How a discount is calculated
A discount is a percentage of the original price. Work out the amount off, then subtract it. Or, faster, multiply the price by what you keep.
Example: a pair of shoes costs $80 and is 25% off. The amount off is 80 × 0.25 = $20, so you pay $60. The quick way is 80 × 0.75 = $60.
The calculator rounds each step half up to the nearest cent, as a shop till does, and uses exact decimal maths so you never see rounding glitches.
Stacked discounts are not added together
Shops often advertise “an extra 10% off sale prices” or let you use a coupon on a reduced item. The second discount comes off the price that is already reduced, not the original. So the percentages multiply; they do not add.
Example: a $100 jacket is 20% off, with an extra 10% at the till.
- After 20% off: 100 × 0.80 = $80.00
- After the extra 10%: 80 × 0.90 = $72.00
- Combined discount: 1 − 0.80 × 0.90 = 0.28, so 28%, not 30%
The gap grows with bigger numbers. “50% off, then another 50% off” is 75% off in total, not 100%. Three 50% discounts in a row come to 87.5%.
| Discounts | Looks like | Real total |
|---|---|---|
| 20% + 10% | 30% | 28% |
| 25% + 15% | 40% | 36.25% |
| 30% + 20% | 50% | 44% |
| 50% + 50% | 100% | 75% |
| 40% + 20% + 10% | 70% | 56.8% |
For percentages, the order does not matter: 10% then 20% gives the same price as 20% then 10%. Order does matter when you mix a fixed amount with a percentage. $10 off and then 20% off a $50 item gives $32, but 20% off and then $10 off gives $30.
Finding the original price
If you only know the sale price and the percentage, divide by what you kept.
Example: a lamp costs $45 after 25% off. The original price was 45 ÷ 0.75 = $60. A common mistake is to add 25% back on: 45 × 1.25 = $56.25, which is wrong, because the 25% was taken from the larger original price.
This works for stacked discounts too. A $72 price after 20% and then 10% off came from 72 ÷ (0.80 × 0.90) = $100.
Amount off instead of percent off
Some offers give a fixed amount, like “$15 off any purchase”. The calculator shows what percentage that is, so you can compare it with a percent-off deal.
Example: $15 off a $60 item is 15 ÷ 60 × 100 = 25% off. On a $200 item, the same $15 is only 7.5% off. A percent-off coupon is usually better on expensive items, and an amount-off coupon is better on cheap ones.
Sales tax after the discount
In most US states, sales tax is charged on the price you actually pay after a store discount. If the $72 jacket above is bought where the combined rate is 8.25%, the tax is 72 × 0.0825 = $5.94 and the total at the till is $77.94. Manufacturer coupons, which the maker pays back to the store, are taxed differently in some states. To find your state’s rate, use the sales tax calculator. In the UK and EU, displayed prices normally already include VAT; the VAT calculator splits a price into net and VAT.
Tips for spotting a real bargain
- Check the “was” price. The US Federal Trade Commission’s pricing guides say a former price should be one the item was really offered at, in good faith, for a reasonable time. A big percentage off an inflated “was” price is not a real saving.
- Compare the final price, not the percentage. 30% off $120 ($84) is still more than 10% off $90 ($81).
- Watch the order of mixed offers when a fixed amount and a percentage both apply.
- Remember shipping and tax. A discount can disappear once delivery costs are added.
For other percentage questions, such as what percent one number is of another, try the percentage calculator.