Sale price and amount saved
A percentage discount takes a share of the original price off. Multiply the original price by the percentage, subtract the result, and you have the sale price. Equivalently, multiply by the share you keep: a 10% discount keeps 90%. On a 45.00 item, 10% is 4.50, so the sale price is 40.50. The amount you save is always the original price minus the final price. A fixed amount off works more simply: a 20.00 coupon on a 95.00 service leaves 75.00, which is the same saving as 21.1% off that price.
A 100% discount leaves a final price of zero and a 0% discount leaves the price unchanged. Negative numbers, percent signs, thousands separators and blanks are flagged as input problems instead of being guessed, so a typo never becomes a quietly wrong price.
Reverse discount: find the original price or the percentage
Sometimes you only see the sale price. If an item costs 80.00 after 20% off, divide the final price by the share that was kept: 80.00 ÷ 0.80 = 100.00. You cannot take 20% of the sale price and add it back, because the discount was calculated on the larger original amount. To find the percentage from two prices, subtract the final price from the original and divide by the original: a 120.00 item now at 90.00 is 25% off.
Some inputs cannot be reversed. A 100% discount always gives a final price of zero, so a zero final price does not reveal the original price, and a 0% discount that saves nothing does not either. The calculator explains these cases instead of guessing, and it asks you to pick which two values you know so the answer is never ambiguous.
If a receipt shows only the amount saved, you can still recover the price: saving 25.00 at 20% off means the original was 25.00 ÷ 0.20 = 125.00, so you paid 100.00.
Percentage and cash coupons: why order matters
Two percentage discounts do not add up. Taking 20% off and then 10% more leaves 0.80 × 0.90 = 72% of the price, so the total saving on 100.00 is 28.00, an effective discount of 28% and not 30%. The second discount applies to a smaller number. With percentages alone the order never changes the answer, because multiplication is commutative.
Mixing a cash coupon with a percentage is different. Take 10.00 off first and then 20% off, and 100.00 becomes 72.00. Take 20% off first and then 10.00 off, and it becomes 70.00. The percentage is worth more when it works on the larger price, so the retailer's stated order decides your result. The ledger shows each step so you can see which order applies. A cash coupon larger than the remaining price is rejected rather than quietly reduced to zero.
Stacked percentages work the same way however many there are. Three offers of 10% each leave 0.9 × 0.9 × 0.9 = 72.9% of the price, an effective discount of 27.1% rather than 30%. A retailer that advertises an extra 10% off on top of a sale price is describing exactly this: each new percentage applies to the price left by the one before it.
Tax and rounding
Tax can be handled in two ways, and the calculator asks which one you mean. If tax is added after the discounts, a final price of 63.00 with a 5% rate becomes 66.15. If the prices you entered already include tax, a 105.00 tagged price with 20% off is 84.00 including tax, which contains 5.00 of tax at 5%. These are estimates from the rate you type. Real receipts follow local rules and the merchant's own rounding.
The calculation keeps full precision and rounds only for display. A 59.99 item at 15% off is exactly 50.9915 before display, which shows as 50.99. Rounded lines can occasionally differ from a rounded total by a cent.
The most common slip is discounting a tax-inclusive price and then adding tax again. Pick the treatment that matches the price tag before you read the payable amount.
Worked checkout example
A 100.00 item has 20% off, then a 10.00 coupon, then a 10% loyalty discount, applied in that order.
| Step | Opening | Saving | Closing |
|---|---|---|---|
| 20% off | 100.00 | 20.00 | 80.00 |
| 10.00 off | 80.00 | 10.00 | 70.00 |
| 10% off | 70.00 | 7.00 | 63.00 |
| Plus 5% tax | 63.00 | 3.15 | 66.15 |
The three offers add up to a 37.00 saving, an effective 37% off, rather than the 40% you would get by naively adding 20%, 10% and the 10 coupon as if they were the same kind of discount. When you know the final price, check the seller's margin at that price, and when a discounted bill is shared, split the discounted bill and the tip.
Order changes this result. Applying the same three offers with the cash coupon last gives 62.00 instead of 63.00, because the 10% loyalty discount then works on a larger price. When a receipt lists offers in a different order from the one you assumed, enter them in the printed order and compare the two totals.
Discount calculator questions
Is 20% off and then 10% off the same as 30% off?
No. The two discounts multiply, so the effective discount is 28%. The second discount applies to a price that is already lower.
How do I find the original price from a sale price?
Divide the final price by the share you paid. For an item that cost 80 after 20% off, divide by 0.80 to get 100. Degenerate cases such as a 100% discount cannot be reversed.
Does the order of a coupon and a percentage discount matter?
It can. A fixed coupon taken before a percentage gives a different price from the same coupon taken after, as the example above shows. Percentages alone are order-independent.
How is tax handled?
You choose whether tax is added after the discounts or already included in the prices you entered. The result is an estimate from your rate, and the actual amount depends on the merchant and local rules.
Is the biggest discount always the best deal?
No. A larger discount on a bigger pack or an item you did not need is not better value. Compare the price per unit and decide whether you need the quantity before treating a discount as a saving.