Discount Calculator

About the Discount Calculator

Sales, coupons, clearance tags and trade discounts all come down to the same few questions. How much will I actually pay? How much am I saving? What was the price before the discount? And what happens when one discount is stacked on top of another?

This discount calculator answers all of them. It works out the sale price and saving from a percentage off, including an extra discount such as a coupon applied on top; it converts an amount off into a percentage so you can compare offers; and it finds the original price behind a sale price. It also shows the two mistakes people most often make with discounts, so you can spot them in a shop or on an invoice.

How to Use the Discount Calculator

Choose what you want to work out:

Percentage off — enter the original price and the discount. Add an extra discount if a second percentage comes off the reduced price.

Amount off — enter the original price and the amount taken off.

Original price — enter the sale price and the discount that was applied.

How Discounts Are Calculated

  sale price      =  price × (1 − discount)
  saving          =  price − sale price
  stacked         =  price × (1 − first) × (1 − second)
  combined rate   =  1 − (1 − first) × (1 − second)
  original price  =  sale price ÷ (1 − discount)

Step-by-Step Example

20% off a price of 100, then a further 10% coupon.

  First discount:   100 × 0.80        =  80
  Extra discount:   80 × 0.90         =  72
  Saving:           100 − 72          =  28
  Combined rate:    1 − 0.80 × 0.90   =  28%

15 off a price of 80.

  Price to pay:     80 − 15           =  65
  As a percentage:  15 ÷ 80           =  18.75%

A sale price of 80 after 20% off.

  Original price:   80 ÷ 0.80         =  100

Stacked Discounts Multiply

When a second discount is applied to an already reduced price, the two percentages do not add up. 20% off and then 10% off is 28% off, not 30%, because the 10% is taken from 80 rather than from 100.

The order does not matter: 10% then 20% gives the same 28% as 20% then 10%. What matters is that each discount applies to what is left after the one before.

Reversing a Discount

To find an original price from a sale price, divide by one minus the discount. It is tempting to add the discount back on — 80 plus 20% is 96 — but that is wrong. The 20% was taken from the higher original price, so the right answer is 80 ÷ 0.80 = 100.

The same logic applies to checking a "was" price on a sale label. If the label says 30% off and the sale price is 70, the original must have been 100.

Comparing Deals

Convert everything to a percentage of the same price. 15 off 80 is 18.75% off, so it beats 15% off but not 20% off.

Multi-buy offers are discounts too. Buy three get one free is four items for the price of three: 25% off each, but only if you wanted four.

Check the final price, not the percentage. A bigger discount on a higher starting price can still cost more than a smaller discount elsewhere.

Discounts and Sales Tax

In most places the discount comes off first and sales tax or VAT is charged on the reduced price. For a percentage discount the order makes no difference to the final total. For a fixed amount off, taking it before tax saves slightly more, because the tax on that amount is saved as well.

Discounts from the Seller's Side

For a business, a discount is paid for out of margin, and the effect on profit is much larger than the percentage suggests.

Take an item with a cost of 60 and a price of 100: 40 of profit, a 40% margin. A 20% discount brings the price down to 80, but the cost stays at 60, so the profit falls to 20 — half of what it was. To earn the same total profit at the lower price, the shop has to sell twice as many.

That is why it is worth checking a promotion with the profit margin calculator before running it. Discounts work best when they bring in customers who would not otherwise buy, clear stock that would otherwise be wasted, or lead to other full-price sales. A discount that simply gives money back to people who would have paid full price anyway only reduces profit.

Rounding on Receipts

Shops round each discounted price to the nearest cent or penny, so a basket of discounted items can differ by a cent or two from the discount applied to the total. The calculator rounds the final price the same way.

Understanding Your Result

Result is the price to pay, or the original price.

You save is the saving in money and as a total percentage.

Working shows the subtraction behind the result.

Watch out shows the combined rate of stacked discounts, or what the common reversing mistake would have given.

Worth knowing gives the rule to remember for that kind of discount.

When Should You Use This Calculator?

Shopping in a sale or with a coupon.

Comparing offers in different forms.

Checking "was" prices on sale labels.

Setting sale prices for your own products.

Applying trade discounts on invoices.

Common Mistakes

Adding stacked discounts. 20% plus 10% off is 28%, not 30%.

Reversing by adding back. Divide by (1 − discount) instead.

Comparing amounts with percentages without converting them.

Forgetting the base price. A bigger percentage off a higher price may still cost more.

Buying extra to get a multi-buy deal you would not otherwise use.