How to Calculate Discounts, Sale Prices and Successive Offers

Sales are designed to make you feel savings without doing the math. A few simple formulas let you see what a deal is really worth.

The Basic Formulas

• Discount amount = original price × discount % ÷ 100
• Sale price = original price − discount amount
• Savings = original price − sale price (the same as the discount amount)

A jacket is listed at 2,499 with 35% off:

• Discount: 2,499 × 0.35 = 874.65
• Sale price: 2,499 − 874.65 = 1,624.35

A one-step shortcut is to multiply by what you pay, not by what you save. At 35% off you pay 65%, so 2,499 × 0.65 = 1,624.35. The Discount Calculator returns the discount, the sale price and the savings together.

Finding the Original Price

Often you know the sale price and the discount and want the original. Divide by the fraction you paid.

Original = sale price ÷ (1 − discount %)

A shirt costs 63 after 30% off. You paid 70% of the original, so 63 ÷ 0.70 = 90. A common mistake is to add 30% to 63, which gives 81.90 and is wrong, because the 30% was taken off the larger number.

Finding the Discount Percentage

If you know both prices:

Discount % = (original − sale) ÷ original × 100

A pair of shoes drops from 4,000 to 3,000. The saving is 1,000, and 1,000 ÷ 4,000 = 25% off. Use the original as the base, not the sale price. If you divide by the sale price you get 33.3%, which is the increase needed to get back to the original, not the discount.

Successive Discounts Do Not Add Up

"Extra 10% off" on top of 20% off sounds like 30%. It is not.

Take 100.

• After 20% off: 80.
• After a further 10% off that price: 80 × 0.90 = 72.

The total discount is 28%, not 30%. In general, multiply the fractions you pay: 0.80 × 0.90 = 0.72. This applies to coupons stacked on sale prices, cashback offers, and member discounts. The order does not change the result, but it does change which amount each discount is taken from, which matters if a coupon has a minimum spend.

Percentage Points Versus Percent

Going from 20% off to 30% off is a rise of 10 percentage points, but the price you pay falls from 80% to 70% of the original, which is a 12.5% reduction in what you pay. Marketing often uses whichever framing sounds bigger.

Buy One, Get One

"Buy one, get one free" is 50% off per item when you buy two. "Buy one, get one half price" is 25% off per item across the pair. "Buy 2, get 1 free" is one third off across three items, about 33.3%. Convert each offer into an effective percentage before comparing them.

Tax and Discounts

In most places sales tax or GST is applied after the discount, so a discount lowers the tax you pay as well. Always check whether a listed price includes tax. If a price is tax-inclusive, work out the discount on that figure as shown, but remember the tax portion shrinks with it.

Reading "Up to" Offers

"Up to 70% off" means that at least one item has that discount. Most items are usually discounted far less. Compare the actual prices of the items you want, not the headline.

Is It Actually a Deal?

• Check the original price. A price that was inflated before the sale does not give you real savings. Compare against other stores or the item's typical price.
• Compute the effective discount with the formulas above.
• Factor in shipping, tax and return policy.
• Ask whether you needed the item in the first place. A 50% discount on something you do not need is still money spent.

For Sellers

Discounts come out of your margin, not your revenue figure. If you sell at 100 and your cost is 60, your margin is 40%. A 10% discount drops the price to 90 and your margin to 33.3%, so your profit per sale falls by 25%, not 10%. Our guide to margin versus markup shows how to price with that in mind, and the Margin Calculator shows the effect of a given discount.

Quick Reference

• Pay fraction = 1 − discount %
• Sale price = original × pay fraction
• Original = sale price ÷ pay fraction
• Stacked discounts: multiply the pay fractions

For one-off percentage questions, the Percentage Calculator covers the general case, and the Discount Calculator is built for shopping.