Three questions, three formulas
Discount math always answers one of three questions. What will I pay? What percent off is this? What did it cost before? Figure out which one you're asking and the formula follows.
The key idea is the remaining-price factor. If something is 25% off, you pay 75% of the price, so the factor is 0.75. Multiply by it to go from original to sale price. Divide by it to go back.
Formula notes
Sale price = original x (1 - discount)Percent off = (original - sale) / original x 100Original = sale / (1 - discount)
Mental math that works in a shop
Everything starts with 10%. Move the decimal point one place left: 10% of $64 is $6.40. From there, 20% is double ($12.80), 5% is half ($3.20), and 15% is 10% plus 5% ($9.60). Subtract from the price and you've got the sale price.
For 25% off, divide by four and subtract. For 50% off, halve it. For 75% off, divide by four and that's what you pay. A $48 item at 75% off costs $12.
- 10% off: move the decimal one place left, then subtract.
- 20% off: double the 10% figure, then subtract.
- 25% off: pay three quarters of the price.
- 33% off: pay about two thirds.
- 50% off: pay half.
Finding the percent off from a price tag
Stores often show a was-price and a now-price without the percentage. Take the difference and divide by the original. A $150 coat reduced to $105 has $45 off, and $45 / $150 = 0.30, so it's 30% off.
A common slip is dividing by the sale price instead. $45 / $105 is about 43%, which makes the deal look better than it is. The percentage always comes from the original price.
Stacked discounts and the 'extra 10% off' trick
"Extra 10% off sale prices" sounds like it adds to the first discount. It doesn't quite. 40% off and then an extra 20% off leaves you paying 0.60 x 0.80 = 0.48 of the price. That's 52% off, not 60%. On a $200 item you pay $96, not $80.
The order of two plain percentage discounts doesn't change the result, since multiplication works either way round. Store rules can still matter, like which items qualify or whether codes can be combined.
Coupons, tax and the real price
A money-off coupon is a fixed amount, so its percentage depends on what you spend. $15 off a $60 order is 25%, but on a $300 order it's 5%. When choosing between a coupon and a percentage deal, work out both on your actual basket.
Then add what the shop adds. Sales tax, shipping and fees can wipe out a small discount. A 15% off deal with $8 shipping on a $40 order costs $42 before tax, more than the full price with free shipping elsewhere. Our discount calculator puts the discounts, coupon, tax and shipping in one breakdown so you can compare the final totals.
Is the original price real?
A percentage is only as honest as the price it's taken from. In the US, the FTC's guides on deceptive pricing cover this. A former price should be the actual price the item was offered at, regularly, for a reasonably substantial period. The UK and EU have their own rules on price reductions. If an item seems permanently on sale, compare the sale price with what other shops charge rather than trusting the percentage.
Frequently asked questions
How do I calculate the amount saved?
Multiply the original price by the discount as a decimal. 35% off $80 saves $80 x 0.35 = $28.
What is 15% off $50?
15% of $50 is $7.50, so the sale price is $42.50. You can also multiply $50 by 0.85.
How do I calculate a discount on several items?
Multiply the unit price by the quantity first, then apply the discount to the total. If the deal is per item, the result is the same for plain percentage discounts.
Why does dividing by the sale price give the wrong percentage?
Because percent off is defined against the original price. Dividing by the smaller sale price makes the saving look bigger than it is.
References
These sources support the method or guidance used for Discount Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Discount Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.