Discount arithmetic looks trivial until you try to run it backwards. Working out 25% off a $60 jacket is a one-step multiplication most people can do in their head. Working out what a jacket originally cost when the tag says "$45, was 25% off" trips up almost everyone, because the obvious move — adding 25% back — gives the wrong answer. This guide covers both directions, plus the stacking rule that shops rely on shoppers not knowing.
Forward: From Original Price to Sale Price
This is the straightforward direction. The saving is original × (discount ÷ 100), and the sale price is original − saving. A $60 jacket at 25% off saves 60 × 0.25 = $15, so you pay $45. Equivalently, and more usefully for mental arithmetic, you can go straight to the answer by multiplying by the fraction you still pay: 25% off means you pay 75%, so 60 × 0.75 = $45 in one step.
That second form is worth internalising because it generalises. Whatever the discount, the multiplier you want is 1 − (discount ÷ 100). Ten percent off is × 0.9, a third off is × 0.667, seventy percent off is × 0.3. Once you think in multipliers rather than subtractions, the reverse direction and the stacking rule both become obvious.
Reverse: From Sale Price Back to Original Price
Here is where the common mistake lives. If a coat is $80 after 20% off, what did it cost before? The instinct is to add 20% to $80, giving $96. That is wrong. The 20% was taken off the original price, which is larger than $80, so 20% of the original is more than 20% of $80.
The correct method is division. Since the sale price is the original times the payable fraction, the original is the sale price divided by that fraction: original = sale ÷ (1 − discount ÷ 100). So $80 ÷ 0.8 = $100. Check it forwards: 20% of $100 is $20, and $100 − $20 = $80. The numbers agree, which the $96 answer never does.
The gap widens as the discount grows. At 10% off the shortcut is out by about 1%; at 50% off it is out by 25%; at 70% off the "add it back" method understates the original price by more than half. If you are reselling, valuing stock, or checking whether an advertised "was" price is honest, the division method is the only one that holds up.
Finding the Percentage from Two Prices
When you can see both prices and want to know how good the deal actually is, the discount is (original − sale) ÷ original × 100. A camera reduced from $250 to $175 has been cut by 75 ÷ 250 = 30%. Note that the denominator is the original price, not the sale price — dividing by the sale price is a different quantity (the markup) and produces a flattering, incorrect figure. On the same camera, dividing by $175 would suggest a 43% discount that nobody received.
Why Stacked Discounts Are Smaller Than They Look
"Take an extra 20% off already-reduced prices" is the most profitable sign in retail, because shoppers add the numbers. An item at 30% off with a further 20% at the till is not 50% off. Using multipliers: you pay 70% of the original, then 80% of that, which is 0.7 × 0.8 = 0.56, or 56% of the original. The true combined discount is 44%, six percentage points less than the intuitive sum.
The effect compounds with more tiers, and it always favours the shop. Three stacked 20% discounts sound like 60% off but deliver 0.8³ = 0.512, i.e. 48.8%. The rule to remember is that stacked discounts multiply the fractions you still pay; they never add the fractions you save.
Where Sales Tax Fits
Sales tax and VAT are charged on the discounted price, not the original, which is why a discount also shrinks the tax you pay. On a $200 item at 50% off with 10% sales tax, the tax is charged on $100, not $200: you pay $100 + $10 = $110. Enter a tax percentage in this tool and it follows the same order — discount first, tax afterwards.
The one common exception is a coupon or rebate applied after tax has been calculated, which some jurisdictions treat differently from a price reduction at the shelf. If the receipt shows tax computed on the pre-discount amount, the retailer is treating the reduction as a manufacturer's rebate rather than a markdown, and the tax figure will be higher than this calculator's.
Judging Whether a Discount Is Real
A percentage is only meaningful relative to an honest starting price. Consumer protection rules in the EU (the Omnibus Directive) and comparable rules elsewhere require that an advertised "was" price reflect the lowest price actually charged in the preceding 30 days, precisely because inflated reference prices make any discount look impressive. Using the reverse mode here to recover the implied original price is a quick sanity check: if the recovered figure is far above what the item has ever sold for, the discount is doing more work in the marketing than in your wallet.
Working Out a Whole Basket
When several items carry different discounts, the useful number is the blended rate across the basket, and it must be weighted by value. Averaging the percentages treats a 50%-off $2 keyring the same as a 10%-off $900 laptop and reports a 30% saving that nobody received. The correct calculation totals the basket before discounts and after, then takes the difference as a percentage of the pre-discount total — about 10.1% in that example. The cart in this tool uses the value-weighted method for exactly that reason.
