Discount Calculator
Optional, applied after the first.
Optional, added at the end.
- 174.99
- You pay
- 75.00
- You save
- 30.00%
- Effective discount
- 174.99
- Before tax
The discount calculator finds the sale price, the amount saved and the effective discount rate. It handles a second stacked discount and optional tax, and it states the thing shoppers most often get wrong: two 20 percent discounts are not 40 percent off. They are 36.
How it works
final = price x (1 - d1/100) x (1 - d2/100) x (1 + tax/100)
- d1, d2
- the two discounts, applied in sequence rather than added together
- tax
- applied last, to the already-discounted price
The second discount applies to the price after the first, not to the original. 20 percent then 20 percent leaves 0.8 × 0.8 = 0.64 of the price, an effective 36 percent off.
Tax is applied after both discounts, which matches how most sales taxes work. The taxable amount is what you actually pay for the goods.
Examples
A single discount
Price
249.99
Discount
30%
Result
You pay 174.99 · You save 75.00
249.99 × 0.7. The saving is the difference, not a separately calculated figure.
Stacked discounts
Price
100
Discount
20%
Extra discount
20%
Result
You pay 64.00 · Effective discount 36%
Not 40 percent. The second 20 percent applies to 80, taking off 16 rather than 20.
With tax added
Price
100
Discount
25%
Tax
20%
Result
Before tax 75.00 · You pay 90.00
Tax applies to the discounted 75, not the original 100. Applying it first would give 96, which is wrong in most tax systems.
Frequently asked questions
Why is 20% off then another 20% off not 40% off?
Because the second discount applies to the already-reduced price. Twenty percent off 100 leaves 80; twenty percent off 80 takes away 16, not 20. The effective discount is 36 percent. Retailers rely on this reading better than it calculates.
Should tax be applied before or after the discount?
After, in most systems, because tax is charged on what you actually pay. This tool applies discounts first and tax last. A few jurisdictions treat certain coupons differently, so check your receipt if the figures disagree.
How do I work backwards from a sale price to the original?
Divide rather than adding the percentage back. A 30 percent discount leaving 174.99 means the original was 174.99 / 0.7 = 249.99. Adding 30 percent to 174.99 gives 227.49, which is wrong.
What order are stacked discounts applied in?
The order does not matter. Multiplication is commutative, so 20 then 30 gives the same result as 30 then 20. What matters is that they multiply rather than add.