Discount Calculator
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Price & Discount
Final Price
Enter a price and discount percentage to see your savings.
How Discounts (and Stacked Discounts) Work
A single percent-off discount is simple multiplication, but "stacking" two discounts -- like an extra 10% off an already-marked-down item -- trips people up because the second discount applies to the already-reduced price, not the original one. This calculator handles both a single discount and a stacked pair, and can also work backward from a known sale price to recover the original price.
A Single Discount
A straightforward percent-off: final = original × (1 − discount%). A 20% discount on a $100 item brings the price to $80.00.
Stacked Discounts Multiply, They Don't Add
Two 20% discounts stacked do not equal 40% off. The second discount applies to the already-reduced price: 0.8 × 0.8 = 0.64, a 36% total discount -- 4 percentage points less than naive addition would suggest.
Working Backward from a Sale Price
If you only know the discounted price a retailer is charging, dividing it by the combined discount factor recovers the original price -- useful for spotting an inflated "original price" on a too-good-to-be-true sale tag.
The Effective Discount Rate
When stacking two discounts, the single number that summarizes your total savings is the effective discount rate: total savings divided by the original price -- not the sum of the two percentages.
Worked Example
Suppose a $100 item is 20% off, and you also have a coupon for an additional 10% off:
- After the first discount: $100 × (1 − 0.20) = $80.00.
- After the second discount: $80.00 × (1 − 0.10) = $72.00.
- Total savings: $100.00 − $72.00 = $28.00.
- Effective discount: $28.00 ÷ $100.00 = 28% -- not the 30% naive addition would suggest.
$100 Item, 20% + 10% Off
- Original Price: $100.00
- Final Price: $72.00
- Effective Discount: 28.00%
Two 20% Discounts Isn't 40% Off
This is the single most common discount-math mistake: stacking two 20% discounts feels like it should equal 40% off, but it actually works out to 36% off. Each discount is applied to whatever price remains after the previous one, so the reductions compound multiplicatively rather than adding together. The gap between "naive addition" and the true stacked discount grows larger the bigger the individual percentages are -- always use the multiplicative formula, never simple addition, when a deal advertises multiple discounts on top of each other.
Key Takeaways
- Stacked Discounts Multiply: Two discounts applied sequentially compound multiplicatively, not additively -- two 20% discounts equal 36% off, not 40%.
- Order Doesn't Change the Total: Applying a 20% then a 10% discount gives the same final price as applying the 10% first, then the 20% -- multiplication is commutative.
- You Can Work Backward: Given only a sale price and the advertised discount, you can recover the claimed original price to sanity-check the deal.
- Use the Effective Rate for Comparisons: When comparing deals with different discount structures, compare the effective (total savings ÷ original price) rate, not the headline percentages.