Discount Percentage — 3 Formulas That Cover Every Situation
Sale tags show percentages, not dollar amounts. Whether you are a shopper checking if a deal is real, a retailer setting markdowns, or a student working through business math, these three formulas solve every discount calculation in under a minute.
Black Friday, end-of-season sales, coupon codes, clearance racks — discounts appear everywhere, and most shoppers check them by eye rather than calculation. That works for round numbers but fails quickly with an irregular discount on an odd-priced item. Is "Was $87, Now $61" actually a 30% discount? (It is 29.9% — close, but the ability to check in seconds changes how you evaluate any deal.)
Find the sale price: $80 × (1 − 0.25) = $60
Find the original price: $60 ÷ (1 − 0.25) = $80
÷ Original × 100
= 25%
(1 − Discount%)
= $60
(1 − Discount%)
= $80
These are the calculations people search for most often. If your number is close to one of these, use it directly.
| Discount | Multiplier | Save on $100 | You Pay | You Pay on $250 |
|---|---|---|---|---|
| 5% off | 0.95 | $5.00 | $95.00 | $237.50 |
| 10% off | 0.90 | $10.00 | $90.00 | $225.00 |
| 15% off | 0.85 | $15.00 | $85.00 | $212.50 |
| 20% off | 0.80 | $20.00 | $80.00 | $200.00 |
| 25% off | 0.75 | $25.00 | $75.00 | $187.50 |
| 30% off | 0.70 | $30.00 | $70.00 | $175.00 |
| 40% off | 0.60 | $40.00 | $60.00 | $150.00 |
| 50% off | 0.50 | $50.00 | $50.00 | $125.00 |
| 60% off | 0.40 | $60.00 | $40.00 | $100.00 |
| 75% off | 0.25 | $75.00 | $25.00 | $62.50 |
When a store advertises "20% off, plus an extra 10% off at checkout," most shoppers assume the total discount is 30%. It is not. Stacked discounts are applied sequentially, and the math works differently.
Formula for stacked discounts: Final price = Original × (1 − D1) × (1 − D2). Convert to decimals before multiplying.
Understanding discount calculations also helps you recognise when a deal is less than it appears. Some patterns are worth knowing.
- Inflated original prices. A 50% discount means nothing if the "original price" was artificially set to make the discount look large. Compare to the price at other retailers before deciding.
- Percentage vs dollar amount. "Save $20" on a $400 item is only a 5% discount. The dollar amount sounds significant but the percentage reveals it is minor.
- Buy-one-get-one framing. "Buy 2 get 1 free" is effectively a 33% discount per item — the same as a standard one-third-off sale, just framed to feel more generous.
- Tiered discounts. "10% off $50, 20% off $100, 30% off $150" push customers to buy more. Calculate the actual dollar saving at each tier before deciding whether the extra spend is worth it.
If you are pricing markdowns, the same formulas apply in reverse. A few things to keep in mind when setting discounts:
- Know your gross margin before setting a discount. If your margin is 40% and you offer a 40% discount, you are selling at cost — zero profit. If your margin is 40% and you offer 50% off, you are selling at a loss.
- Round discount percentages are more persuasive than odd numbers. "27% off" does not register as clearly as "25% off," even though 27 is mathematically more.
- Track your sell-through rate. A 20% discount that sells the rest of a slow-moving inventory in two weeks is more profitable than holding the stock at full price for six months.
Three formulas cover every discount situation: divide the difference by the original to find the percentage, multiply the original by the remaining fraction to find the sale price, and divide the sale price by the remaining fraction to find the original. The most important thing to remember is that stacked discounts are multiplicative, not additive — 20% plus 10% is 28%, not 30%. These calculations take ten seconds once you know the formula, and they change how clearly you see any deal.
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