What this calculator does
This tool answers three separate questions about a discount. Pick “Price after discount” to see what you pay once one or two discounts are applied. Pick “Find the percentage off” when you know the original price and the sale price and want the rate between them. Pick “Find the original price” when you only have the sale price and the percentage that was taken off, and want to know what the item cost before the sale. Each mode runs its own arithmetic — there is no single formula that covers all three, so use the card that matches what you actually have.
The formulas
Price after discount: amount off = price × percent ÷ 100, then final price = price − amount off. A fixed amount off skips the multiplication and is subtracted directly. For 1,980 at 15% off: 1,980 × 15 ÷ 100 = 297, and 1,980 − 297 = 1,683. The same result comes from multiplying by the share you keep: 1,980 × 0.85 = 1,683.
Percentage off between two prices: percent off = (original − sale) ÷ original × 100. For 5,000 down to 3,500: 1,500 ÷ 5,000 × 100 = 30% off.
Original price from a sale price: original = sale ÷ (1 − percent ÷ 100). For 700 after 30% off: 700 ÷ 0.70 = 1,000.
Stacking two discounts
The “Price after discount” panel has a second, optional discount field. It is not added to the first — it is taken off the price that is left after the first discount has already been applied. 30% off followed by a 10% coupon on 1,000 is 1,000 × 0.70 = 700, then 700 × 0.90 = 630. That is 630 paid, 370 off, an effective 37% off in total — not 40%. The calculator lists both stages and shows the combined percentage as a separate stat so you can see how far it is from simply adding the two rates.
Either discount can be a percent off, a fixed amount off, or (for pages that show it) tenths off. You can mix them: a 20% discount followed by a flat 5 off the reduced price, for example. A fixed amount can never be larger than the price it is taken from — the calculator rejects that and points at the field that is wrong.
Worked examples
Example 1 — single percent, rounded down. Item at 1,980, 15% off, rounding set to “down”, 0 decimals: amount off is 297, final price is 1,683.
Example 2 — two stacked percentages. Item at 1,000, 30% off then a 10% coupon: after the first discount the price is 700, after the second it is 630. Total discount is 370, an effective 37% off.
Example 3 — fixed amount off, with cents. Item at 49.99, 8.00 off, rounding “nearest”, 2 decimals: the final price is 41.99 and the discount is exactly 8.00, because a fixed amount is never rounded — only a percentage discount produces a fraction of a cent to round.
Example 4 — rounding at work. Item at 999, 33% off: the exact price is 669.33. With 0 decimals that rounds to 669 on “down” or “nearest”, and to 670 on “up”. The stored discount amount always matches whichever final price you chose, so price paid plus discount equals 999 in every case.
Working backwards
Use “Find the percentage off” when a shop shows both prices and you want the rate: 5,000 down to 3,500 is 1,500 ÷ 5,000 = 30% off. Use “Find the original price” when a receipt or label only shows the sale price and the discount rate: 700 after 30% off is 700 ÷ 0.70 = 1,000. This is the reverse of the first mode, and it is useful for checking whether a “30% off” sticker matches the price actually charged.
Reading the result
Every mode shows a primary number plus supporting stats: the price to pay, the total discount, and the effective discount rate when more than one discount is stacked. The “How it was calculated” list below the result spells out each stage in order, including the rounding step when the exact price and the rounded price differ, so you can check the arithmetic rather than trust it blindly.
Rounding
Percentages often leave a fraction of the smallest coin. Choose how the final price is rounded — down, to the nearest, or up — and how many decimal places the currency uses, none or two. Rounding is applied once, to the final price, and the discount amount is worked out afterwards as price minus that rounded final price. That order matters: it means the price paid and the discount you are shown always add back up to the original price, exactly, with nothing left over from the rounding.
Edge cases
- 100% off. A percentage discount of exactly 100% is allowed and brings the final price to 0. A percentage above 100% is rejected, since you cannot discount more than the whole price.
- Zero or negative price. The price, sale price, or original price must be greater than 0. A price of 0 or a negative number is rejected with an error on that field.
- Negative discount. A discount cannot be negative — the calculator has no separate “mark-up” mode, so a price increase is not something to enter here.
- Sale price above original. In “Find the percentage off”, a sale price higher than the original is rejected, since that is a mark-up rather than a discount.
- 100% in “Find the original price”. A rate of 100% is rejected there, because dividing by zero has no answer — any original price would give a sale price of 0.
- Amount larger than the price. A fixed amount off cannot exceed the price it is taken from, in either the first or the second discount field.
Common mistakes
The biggest one is adding two percentages together. 30% off plus 10% off is not 40% off — it is 37% off, because the second discount applies to a smaller number. The gap grows with the size of the discounts: 50% off plus 50% off is not free, it is 75% off (you pay a quarter of the price). Another common slip is comparing a percent-off deal with a fixed-amount deal by eye. The two only tie at one specific price — work out that price, or run both through the “Price after discount” panel, instead of guessing which is bigger.
Limitations
This calculator handles up to two stacked discounts, not three or more, and it does not compute sales tax, shipping, or store credit. If a discount and a tax both apply, work out the discounted price here first, then run that figure through a tax calculator such as the consumption tax calculator — the order in which discount and tax are applied is set by the store, not by this tool.
Related tools
To work out a percentage of any number, not just a discount, use the percentage calculator. For exam or attendance percentages rather than prices, see the percentage calculator for marks.
Frequently asked questions
How do you calculate a discount?
Multiply the price by the percentage off and divide by 100 to get the discount, then subtract it. 80 at 25% off is 80 × 25 ÷ 100 = 20 off, so you pay 60. Equivalently, multiply by what you keep: 80 × 0.75 = 60.
Are two discounts added together?
No. A second discount is taken from the already reduced price. 30% off and then a 10% coupon on 1,000 is 1,000 × 0.7 × 0.9 = 630, an effective 37% off — not 40%.
How do I find what percentage off a sale price is?
Subtract the sale price from the original, divide by the original and multiply by 100. 50 reduced to 35 is 15 ÷ 50 × 100 = 30% off. Choose “Find the percentage off”.
How do I find the original price before a discount?
Divide the sale price by the fraction you paid. After 30% off you paid 70%, so 70 ÷ 0.7 = 100. Choose “Find the original price”.
How is the final price rounded?
Choose rounding down, to the nearest or up, and how many decimal places the currency uses. The rounding is applied once to the final price, and the discount amount is the original price minus that, so the two always add up.
Can the discount be a fixed amount?
Yes. Choose “Amount off” and enter the amount. It cannot be larger than the price it is taken from.
What happens if I enter a 100% discount?
It is accepted and the final price is 0. A percentage above 100% is rejected, since a discount cannot remove more than the whole price.
Why does “Find the original price” reject 100% off?
At 100% off, any original price gives a sale price of 0, so there is no single original price to work back to. Enter a rate below 100%.
Can I use this calculator for a price increase instead of a discount?
No. Every discount value must be zero or positive and is subtracted from the price. For a mark-up, work out the increase yourself before entering the price.
Does this calculator include sales tax?
No, it works out the discounted price only. If tax also applies, work out the discount first, then run that price through a separate tax calculator, since stores differ on whether tax is charged before or after the discount.