Percentage Off Sale Price Calculator

Discount Calculation Guide

What's the key thing to understand about Sale Price Formulas?

Sale price = Original × (1 − discount%/100). Saving = Original × discount%/100. To find original from sale price: Original = Sale price ÷ (1 − discount%/100). Example: £80 with 25% off = £80 × 0.75 = £60. Saving = £20. Working backwards: a £60 item after 25% off had an original price of £60 ÷ 0.75 = £80.

What should I know about Spotting Misleading Discounts?

'Was £100, now £80' — this is 20% off, not 25%. A common trick: items are marked up temporarily, then 'discounted' to appear as a better deal than the usual price. Check the price history using browser extensions like CamelCamelCamel for Amazon, or Pricespy for other retailers. UK trading standards require that the 'was' price must have been the genuine selling price for at least 28 days in the 6 months before the sale.

What's the key thing to understand about VAT and Discounts?

When calculating discounts in a business context, be clear whether prices are inclusive or exclusive of VAT. A trade discount applied before VAT is more valuable than the same nominal discount applied after VAT. 20% discount on £100 ex-VAT = £80 ex-VAT (£96 inc). 20% off the £120 inc-VAT price = £96 — same number but the pre-VAT value differs. Trade prices and trade discounts are almost always quoted ex-VAT.

What should I know about Compound Discounts?

Multiple discounts do not add linearly. A 20% discount followed by a further 10% discount is NOT 30% off. It is 1 − (0.80 × 0.90) = 1 − 0.72 = 28% off. Example: £100 after 20% = £80. Then 10% off £80 = £72. Total saving: £28, not £30. This is why 'extra 10% off sale items' is always less valuable than it appears — the second discount applies to the already-reduced price.

What's the key thing to understand about Calculating the Original Price from a Sale Price?

If you know the discounted price and the discount percentage but need to find the original price, the formula works in reverse from the standard discount calculation. Since sale price = original price × (1 − discount%), rearranging gives original price = sale price / (1 − discount%). For example, if a jacket is on sale for $63 after a 30% discount, the original price was 63 / (1 − 0.30) = 63 / 0.70 = $90. A common mistake is to instead add the discount percentage directly to the sale price (63 + 30% of 63 = 63 + 18.90 = $81.90) — this gives the wrong answer because 30% of the smaller sale price is not the same amount as 30% of the larger original price. The correct method always divides by (1 − discount%) rather than adding a percentage of the sale price itself, since the discount percentage was originally calculated against the larger, original base value.

What's the difference between a Discount and a Markup?

A discount and an equal-percentage markup are not mirror images of each other, because each is calculated from a different starting value. If a $100 item is discounted by 20%, it drops to $80. If that $80 price is then marked back up by 20%, it only rises to $80 × 1.20 = $96 — not back to $100 — because the 20% markup is calculated on the smaller $80 base, not the original $100. To fully reverse a 20% discount and return to the original price, you would actually need a 25% markup ($80 × 1.25 = $100), since the percentage needed to reverse a discount is always larger than the discount itself: the formula is discount% / (1 − discount%) × 100. This asymmetry is worth remembering whenever a retailer advertises a 'discount, then restored to full price' claim, or when comparing a round-trip of price cuts and increases — the percentages involved are never simply equal and opposite.

What's the difference between 50% Off and Buy One Get One Half Price?

"50% off" and "buy one, get one 50% off" sound similar but produce very different savings. A straight 50% discount on a single $100 item means you pay $50 — a 50% saving on your total spend. "Buy one, get the second 50% off" applied to two $100 items means you pay $100 + $50 = $150 for two items instead of $200, which is a 25% saving on the total, not 50%. The confusion arises because the 50% discount only applies to one of the two items, not to the combined purchase. Retailers often phrase promotions this way because "50% off" sounds more generous than the mathematically accurate "25% off your total," so it's worth converting any multi-item promotion into a total-spend percentage before assuming it beats a simpler straight discount.

Worked Example: Stacking Two Discounts

A jacket originally costs £120. A store first takes 20% off, then applies an additional 10% off the already-reduced price (common in end-of-season stacked sales). After the first discount: Price after 20% off = £120 × (1 - 0.20) = £120 × 0.80 = £96.00 After the second discount is applied to that new price (not the original): Price after further 10% off = £96.00 × (1 - 0.10) = £96.00 × 0.90 = £86.40 The final price is £86.40 — but the combined discount is NOT simply 20% + 10% = 30%. The actual overall discount is (£120 - £86.40)/£120 = £33.60/£120 = 28.0%, slightly less than the naively-added 30% because the second discount applies to an already-reduced amount, not the original price. This is a common point of confusion in 'stacked' sales advertising, and it's why successive percentage discounts should always be multiplied together as decimal factors (0.80 × 0.90 = 0.72, i.e. 72% of original = 28% off), never added.

Discount Stacking Reference Table

Notice the gap between the naive sum and the true combined discount grows as the individual discounts get larger — at 50% + 50%, a shopper might expect the item to be free, but it's actually still 25% of the original price (a 75% discount, not 100%). The correct formula for any number of stacked percentage discounts d₁, d₂, d₃... is to multiply the remaining fractions together: final price = original × (1-d₁) × (1-d₂) × (1-d₃)..., then subtract that product from 1 and convert to a percentage to get the true combined discount.

Worked Example: Finding the Original Price From a Sale Price

A sale sign says an item is now £64 after a 20% discount. To find the original price, note that £64 represents 80% of the original (100% - 20% discount): Original price = sale price / (1 - discount) = 64 / (1 - 0.20) = 64 / 0.80 = £80.00 A common mistake is to instead calculate 20% of £64 and add it back (£64 + £12.80 = £76.80) — this is wrong, because 20% of the ORIGINAL price was removed, not 20% of the sale price. The correct method always divides by (1 - discount), never multiplies the sale price by (1 + discount), since those two percentages are taken from different bases. As a quick check: 20% of the true original (£80) is £16, and £80 - £16 = £64, confirming the answer. This distinction — percentage of what base — is the single most common source of error in percentage-reversal problems, whether for sale prices, tax-inclusive pricing, or working backward from a tip total to a pre-tip bill.

Discount vs. Markup: Why They're Not Symmetric

A 20% discount followed by a 20% markup does NOT return to the original price — this asymmetry trips up a lot of people. Starting at £100, a 20% discount gives £80. Applying a 20% markup to that £80 gives £80 × 1.20 = £96, not £100. The reason is that the discount was 20% of the larger original price (£20), while the markup is 20% of the smaller discounted price (£16) — the two percentages are taken from different bases, so they don't cancel. This is the same underlying principle as the original-price-recovery calculation: percentage changes are always relative to whatever amount they're applied to at that moment, never to some other fixed reference amount, which is why reversing a percentage change always requires dividing by the appropriate factor rather than simply applying the opposite percentage.