Discount Percentages Explained: Sales, Stacking and Fake Deals
Retail pricing is percentage arithmetic with a marketing budget attached. The maths itself is simple, but the way discounts are presented — stacked, layered on top of tax, compared against an inflated "was" price — is designed to be read quickly rather than checked. This guide covers the one-step method for any discount, the traps that make deals look better than they are, and how to work backwards from a sale price when you want to know what was really taken off.
Multiply by what is left, not by what comes off. A 30% discount leaves 70%, so the sale price is Price × 0.70 in a single step. To find the discount percentage from two prices, use (Original − Sale) ÷ Original × 100. Stacked discounts multiply: 20% off then 10% off is 28% off, never 30%.
The one-step method
Most people calculate the discount amount and then subtract it. That is two operations and two chances to slip. Instead, work out the fraction of the price you still pay:
- 10% off → pay 90% → × 0.90
- 25% off → pay 75% → × 0.75
- 40% off → pay 60% → × 0.60
- 70% off → pay 30% → × 0.30
A $84 pair of boots at 25% off is 84 × 0.75 = $63. Done in one move, with the answer already in the form you care about — the amount at the till.
Finding the discount percentage from two prices
When the sign says "$120, now $87" and you want to know the real cut: subtract, divide by the original, multiply by 100. (120 − 87) ÷ 120 × 100 = 27.5%. The denominator matters — dividing by the sale price instead gives 37.9%, which is the amount the retailer would have to add back to return to full price, not the discount.
Reversing a sale price back to the original
If you know the sale price and the discount but not the original, divide rather than multiply. A jacket costs $63 after 25% off, so the original was 63 ÷ 0.75 = $84. The general rule is Original = Sale ÷ (1 − discount). This is the same operation the Reverse Percentage Calculator performs, and it is the single most common percentage error in retail contexts: adding 25% back to $63 gives $78.75, which is wrong.
Why stacked discounts don't add up
"Extra 10% off already-reduced items" is not 10 percentage points added to the first discount. The second discount applies to the already-reduced price, so the multipliers combine:
| Stacked offer | Multipliers | Real discount | Looks like |
|---|---|---|---|
| 20% + 10% | 0.80 × 0.90 = 0.72 | 28% | 30% |
| 30% + 20% | 0.70 × 0.80 = 0.56 | 44% | 50% |
| 50% + 50% | 0.50 × 0.50 = 0.25 | 75% | 100% |
| 40% + 15% code | 0.60 × 0.85 = 0.51 | 49% | 55% |
The gap is never in the shopper's favour. The rule generalises: multiply all the "what's left" fractions together, then subtract from 1.
The second discount is taken off an already-reduced price, so the gap always favours the retailer.
Discounts and sales tax
Order does not matter mathematically — a 20% discount and 8% tax give the same total whichever you apply first, because multiplication is commutative (0.80 × 1.08 = 1.08 × 0.80). What matters legally is that tax is charged on the discounted price, so a genuine discount also reduces the tax you pay. In VAT-inclusive markets, the shelf price already contains the tax, so the discount applies to the gross figure; see the VAT Calculator to separate the two.
Spotting a fake deal
- Inflated reference price. "Was $200, now $99" only means something if the item genuinely sold at $200. Many jurisdictions require the "was" price to have been charged for a set period.
- Percentage off a bundle. "50% off the second item" is 25% off the pair, not 50%.
- Up to X% off. "Up to 70% off" describes the single best line in the store, not the rack you are standing at.
- Discount on an inflated shipping-inclusive price. Compare final totals, not headline prices.
Quick discount table
| Discount | You pay | On $50 | On $200 |
|---|---|---|---|
| 10% | × 0.90 | $45.00 | $180.00 |
| 15% | × 0.85 | $42.50 | $170.00 |
| 25% | × 0.75 | $37.50 | $150.00 |
| 33% | × 0.67 | $33.50 | $134.00 |
| 50% | × 0.50 | $25.00 | $100.00 |
| 70% | × 0.30 | $15.00 | $60.00 |
Practice problems
A $340 sofa is 35% off. What do you pay?
You paid $76.50 after a 15% discount. What was the original price?
30% off, plus an extra 25% at checkout, on $160.
Was $89, now $62.30. What is the discount?
For the formulas behind these steps, see The Percentage Formula. For the retailer's side of the same arithmetic — how a discount eats into profit — read Margin vs Markup. For the general case of undoing a percentage, see How to Calculate Percentage Decrease, and when prices move the other way, How to Calculate Percentage Increase.
Sources and method: stacked-discount arithmetic follows the standard treatment of discounts and allowances; reference-price rules vary by jurisdiction. Written and reviewed by The Snap PercentCalc Team.
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