A shop says 30 percent off, and you want to know what you’ll actually pay. The maths is short, but it helps to see the sale price and the saving together.
There’s a box for a second discount too, for the times a coupon lands on top of a sale.
How to use the Percent Off Calculator#
- Enter the price. Use the price before any discount.
- Enter the discount. Type the percentage off.
- Add a second discount. Optional. It’s taken off the already reduced price.
The formula#
30 percent off 120 means paying 70 percent of it: 120 × 0.70 = 84. You save 36. If you then use a 10 percent coupon, you pay 84 × 0.90 = 75.60, so your total saving is 44.40, which is 37 percent of the original price, not 40.
Stacked discounts#
Two discounts of 30 and 10 percent don’t add up to 40 percent. The second is taken from the reduced price, so it’s worth less. Total discount is 1 − (0.70 × 0.90) = 37 percent. Always check whether a shop applies a coupon to the original price or the sale price.
Why two discounts don’t add up#
A shop advertises 30 percent off, with an extra 20 percent off at the till. Most people expect 50 percent off, but the second discount applies to the already reduced price. On an item priced at 100: after 30 percent off it costs 70, and 20 percent off 70 is 56. The total discount is 44 percent, not 50. The order does not matter, since the multipliers are just multiplied: 0.7 × 0.8 = 0.8 × 0.7 = 0.56.
| Offer | Multiplier | Final price on 100 | Real discount |
|---|---|---|---|
| 20% off | 0.80 | 80.00 | 20% |
| 30% then 20% | 0.70 × 0.80 | 56.00 | 44% |
| 50% then 10% | 0.50 × 0.90 | 45.00 | 55% |
| 25% then 25% | 0.75 × 0.75 | 56.25 | 43.75% |
| 10% then 10% then 10% | 0.9³ | 72.90 | 27.1% |
Working back to the original price#
If you only know the sale price, divide by the multiplier. A jacket costs 75 after 25 percent off, so the original price was 75 ÷ 0.75 = 100. Do not add 25 percent to 75, which gives 93.75. This is the same trap that catches people with tax: to remove 7.5 percent VAT from a price, you divide by 1.075, not take 7.5 percent off.
When you compare offers from different shops, use the final price, not the discount percentage. A 40 percent discount on an inflated starting price can cost more than a 20 percent discount on an honest one.
A mental shortcut and tax#
For quick sums, start from 10 percent: move the decimal point one place left. 10 percent of 85 is 8.50, so 30 percent is 25.50, and 15 percent is 8.50 plus half of it, 4.25 more. For 25 percent, take off a quarter. Subtract to get the sale price. If you’re comparing shops, work out the final price in each rather than comparing the percentages.
Most shops take the discount first and then add sales tax or VAT to the reduced price, so the tax is lower too. Check the receipt if it matters. To see how a tax is added, use our VAT calculator or the sales tax calculator.
Frequently asked questions#
Multiply the price by 1 minus the discount as a decimal. For 30 percent off, multiply by 0.70.
Divide the sale price by 1 minus the discount. A sale price of 84 after 30 percent off means the original was 120.
No. The second is taken from the reduced price, so the total is less than the sum.
No. Add sales tax or VAT afterwards if it applies.
Multiply the original price by one minus the discount as a decimal. For 20 percent off 85, the multiplier is 0.8, and 85 × 0.8 = 68. The saving is 85 − 68 = 17. The calculator also handles a second, extra discount and shows the price after each step.
No. The second discount applies to the price that is left after the first, so the total is smaller. 30 percent off then 20 percent off gives a combined discount of 44 percent, because 0.7 × 0.8 = 0.56 of the original price is paid. Use the extra discount box to see this for any price.
Subtract the sale price from the original, divide by the original and multiply by 100. A coat that was 80 and is now 60 has a discount of 20 ÷ 80 = 25 percent. If you only know the sale price and the percent off, divide the sale price by one minus the discount to find the original.