A discount is one of the simplest percentage applications, and one of the most frequently miscalculated. Stacked promotions, post-tax discounts, and "up to" advertising all introduce small confusions that can change the real cost of an item by 5–10%.
Key Takeaways
- Sale price = Original × (1 − discount rate). This is the only formula you need for a single discount.
- Stacked discounts multiply, they don't add. 20% off + 10% off = 28% off, not 30%.
- Discount applied before tax saves more than the same discount applied after tax.
- Reverse-discount math (finding the original price from a sale price) uses Original = Sale ÷ (1 − rate).
- "Up to" discount advertising rarely means everything is at the maximum percentage off.
The Core Formula
Sale Price = Original Price × (1 − Discount Rate)
For a 25% discount on a $80 jacket:
Sale Price = 80 × (1 − 0.25) = 80 × 0.75 = $60
To find the discount amount alone:
Discount = Original × Rate
= 80 × 0.25 = $20 off
Both forms produce the same final number. The first is faster when you only need the sale price; the second is useful when you want to see what you saved.
Stacked Discounts: Why They Are Less Than They Sound
Two discounts applied in sequence multiply, not add.
Combined rate = 1 − [(1 − rate1) × (1 − rate2)]
A 30% off promotion plus an extra 20% off at checkout:
Combined = 1 − (0.70 × 0.80) = 1 − 0.56 = 44% off, not 50%.
A $100 item:
- After first 30% off: $70
- After additional 20% off: $56
That is a 44% total discount. The order doesn't matter; applying 20% first then 30% lands on the same $56.
| First Discount | Second Discount | Total Effective Discount |
|---|---|---|
| 10% | 10% | 19% |
| 20% | 10% | 28% |
| 25% | 25% | 43.75% |
| 30% | 20% | 44% |
| 50% | 25% | 62.5% |
This is the most common percentage trap in retail. "Up to 70% off plus an extra 30%" sounds like a complete discount; it is actually 79%.
Discount Before vs After Tax
A discount applied before tax reduces both the item price and the tax owed. A discount applied after tax only reduces the item portion. The pre-tax discount is always slightly better.
Example: $100 item, 8% sales tax, 20% discount.
Discount before tax:
- Discounted price: $80
- Tax: $6.40
- Total: $86.40
Discount after tax:
- Pre-discount with tax: $108
- Apply 20% to item only: discount = $20
- Total: $108 − $20 = $88
Difference: $1.60 on a $100 purchase. Small per item, meaningful on larger receipts. Most U.S. retailers apply discount before tax (the legally typical approach), but coupon-as-cash promotions and rebates may apply after.
Reverse-Discount Math: Finding the Original Price
If a sale tag shows the price after discount and the percentage off, the original can be reverse-engineered:
Original = Sale Price ÷ (1 − Discount Rate)
A "40% off" tag showing $36:
Original = 36 ÷ 0.60 = $60
The savings: $24. This is useful for comparison shopping and for verifying that an advertised discount matches the actual price drop.
A subtle scam to watch for: stores that mark up prices specifically to discount them back. If "40% off" leaves you near the typical market price for that item, the discount may be largely cosmetic. Always cross-check the post-discount price against alternatives.
Worked Example: A Realistic Shopping Trip
A shopper buys:
- Jacket marked $120, 25% off
- Two shirts marked $40 each, buy-one-get-one 50% off
- Pants marked $80, 30% off
Plus an extra 10% coupon applied to the entire order, then 8% sales tax.
Jacket: 120 × 0.75 = $90.00 Shirts: 40 + (40 × 0.50) = $60.00 Pants: 80 × 0.70 = $56.00 Subtotal after item discounts: $206.00
10% extra off: 206 × 0.90 = $185.40 Tax (8%): 185.40 × 0.08 = $14.83 Final total: $200.23
If all the discounts had been applied to the original $280 marked price as one number:
Effective discount: (280 − 185.40) / 280 = 33.8%
The shopper saved a real 33.8%, despite individual tags showing rates of 25–50%.
"Up to" Discount Advertising
"Up to 70% off" is the most over-promised phrase in retail. It typically means a small number of clearance items are at the maximum percentage off, while most of the store is at much lower discounts. Always check the items you actually want before assuming the headline applies.
A useful habit: take the advertised maximum and mentally halve it as a working assumption for the broad inventory. If the store advertises "up to 60% off" and you find your item at 30% off, you got the average: not a bad deal, but not the headline either.
Common Mistakes
Adding stacked discounts. 20% + 10% is not 30%. It is 28%.
Forgetting tax timing. A discount before tax saves slightly more than the same discount after tax.
Treating a coupon as cash when it isn't. A "$10 off" coupon reduces price like cash; a "10% off" coupon scales with the purchase. Different math on the same receipt.
Confusing percentage off with percentage of original. "Now 60% of the original price" is a 40% discount, not a 60% discount.
Ignoring shipping/handling. A 20% off + free shipping promotion is often the better deal than 30% off with paid shipping on small orders.
Applying the discount rate to the discount amount. Don't multiply percentages onto percentages: just compute the final sale price directly.
Practical Scenarios
Scenario 1: Comparing two stores. Store A sells the same item at $100 with 30% off. Store B at $120 with 40% off. Store A: $70. Store B: $72. Store A is the better deal despite the smaller advertised discount.
Scenario 2: Loyalty program timing. A 15% loyalty discount stacked with a 25% sale produces 1 − (0.85 × 0.75) = 36.25% off. Worth using the loyalty card during a sale.
Scenario 3: Negotiating B2B price. A supplier offers "10% off + 5% rebate." The combined effective discount is 1 − (0.90 × 0.95) = 14.5%, not 15%.
Scenario 4: Black Friday math. A laptop normally $1,200 is listed at $899 with "save $300!" The advertised discount: $301. Real discount rate: 301 / 1,200 = 25.1%. Trustworthy advertising. A similar listing at $999 with "save $300" implies an original of $1,299, which may or may not be the actual historical price.
FAQ
How do I calculate the sale price after a discount? Multiply the original price by (1 − discount rate as decimal). A 25% discount on $80: 80 × 0.75 = $60.
Do stacked discounts add or multiply? Multiply. 20% off + 10% off is 28% off (1 − 0.80 × 0.90 = 0.28), not 30%.
How do I find the original price from a sale price? Divide the sale price by (1 − discount rate). A $42 sale tag at 30% off: 42 / 0.70 = $60 original.
Is a discount before or after tax better? Before tax is slightly better because it reduces the tax owed. Most U.S. retailers apply discounts before tax by default.
How do I calculate the percentage saved on a final price? (Original − Final) / Original × 100. A $120 item bought for $84: (120 − 84) / 120 × 100 = 30% saved.
Why doesn't "10% off + 10% off" equal "20% off"? Each discount applies to the price that exists at that step. The second 10% is calculated on the already-discounted amount, not on the original.
Can a discount be larger than 100%? No. A discount cannot exceed 100% (that would mean paying you to take the item). What can exceed 100% is markup, where the selling price is more than double the cost.
Related Tools
The Discount Calculator handles single discounts, stacked discounts, and reverse-discount math. The Percentage Calculator handles the general case. For receipts with tax, the Sales Tax Calculator computes the post-tax total, and the Tip Calculator handles restaurant math.
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Final Thoughts
Discount math is just percentage math with a sale tag, and the same rules apply: subtract first, multiply with care, and never add two percentages together hoping they will sum. The most useful habit in shopping is computing the final price yourself rather than trusting the headline rate. A 60-second mental check at the register catches every "up to" exaggeration, every stacked-discount overstatement, and every "savings" claim that doesn't quite add up.