 because at 20% off you're paying 80% of the original.
£75 ÷ (1 − 0.25) = £75 ÷ 0.75 = £100.
Now verify: £100 × (1 − 0.25) = £100 × 0.75 = £75 ✓.
If the tag says "was £110, now £75 - 25% off," the maths says the "was" should be £100, not £110. The actual discount from £110 is only 31.8% - the label is technically misleading. In the UK, the Omnibus Directive (implemented 2022) requires the "was" price to reflect the lowest price in the previous 30 days, so this kind of inflated reference price is increasingly regulated.
Stacked discounts - why 20% + 15% is not 35%
Retailers frequently advertise "additional discounts" on top of existing sale prices. A common version: "Sale items already 20% off - take an extra 15% at checkout." Shoppers instinctively add the two percentages and expect 35% off the original. That's not how it works.
The second discount applies to the already-reduced price - not the original. Each discount takes a percentage of a smaller number, so the combined saving is always less than the sum of the two rates.
After 20% off: $200 × 0.80 = $160
After extra 15% off: $160 × 0.85 = $136
Total saving: $200 − $136 = $64
Effective discount: ($64 ÷ $200) × 100 = 32% - not 35%
The formula for any stacked discount:
Combined = 1 − (1 − D1) × (1 − D2)
= 1 − (0.80 × 0.85) = 1 − 0.68 = 0.32 = 32% combined
Combined = 1 − (1 − 0.10) × (1 − 0.20) = 1 − 0.90 × 0.80 = 1 − 0.72 = 28% combined. Not 30%.
On a $150 item: $150 × (1 − 0.28) = $150 × 0.72 = $108. You save $42.
If the same discounts applied in the opposite order - 20% sale first, then 10% loyalty - you'd get exactly the same answer. The order of stacked percentage discounts doesn't matter: 0.90 × 0.80 = 0.80 × 0.90 = 0.72 either way.
Spotting fake "was" prices
The reverse formula is your main tool for checking whether a claimed original price was genuine. Here's how to use it as a quick sanity check whenever you see a sale sign.
Step 2: Calculate what the original should be: Sale Price ÷ (1 − Discount ÷ 100)
Step 3: Compare to the "was" price on the tag.
Example: "Was $180, now $108 - 40% off"
Your calculation: $108 ÷ (1 − 0.40) = $108 ÷ 0.60 = $180 ✓ Genuine
Example: "Was $220, now $108 - 40% off"
Your calculation: $108 ÷ 0.60 = $180 (not $220)
Actual discount from $220: ((220−108)÷220)×100 = 50.9% - the tag says 40%, reality is 50.9%. They've inflated the "was" price.
In most major markets, no - but the enforcement has varied historically.
UK: Since May 2022, the Omnibus Directive requires the "was" price to be the lowest price charged in the previous 30 days. So a retailer can't briefly raise a price to $200, immediately discount it to $120, and call it "40% off" - the 30-day rule prevents it.
EU: Same Omnibus Directive applies across all member states from May 2022.
US: The FTC's Price Guides say the "former price" must be a bona fide price at which the item was offered for a substantial period. But enforcement is looser than in the EU/UK, and "substantial" is interpreted variably.
Australia: The ACCC prohibits misleading price comparisons under the Australian Consumer Law - a "was" price must genuinely reflect what the item sold for, not an inflated figure set to make the discount look bigger.
The maths check works regardless of jurisdiction. If the numbers don't add up, the claim is misleading even if it's technically legal in that market.
What to watch out for right now
Dynamic pricing makes "original prices" more complex. On platforms like Amazon, prices can change multiple times per day based on demand, competition, and algorithmic pricing. A product listed as "30% off" might be discounted from a price that existed for 6 hours last Tuesday. Browser extensions like CamelCamelCamel (for Amazon) let you see the price history graph - if the "original" price was only ever set briefly to establish an inflated anchor, you'll see it in the data.
Black Friday and seasonal sales in 2026 continue to use the tactic of raising prices weeks in advance, then "discounting" to approximately the original level. UK consumer group Which? found in their 2024 review that over 90% of Black Friday deals had been available at the same price or cheaper in the preceding 6 months. The reverse formula takes 10 seconds to run and tells you whether a "was" price makes mathematical sense - even before you look up the price history.
BNPL (Buy Now Pay Later) discounts sometimes advertise a "5% cashback" or "extra 10% off via app" that stacks with a sale. Remember the stacked discount formula: those don't add. 20% sale + 10% cashback = 28% effective saving, not 30%. The calculator at the top of this page handles stacked discounts if you select that mode.