A discount calculation answers two questions that are easy to conflate: what you pay, and what you save. Retail pricing is designed so the second number feels larger than it is, and the arithmetic that trips people up most is stacked discounts — an extra 20% off an item already reduced by 30% is not 50% off.
Stacked discounts multiply rather than add. Thirty percent off leaves you paying 70%; a further 20% off leaves 80% of that, so 0.70 × 0.80 = 0.56. The real reduction is 44%, not 50%. The gap grows with every layer.
The three formulas
- Amount saved: original price × discount ÷ 100.
- Final price: original price × (100 − discount) ÷ 100.
- Discount percentage from two prices: (original − sale) ÷ original × 100.
What common discounts actually leave you paying
| Discount | You pay | On $100 | On $250 |
|---|---|---|---|
| 10% | 90% | $90.00 | $225.00 |
| 20% | 80% | $80.00 | $200.00 |
| 25% | 75% | $75.00 | $187.50 |
| 33% | 67% | $67.00 | $167.50 |
| 50% | 50% | $50.00 | $125.00 |
| 70% | 30% | $30.00 | $75.00 |
Reading retail offers accurately
- Buy one get one free: a 50% discount, but only if you wanted two.
- Buy two get one free: 33% off, again conditional on needing three.
- Buy one get one half price: 25% off across the pair.
- Spend $100 save $20: 20% at exactly $100, and progressively less above it — $20 off a $180 basket is 11%.
- Percentage off a marked-up "was" price: the reduction is real only if the original price ever was.
Tax, and the order of operations
Discounts apply before sales tax, so the tax is charged on the reduced price — a small extra saving that is easy to overlook. Where prices already include VAT, as in most of Europe, the displayed discount is on the tax-inclusive figure and no adjustment is needed. If you are comparing a US price against a European one, remember you are comparing a pre-tax number against a post-tax number.