Stacked Discount Calculator
The real price and total discount when one discount comes on top of another.
Good to know. 20% off and then another 10% is 28% off, not 30%. The second discount gets a smaller price to work on.
How it works
In plain words
Each discount multiplies what is left of the price: 20% off leaves 80%, a further 10% off leaves 90% of that. Multiply the remaining shares together; one minus the result is the total discount.
The formula
final price = price × (1 − d₁) × (1 − d₂) × (1 − d₃) total discount = 1 − (1 − d₁) × (1 − d₂) × (1 − d₃)
Worked example
100 with 20% off is 80, and a further 10% off that is 72.00. Together it is a 28% discount, not 30%.
Sources
No outside data or rates: this is plain arithmetic.
4 automated tests check its answers on every change.
About the stacked discount calculator
When a shop offers “an extra 10% off sale prices”, the second discount comes off the price after the first one. That makes the combined discount smaller than the two percentages added together: 20% then 10% is 28% in total, not 30%.
The easiest way to work it out is with what is left after each discount. 20% off leaves 80% of the price; a further 10% off leaves 90% of that. 0.8 × 0.9 = 0.72, so you pay 72% and save 28%. The order doesn’t matter: 10% then 20% gives the same 72%.
The same thinking explains a classic trap: 50% off and then another 50% off is 75% off, not free. And a price that goes up 10% and then comes down 10% ends 1% lower than it started.
Coupons for a fixed amount, such as 10 off, work differently: whether they come before or after a percentage discount changes the result. Take a percentage off after a fixed coupon and you save slightly less. For a single discount, use the discount calculator; to add sales tax or VAT, the sales tax or VAT calculators.
Questions people ask
What is 20% off plus an extra 10% off?
A total of 28%. 100 becomes 80, then 72.
Do stacked discounts add up?
No. Each comes off the already reduced price, so the total is always less than the sum of the percentages.
Does the order of the discounts matter?
Not for percentages: 10% then 20% gives the same price as 20% then 10%.