Discount Calculator

How it works

A percent discount takes a share of the list price off: 25% off $80 removes 0.25 × $80 = $20, leaving $60. The quickest way to get the sale price directly is to multiply the list price by what is left after the discount, 1 − 0.25 = 0.75. A discount given as a fixed amount is simply subtracted, and dividing it by the list price turns it into the equivalent percent.

Stacked discounts, such as "20% off, then an extra 10% off at the register", are applied one after another, each to the price the previous one left. The percentages do not add: 20% then 10% leaves 0.8 × 0.9 = 72% of the price, a combined discount of 28%, not 30%. The calculator multiplies the remaining fractions together and reports the true combined percent next to the misleading sum.

Given two prices, the discount percent is the difference as a share of the original: ($80 − $60) ÷ $80 = 25%. This is the figure to check against an advertised "percent off", since a discount is always a share of the list price, never of the sale price.

Formula

sale = list × (1 − d ÷ 100)              saved = list − sale
sale = list − amount                     d = amount ÷ list × 100
stacked: sale = list × (1 − d₁÷100) × (1 − d₂÷100) × (1 − d₃÷100)
         combined discount = (1 − Π(1 − dᵢ÷100)) × 100
implied: d = (list − sale) ÷ list × 100

Example

An $80 jacket at 25% off: the discount is 0.25 × $80 = $20, so the sale price is $60 and the total discount is 25%. The same jacket with $20 off gives the same $60, which is 20 ÷ 80 = 25% off.

Stacked discounts of 20% then 10% on the $80 jacket: $80 × 0.80 = $64, then $64 × 0.90 = $57.60. You save $22.40, a combined 28% discount, not the 30% the two percentages add up to.

A $100 item at 20%, 10% and 5% in sequence costs $100 × 0.8 × 0.9 × 0.95 = $68.40, a single equivalent discount of 31.6%. And if a $60 sale price is quoted against an $80 list price, the implied discount is ($80 − $60) ÷ $80 = 25%.

Assumptions and limitations

• Percentages are entered as ordinary numbers: 25 means 25%.
• Stacked discounts are applied in the order given, each to the price the previous one left. Because multiplication is commutative, the order does not change the final price; it only changes the intermediate amounts.
• Sales tax, shipping, coupons with minimum spends and rounding to the cent at the register are not modelled; results are shown to the cent but computed in full precision.
• A discount cannot exceed 100% or the list price, and a sale price cannot exceed the list price (that would be a mark-up, not a discount).

Frequently asked questions