Math Calculators
Percent Off Calculator
A percent off takes a share off a price, and a second discount takes its share off what remains, so a stack of discounts is never the sum of its percentages. Enter a price and up to three discounts to see the final price, the saving and the single discount the stack equals.
Calculator
Formula
A discount is applied to what is left, not to the original price, so the final price is the price multiplied by each discount’s remainder: final = P × (1 − d₁/100) × (1 − d₂/100) × …, the saving is P − final, and the single discount the stack equals is (1 − (1 − d₁/100) × (1 − d₂/100) × …) × 100. Two discounts therefore never add up: 30 % then 10 % on 200 gives 200 → 140 → 126, a saving of 74 and an effective discount of 37 %, not 40 %. The stack can sum above 100 % without any single discount exceeding 100 %: 60 % then 60 % gives 84 % effective. A single discount is a one-step stack, and its effective discount is that discount. The pair — the second item at d % off — costs 2P − P × d/100, saves P × d/100, and its effective discount on the pair is d / 2, so a second item at 100 % off is two for one.
About This Calculator
What It Does
This page answers the percent-off arithmetic in two modes. Successive discounts takes an original price and up to three discounts, where discount 1 is required and discount 2 and discount 3 may be left blank; it prints the final price, the total saving, the single discount the stack equals, and the running price after each step. Second item at a discount takes a unit price and one discount on the second item; it prints what the pair costs, what the second item’s discount is worth, and the pair’s effective discount. Both modes print the same three answers: what you pay, what you save, and the effective single discount.
Worked Example
The page opens on successive discounts with a price of 200 and discounts of 30 % and 10 %, and the third slot blank. The first discount takes 60 off and leaves 140; the second takes 14 off that and leaves 126. The saving is 74, and the single discount the stack equals is 37 %, which the page prints beside the money — not the 40 % the two percentages would suggest. Switch to the second-item mode with a unit price of 100 and the second item at 50 % off: the pair costs 150, saves 50, and its effective discount on the pair is 25 %. Set the second item to 100 % off and the pair costs 100 — two for one — at 50 % off the pair.
Real-World Usage
Use it when a sale is described in more than one percentage: a store-wide 30 % with a further 10 % on the reduced price, a markdown followed by a member discount, or a clearance rack with its own extra cut. It answers the question a checkout raises — what is this actually going to cost, and how much am I really saving — and the second-item mode answers the offer shoppers meet most often, the second one at half price.
Local Context
The percent-off arithmetic is the same everywhere and the page carries no country setting, so one page serves every country. Two conventions are worth knowing. The price is shown in your own currency and the figures are grouped and separated the way your language writes numbers, so the same answer reads 126,00 € in German and €126.00 in English. And a discount is a percentage of whatever price the shop applied it to: in countries where prices are shown including VAT the discount comes off that tax-inclusive price, while where tax is added at checkout it comes off the price before tax, which is what this page assumes.
Sources and Methodology
The arithmetic on this page is the multiplicative discount identity — final = P × Π(1 − dᵢ/100) — together with its rearrangement for the effective single discount, and both are written into the calculator module rather than quoted from a source. The second-item case is the same identity applied to a pair of items, giving d / 2 on the pair. The page’s own conventions are stated on it: money in the page’s currency, the effective discount to at most two decimals with trailing zeros trimmed, and a refusal for any single discount above 100 %.
Last reviewed: October 2026.
Frequently Asked Questions
Why is 30 % then 10 % not 40 % off?
Because the second discount applies to the reduced price, not to the original. On 200: the first 30 % takes 60 off and leaves 140; the second 10 % takes 14 off that 140 and leaves 126. The saving is 74, which is 37 % of 200 — the single discount the stack equals, and the figure the page prints beside the money.
What happens if I leave a discount blank?
It is not applied. Discount 1 is required, and discount 2 and discount 3 are optional: leave either blank and the stack simply has fewer steps, with no error. That is how a one-step markdown and a two-step stack are both read on the same page.
Can a stack total more than 100 % off?
Yes, and it is one of the things this page shows: 60 % then 60 % saves 84 % of the original price without any single discount exceeding 100 %. What is refused is a single discount above 100 %, because it would pay the buyer.
How does the second-item case work?
You pay the full price for the first item and the reduced price for the second, so the pair costs 2P − P × d/100 and saves P × d/100. Its effective discount on the pair is d / 2: a second item at 50 % off is 25 % off the pair, and a second item at 100 % off — two for one — is 50 % off the pair.