Discount Calculator

The formula, and the quick way to do it in your head

A discount of d% leaves you paying (100 − d)% of the price: sale price = original × (1 − d ÷ 100), and the saving is the difference. An $80 jacket at 25% off costs $80 × 0.75 = $60, and you save $20.

Thinking in terms of what you pay rather than what you save is the useful habit. 30% off means paying 70%; 15% off means paying 85%. For the common round numbers there are shortcuts: 10% is the price with the decimal point moved one place left, 20% is a fifth of it, 25% is a quarter and 50% is half. So 20% off $80 is $80 − $16 = $64 without reaching for a calculator.

Shops round the result to the cent at each step, and so does this calculator, which is why its figures match a till receipt rather than drifting by a cent.

Why 20% then 10% is 28% off, not 30%

Stacked discounts are the reason most people open a discount calculator. A store advertises 20% off, and then a coupon takes an extra 10% off sale prices. It is tempting to add them up to 30%, but the second discount is taken off the already-reduced price, not the original one.

On $80: 20% off takes $16 and leaves $64. The extra 10% takes $6.40 off that $64, leaving $57.60. Altogether you have saved $22.40, which is 28% of $80. The general rule is that the combined discount is 1 − (1 − a) × (1 − b): here 1 − 0.80 × 0.90 = 1 − 0.72 = 0.28. Add a second discount in the calculator and it shows each step, the total discount, and the figure you might have expected instead.

Two consequences are worth knowing. The order of percentage discounts makes no difference — 10% then 20% also comes to 28% — because multiplication does not care about order. And stacking never adds up the way the headline suggests: two 50% discounts are 75% off, not free, and "up to 70% off plus an extra 20%" is at most 76% off, not 90%.

Order does matter when one of the discounts is a fixed amount. On $100, taking $10 off and then 20% leaves $72, while 20% off and then $10 leaves $70. This calculator handles percentages; for a fixed-amount coupon, subtract it at the point in the sequence where the shop applies it.

Working backwards from two prices

Switch to "Discount from two prices" to find out how big a reduction really is: discount = (original − sale price) ÷ original × 100. A $120 item reduced to $90 is $30 off, and $30 ÷ $120 is 25%.

The usual mistake is dividing by the sale price instead. $30 ÷ $90 is 33%, which overstates the discount, because the percentage is always measured against the price before the reduction.

A discount is also only as real as the original price. A "was" price that was barely ever charged makes any reduction look generous. In the US, the Federal Trade Commission's Guides Against Deceptive Pricing say a former price used in a comparison should be one the item was genuinely offered at, in good faith, for a reasonably substantial period. If an item seems to be permanently on sale, the sale price is the real price.

Multi-buy deals: BOGO, 3 for 2 and bundle prices

Multi-buy offers hide their discount in the quantity. Buy one, get one free is 50% off each item — but only if you wanted two. Buy one, get one half price is 25% off the pair. Three for the price of two is 33.3% off. Choose the multi-buy option, enter the regular price and the deal, and the calculator gives the effective discount, the real price per item and what you pay.

Bundle prices work the same way. Three for $10 on something that normally costs $3.79 each saves $1.37 on $11.37, which is about 12% — less than the round number suggests. Occasionally a bundle costs more than buying the items singly, and the calculator says so when it does.

The saving is only a saving if you would have bought the extra items anyway. A second jar of something you will throw away is not 50% off; it is the full price of one jar, plus a jar you did not need.

Sales tax is added after the discount

In the US, prices on the shelf usually exclude sales tax, and tax is calculated on the price after a store's own discount. The $57.60 jacket above, at an 8% sales tax rate, costs $4.61 in tax and $62.21 at the register. Enter your rate in the sales tax field to see that figure alongside the sale price.

Manufacturer coupons can be treated differently. Because the manufacturer reimburses the store, many states tax the price before the coupon is taken off, so your tax bill does not fall with the discount. Store coupons and in-store markdowns generally do reduce the taxable price.

Outside the US, displayed prices normally already include VAT or GST, so leave the tax rate at 0 — the discounted price is the price you pay.