Double Discount Calculator
Enter an original price and two discount percentages to find the final price, total savings, and the true combined discount rate. The second discount applies to the already-reduced price, not the original, so stacking 20% plus 10% saves less than 30% would. Switch on sales tax to see the amount you actually pay at the register.
How sequential discounts work
A double discount means two percentage reductions applied one after the other. The first discount reduces the original price, and then the second discount is taken off the new, already-reduced price - not the original. This is why stacking 20% off and then 10% off does not equal a flat 30% discount. The formula is: final price = original price x (1 - first discount / 100) x (1 - second discount / 100). For a $100 item with 20% and 10% off: $100 x 0.80 x 0.90 = $72.00, which is a 28% combined discount, not 30%.
Effective combined discount rate
The effective discount is the single percentage that would produce the same final price as the two stacked discounts. It is calculated as: effective discount = 1 - (1 - d1/100) x (1 - d2/100), then expressed as a percentage. For two 10% discounts the effective rate is 1 - 0.90 x 0.90 = 19%, not 20%. The "missing" percentage grows as the individual rates increase: two 50% discounts combine to just 75%, not 100%. This gap matters when comparing a stacked promotion against a competitor offering a flat rate.
Does the order of discounts matter?
No. Because multiplication is commutative, applying discount A first and then B gives the same final price as applying B first and then A. Original price x (1 - A) x (1 - B) = original price x (1 - B) x (1 - A). The intermediate price shown after the first step will differ depending on which discount you apply first, but the final result and total savings are identical. Some retailers present the larger discount first to make the offer look more dramatic, even though your final bill is unchanged.
Adding sales tax after discounts
In most jurisdictions, sales tax is calculated on the final selling price after all discounts. Enable the tax toggle in this calculator to add a tax rate to the post-discount price. For example, a $100 item discounted to $72.00 with 8% tax becomes $72.00 x 1.08 = $77.76. Note that some promotional offers calculate tax on the original price and some on the pre-tax discounted price - always check the retailer's terms if the difference matters to you.
Effective discount for common stacked percentage pairs
| First discount | Second discount | Naive sum | Effective rate | Difference |
|---|---|---|---|---|
| 5% | 5% | 10% | 9.75% | -0.25% |
| 10% | 10% | 20% | 19.00% | -1.00% |
| 15% | 10% | 25% | 23.50% | -1.50% |
| 20% | 10% | 30% | 28.00% | -2.00% |
| 20% | 20% | 40% | 36.00% | -4.00% |
| 25% | 15% | 40% | 36.25% | -3.75% |
| 30% | 20% | 50% | 44.00% | -6.00% |
| 40% | 30% | 70% | 58.00% | -12.00% |
| 50% | 50% | 100% | 75.00% | -25.00% |
Both discounts are applied sequentially. The effective rate is always less than the sum of the two individual percentages.
Frequently asked questions
Is 20% off then 10% off the same as 30% off?
No. Applying 20% off first reduces a $100 item to $80. Taking a further 10% off $80 gives $72. That is a 28% effective discount, not 30%. The second markdown always applies to the reduced price, so stacked discounts always produce a smaller combined rate than the sum of their individual percentages.
What is the effective discount for two 10% discounts?
Two 10% discounts applied sequentially produce an effective rate of 19%. The calculation is: 1 - (1 - 0.10) x (1 - 0.10) = 1 - 0.81 = 0.19, or 19%. The naive sum of 20% would only apply if the second 10% were taken off the original price, which is not how stacked discounts work.
Does it matter which discount I apply first?
No. The order does not affect the final price or total savings. Multiplication is commutative, so applying a 20% discount and then a 10% discount produces exactly the same result as applying 10% first and then 20%. The intermediate price after the first step will differ, but the end result is identical.
How do I calculate the effective rate myself?
Convert each percentage to a decimal multiplier (100% - discount%), multiply the two multipliers together, then subtract from 1 and convert back to a percentage. For example, 25% and 15%: multipliers are 0.75 and 0.85. Product = 0.75 x 0.85 = 0.6375. Effective discount = (1 - 0.6375) x 100 = 36.25%.
Should sales tax be applied before or after the discounts?
In nearly all retail situations, tax is calculated on the final discounted price. So both discounts are applied first, then the tax rate is added to the result. For example, a $50 item discounted by 20% and 10% costs $36 before tax; at 8% tax that becomes $36 x 1.08 = $38.88.
Can I use this calculator for employee discounts on top of sale prices?
Yes. Enter the sale markdown as the first discount and the employee discount as the second. The calculator shows the intermediate price after the sale markdown, the final price after the employee discount, and the true effective rate so you can see how the two promotions combine.