Which tab matches your question
Three everyday questions all involve a price and a discount, but only one of them fits the numbers you actually have in front of you. Percent off is for the ordinary case: a price tag and a percentage, like "25% off £80", and the tool multiplies the two together. Amount off is for a flat sum rather than a rate, a £20 voucher or a fixed markdown rather than a percentage, and it works out the equivalent percentage for you once the numbers are in. Work back covers the case where the price and percentage you can see are the after-discount figures, a receipt or a "was/now" label, and the original price is the unknown.
Picking the wrong tab does not break anything, it just answers a different question to the one being asked. Typing a sale price into the percent-off tab's original-price field, for instance, would calculate a further discount on top of a price that has already been reduced once, which is exactly the stacking trap the second section below explains. When two numbers on a receipt do not seem to add up, checking which of the three shapes actually applies is usually the fastest way to find out why.
Reading the results back works the same way in reverse. The headline number always answers the question the active tab is asking, whether that is a sale price or an original price, and the three lines underneath break it into the parts worth double-checking: how much is saved in real money, what percentage that represents, and which price the calculation started from. The donut chart and the table beneath it stay anchored to whichever price counts as the "original" for the current tab, so the same £80 or £75 keeps reappearing as the 100% mark, letting you sanity-check the answer against a price you already recognise rather than trusting the headline number blind.
How discount and sale price maths works
A percentage discount always comes off the price it is applied to, so the sale price is whatever fraction of the original is left after the cut. Taking 25% off means keeping 75%, so multiply the original price by 0.75 rather than working out the discount and subtracting it as a separate step.
A price of £80 with 25% off: the discount is 80 × 0.25 = £20, so the sale price is £60. Both routes, subtracting the discount or multiplying by 0.75 directly, land on the same number; the second is quicker once you trust it.
A fixed amount off works the same way in reverse: the discount is already a currency figure rather than a percentage, so the sale price is simply the original price minus that amount, and the effective percentage is the discount divided by the original price, expressed out of 100. A £20 voucher on an £80 order is a 25% effective discount, the same result as the percentage example above, arrived at from the other direction.
Stacking two discounts without double-counting
Combining two percentage discounts is the single most common source of a wrong sale price, because the instinctive answer, just adding the two percentages, is not how the second discount behaves. Each discount is applied to whatever price came before it, not to the original, so a second discount always erodes a smaller amount than the first one did.
Take a $100 item marked down 20%, with an extra 30% off at the till. The first discount leaves $80. The 30% is then taken off that $80, not the original $100, so it removes $24 rather than $30, leaving a final price of $56. The combined discount is 44%, not the 50% that adding 20 and 30 would suggest. The gap between the two answers grows with the size of the discounts, which is exactly why "stack these two codes" offers are more conservative than they sound.
The order the two discounts are applied in makes no difference to the final price, because multiplying by 0.8 and then by 0.7 gives the same result as multiplying by 0.7 and then by 0.8. What does change the result is which price each discount is calculated from, and it is always the price immediately before it, never the original sticker price.
Working backwards to the original price
Sometimes the sale price and the discount rate are known and the original price is the unknown, for instance checking a "40% off" label against a receipt. The temptation is to add the discount back onto the sale price, but a 40% discount was calculated from the original price, not from the smaller sale price, so adding 40% of the sale price back is not enough to undo it.
A jacket sells for $45 after 40% off: 45 ÷ (1 − 0.4) = 45 ÷ 0.6 = $75. Checking it forwards confirms the answer: 40% of $75 is $30, and 75 minus 30 is 45. Adding 40% of the $45 sale price back, by contrast, gives only $63, some way short of the true $75 original. A discount right at 100% has no original price to solve for either, since dividing by zero is undefined; anything can be marked down to nothing, so a 100% figure carries no information about where it started.
Reading the effective rate, not just the sticker
The percentage on the tag is only half the story once real money is involved. A 50% discount on a $20 item saves $10; a 20% discount on a $200 item saves $40, four times as much cash for a headline rate that looks less than half as generous. When two offers are genuinely being compared, the amount saved and the final price paid settle the question far better than the percentage alone, especially once a stacked or voucher discount is involved and the sticker rate stops being the whole calculation.
Questions people ask
Is 20% off then 10% off the same as 30% off?
No, and it is always a little less generous than 30%. The second discount applies to the already-reduced price, so 20% then 10% works out to a combined 28% off, not 30%. The only way to get exactly 30% off is a single 30% discount applied once.
Does the order of two stacked discounts change the final price?
No. Multiplying a price by 0.8 and then 0.7 gives exactly the same result as multiplying by 0.7 and then 0.8, since multiplication does not care about order. What does matter is that each discount is worked out from the price that came immediately before it, never from the original price a second time.
How do I find the original price from a sale price and a discount?
Divide the sale price by one minus the discount rate. A $60 sale price after 25% off was 60 ÷ 0.75 = $80 originally. Adding the discount percentage of the sale price back on is a common mistake and always undershoots the true original.
Can a discount make a price free or negative?
A 100% discount brings the price to exactly zero, free. A discount cannot sensibly exceed the price itself, so a fixed amount off that is bigger than the original price gets capped at the price, leaving nothing owed rather than a negative total.
What is the difference between percent off and percentage points?
Percent off is measured against the price it is taken from. A discount that improves from 20% off to 30% off is ten percentage points bigger, and the extra amount saved on that later, larger discount is calculated from a price that has already fallen once, if the two are stacked rather than being alternatives.
Do shops apply the discount before or after tax?
It varies by shop and by jurisdiction, and the receipt usually states which happened. Most commonly the discount is taken off the pre-tax price and tax is then charged on the reduced amount, but a coupon restricted to "before tax" pricing is worth reading carefully, since the two orders give slightly different final totals.
This calculator works out sale prices, effective percentages and original prices from the figures entered. It does not know a specific retailer's terms, exclusions or tax treatment, which are worth checking against the offer itself before relying on the total.