Sale Prices Explained: Working Out What You Really Pay

The basic sale price calculation

A discount of D% means you pay (100 − D)% of the original price. So instead of calculating the discount and then subtracting it, you can do one multiplication.

Sale price = original price × (1 − discount ÷ 100)

25% off 80: 80 × 0.75 = 60. You save 20.
30% off 45.00: 45 × 0.70 = 31.50. You save 13.50.
35% off 120: 120 × 0.65 = 78. You save 42.

If you want the amount saved instead, multiply the price by the discount directly: 25% of 80 is 20. Either route gives the same result, so pick the one that matches the number you want to see. The percentage calculator has a row for exactly this: a price with a percentage taken off.

Working out the discount from two prices

You see a jacket marked 85 that is now 68. What is the discount? Find the difference, then divide by the original price.

Difference: 85 − 68 = 17.
Divide by the original price: 17 ÷ 85 = 0.2.
Multiply by 100: 20% off.

This is a useful check when a shop shows only the old and new prices. Some tags state a rounded percentage, or one that applies only to certain sizes or colours, so it takes ten seconds to confirm it for the item you are holding.

Finding the price before the discount

Suppose you paid 64 after a 20% discount and you want to know the original price. The sale price is 80% of the original, so divide by 0.80.

Original price = sale price ÷ (1 − discount ÷ 100)

64 ÷ 0.80 = 80. Check it: 80 × 0.80 = 64. Correct.

A tempting shortcut is to add 20% back on to 64, which gives 76.8. That is wrong, because the 20% was taken from the larger original price, not from 64. Reversing a percentage always means dividing, never adding the same percentage back. The percentage guide explains this idea in more detail.

Stacked discounts do not add up

Stores often advertise "20% off, plus an extra 10% off at checkout". It is natural to think that is 30% off, but the second discount is applied to the already reduced price, so it takes off less.

Step	Calculation	Price
Original price	start	100
After 20% off	100 × 0.80	80
After a further 10% off	80 × 0.90	72
Single 30% off, for comparison	100 × 0.70	70

The two-step deal leaves you paying 72, which is a combined discount of 28%, not 30%. The shortcut is to multiply the remaining fractions: 0.80 × 0.90 = 0.72, so you pay 72% of the original price.

The same method works for any pair. Take 25% off followed by 20% off: 0.75 × 0.80 = 0.60, so you pay 60% and the combined discount is 40%, not 45%.

The same logic applies to three steps. Three successive 10% discounts leave 0.9 × 0.9 × 0.9 = 0.729 of the price, a total of 27.1% off rather than 30%. The order of percentage discounts does not matter (0.9 × 0.8 equals 0.8 × 0.9), but mixing a percentage with a fixed amount does matter, as the next section shows.

Percentage coupons versus fixed-amount coupons

Take an item priced at 50 and two coupons: 10 off, and 20% off. What you pay depends on the order.

10 off first, then 20% off: (50 − 10) × 0.80 = 40 × 0.80 = 32.
20% off first, then 10 off: 50 × 0.80 − 10 = 40 − 10 = 30.

Here the percentage-first order is cheaper by 2, because the fixed 10 is then taken off in full instead of being shrunk by the percentage afterwards. Shops usually decide the order, so if you have a choice between coupons, work out both totals before paying.

A quick checklist before you buy

Write down the original price and the price you will actually pay at the till.
Compute the real discount: (original − final) ÷ original × 100.
For stacked offers, multiply the remaining fractions rather than adding the percentages.
Compare unit prices (price per 100 g, for example) if package sizes differ.

Worked example with a coupon: shoes listed at 90 with 15% off and then a 5 coupon at the till. 90 × 0.85 = 76.50, and 76.50 − 5 = 71.50. The real discount is (90 − 71.50) ÷ 90 = 20.6%, so the deal behaves like a 20.6% discount rather than a flat 20%.

Unit prices: a 500 g pack at 4.00 costs 4.00 ÷ 5 = 0.80 per 100 g. A 750 g pack at 5.25 costs 5.25 ÷ 7.5 = 0.70 per 100 g. The bigger pack costs more in total but less per gram.

This guide covers the arithmetic only. It cannot tell you whether the "original" price was ever really charged, so if a deal looks surprisingly large, compare the item with other shops.

FAQ

Is 50% off then another 50% off the same as free?
No. The first step leaves 50%, and the second takes half of that, leaving 25% of the original price. That is a 75% total discount.

How do I add delivery or tax to a sale price?
Treat them as separate steps. Work out the sale price first, then add any fixed delivery fee. How tax is applied differs by place, so check how your shop handles it.

Which is better: 40% off, or 20% off plus another 20% off?
40% off. Two 20% steps leave 0.8 × 0.8 = 0.64 of the price, which is only a 36% discount.

Open the calculator: Percentage Calculator →