“30% off” sounds simple until you’re standing in a store trying to do the math in your head, or trying to figure out why two “30% off” stacked with “10% off” doesn’t actually mean 40% off. Here’s exactly how discount math works.
The Basic Discount Formula
Discount Amount = Original Price × (Discount % ÷ 100)
Sale Price = Original Price − Discount Amount
Real Example: $85 Item, 30% Off
Let’s calculate.
- Original price: $85
- Discount: 30%
Discount amount: $85 × 0.30 = $25.50
Sale price: $85 − $25.50 = $59.50
Why Stacked Discounts Don’t Simply Add Up
This trips up more shoppers than any other discount math. If a store offers “20% off, plus an additional 10% off,” that is not the same as 30% off total. Here’s why.
Starting price: $100
First discount (20%): $100 × 0.80 = $80
Second discount (10% of the new $80, not the original $100): $80 × 0.90 = $72
The final price is $72, meaning the true combined discount is 28%, not 30%. The second discount applies to the already-reduced price, not the original one. Consumer Reports’ guide to discount stacking covers this exact scenario, which retailers rarely clarify at checkout.
Reversing the Calculation: Finding the Original Price
Sometimes you see a sale price and want to know the original price before the discount.
Original Price = Sale Price ÷ (1 − Discount % as a decimal)
Example: A $59.50 sale price after a 30% discount:
$59.50 ÷ 0.70 = $85 original price
This confirms the math checks out against our earlier example.
Dollar-Off vs Percent-Off: Which Saves More?
Retailers sometimes offer a choice between a flat dollar discount and a percentage discount. The better deal depends entirely on the price point.
Example: Choosing between “$20 off” and “15% off” on a $150 item:
- $20 off: $150 − $20 = $130
- 15% off: $150 × 0.85 = $127.50
Here, the percentage discount wins by $2.50. But on a cheaper $80 item, the same comparison flips:
- $20 off: $80 − $20 = $60
- 15% off: $80 × 0.85 = $68
Now the flat dollar discount wins by $8. NerdWallet’s guide to smart shopping math recommends calculating both options quickly whenever a store offers a choice, since the better deal shifts depending on the original price.
The Psychology Behind Discount Pricing
Retailers use specific discount framing deliberately. A study on consumer perception published via the American Marketing Association found that percentage discounts tend to feel more appealing on lower-priced items, while dollar-amount discounts feel more appealing on higher-priced items, even when the actual savings are mathematically identical. This is exactly why you’ll often see “$5 off” on cheap items but “25% off” on expensive ones in the same store.
Common Discount Math Mistakes
- Assuming stacked percentage discounts add together, when they actually compound off a shrinking base price
- Comparing discounts without checking the base price first, since dollar-off and percent-off can win depending on the item’s cost
- Forgetting that sales tax typically applies after the discount, not before, meaning the final total is calculated from the reduced price
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Frequently Asked Questions
How do you calculate 30% off a price?
Multiply the original price by 0.30 to find the discount amount, then subtract that from the original price. For an $85 item, 30% off equals $25.50 off, for a final sale price of $59.50.
Do stacked discounts add together?
No. Stacked percentage discounts compound sequentially, with each discount applying to the already-reduced price from the previous discount, not the original price. This means “20% off plus 10% off” equals a 28% total discount, not 30%.
How do I find the original price from a sale price?
Divide the sale price by (1 minus the discount rate as a decimal). For example, a $70 sale price after a 30% discount means the original price was $70 divided by 0.70, which equals $100.
Is percentage off or dollar off better?
It depends on the item’s price. Percentage discounts tend to save more on higher-priced items, while flat dollar discounts tend to save more on lower-priced items, so it’s worth calculating both when given a choice.
Does sales tax apply before or after a discount?
Sales tax is almost always calculated on the discounted (final) price, not the original price, meaning the discount reduces both the item cost and the tax amount charged on that purchase.
What is a good discount percentage?
There’s no universal answer, since it depends on the retailer’s typical margins and the specific product category, but discounts of 20–30% are common for standard seasonal sales, while clearance items often reach 50% or higher.