Discount Calculator
Calculate the amount saved and the final price after one or more discounts.
E.g. "20% + an extra 10%": the second discount applies to the price already reduced, not to the initial price.
How is this result calculated?
With a single discount, the final price follows the formula final_price = initial_price × (1 − discount/100).
With an extra discount (successive discounts, such as "20% + an extra 10%"), the second discount is not added to the first: it applies to the price already reduced by the first discount, i.e. final_price = initial_price × (1 − discount1/100) × (1 − discount2/100). This is why the total reduction obtained — the effective discount rate — is always lower than the simple sum of the two displayed percentages.
Frequently asked questions
Why don't two 20% discounts add up to a 40% total reduction?+
Because the second discount doesn't apply to the initial price, but to the price already reduced by the first one. On €100, a 20% discount gives €80, then an extra 20% discount on that €80 gives €64 — a 36% total reduction, not 40%.
How do you calculate a discount by hand?+
Multiply the initial price by (1 − discount/100). For example, for a 20% discount on €100, calculate 100 × (1 − 0.20) = 100 × 0.80 = €80. The amount saved is then the difference between the initial price and this result, i.e. €20.
What's the difference between the discount percentage and the effective discount rate?+
The discount percentage is the one announced at each step (e.g. 20% then 10%). The effective discount rate is the percentage actually saved relative to the initial price once all discounts have been applied in cascade: it is always lower than the simple sum of the announced percentages as soon as there is more than one discount.
What's the difference between a cascading discount and a combined discount?+
A cascading (or successive) discount applies each discount to the price already reduced by the previous one, which always gives a total reduction lower than the sum of the percentages. A "combined" discount in the sense of directly adding the percentages (e.g. 20% + 10% = 30% applied at once to the initial price) is a different calculation, more favorable to the buyer, but rarely the one used in practice by retailers.
What happens with a 100% discount?+
The final price becomes €0: the item is entirely free. If an additional discount is added after a 100% discount, it then applies to a price that is already zero and has no further effect, so the final price stays at €0.