Discount Maths: Stacked Discounts, Working Backwards and Tax
By Akmal Ali · Published · Updated · 4 min read
Multiply the original price by the discount percentage and divide by 100 to get the amount saved, then subtract it from the price: 25% off 80 saves 20, so the sale price is 60. To find the original price from a sale price, divide by one minus the discount: 60 ÷ 0.75 = 80.
A shelf label says “25% off”, a checkout adds a 10% coupon on top, and a website shows a crossed-out price next to a new one. Each of these is the same small piece of arithmetic, done forwards or backwards. Once you know the two formulas below, you can check any sale price in your head or on a phone.
The discount formulas
discount amount = original price × discount % ÷ 100
sale price = original price − discount amount
You can also combine them into one step. Taking 25% off leaves 75% of the price, so multiply by 0.75:
sale price = original price × (1 − discount % ÷ 100)
Worked examples
| Original price | Discount | Amount saved | Sale price |
|---|---|---|---|
| 80.00 | 25% | 80 × 25 ÷ 100 = 20.00 | 60.00 |
| 49.99 | 15% | 49.99 × 15 ÷ 100 = 7.50 | 42.49 |
| 1,200.00 | 12.5% | 1,200 × 12.5 ÷ 100 = 150.00 | 1,050.00 |
The second example rounds 7.4985 to 7.50. Shops round to the nearest cent or penny, so a till can be one unit different from a calculation that keeps every decimal.
Discount Calculator
Enter the price and the percentage off to see the sale price and your saving, including a second discount on top.
Quick mental maths
- 10% off: move the decimal point one place left and subtract. 10% of 64 is 6.40, so you pay 57.60.
- 20% off: double the 10% figure. 20% of 64 is 12.80.
- 25% off: take a quarter off. 25% off 64 leaves 48.
- 15% off: 10% plus half of it again. 15% of 64 is 6.40 + 3.20 = 9.60.
How do you work backwards from a sale price?
Find the discount percentage from two prices
discount % = (original price − sale price) ÷ original price × 100
A coat was 120 and is now 90. The saving is 30, and 30 ÷ 120 × 100 = 25% off. The percentage calculator does this in its percentage-change box: a change from 120 to 90 is −25%.
Find the original price from a sale price
original price = sale price ÷ (1 − discount % ÷ 100)
You paid 60 after 25% off. The original price was 60 ÷ 0.75 = 80. Adding 25% back to 60 gives 75, which is wrong, because the 25% was taken from 80, not from 60.
How do two discounts in a row add up?
When a coupon applies on top of a sale, the second percentage is taken from the already reduced price. Multiply the remaining shares:
final price = original × (1 − first ÷ 100) × (1 − second ÷ 100)
30% off and then an extra 20% off leaves 0.7 × 0.8 = 0.56 of the price, which is 44% off in total, not 50%. The order doesn’t matter: 20% then 30% gives the same result.
Percentage off or a fixed amount off?
“15% off” and “10 off” are worth the same on a price of about 66.67. Below that, the fixed amount saves more; above it, the percentage does. On 60, 15% off saves 9, so the 10 off wins. On 80, 15% saves 12. To find the break-even price for any pair, divide the fixed amount by the percentage as a decimal: 10 ÷ 0.15 = 66.67.
Common mistakes
- Reading “up to 50% off” as 50% off. It means some items are reduced by that much. Check the price of the one you want.
- Comparing a discount on a small pack with a bigger pack at full price. 25% off can still cost more per kilogram or litre. Compare the price per unit with the unit price calculator.
- Trusting the crossed-out price. A “was” price is the shop’s own reference. What matters is what you pay now compared with what the item usually costs elsewhere.
What about tax?
With a percentage discount, and tax charged on the price you actually pay, the order of tax and discount doesn’t change the final price. 20% off 100 with 10% tax is 100 × 0.8 × 1.1 = 88, whichever is applied first. A fixed amount off is different: 10 off before 10% tax gives 99, but 10 off after tax gives 100. To add or remove tax itself, use the tax calculator. For other percentage questions, see how to calculate percentage.
Frequently Asked Questions
Is buy one, get one free the same as 50% off?
Only if you wanted two. Each item then costs half price, so it works out as 50% off per item, but if you only needed one, you spend the same as without the offer.
Is 3 for 2 better than 30% off?
If you want all three items, yes: paying for two of three is 33.3% off each. If you only need one or two, the 30% discount is the better deal.
How do I calculate a discount in a spreadsheet?
With the price in A2 and the discount as a percentage in B2 (for example 20%), the sale price is =A2*(1-B2) and the amount saved is =A2*B2. For an extra discount in C2, use =A2*(1-B2)*(1-C2).