Discount Calculator

Also handles stacked discounts — where '30% off then an extra 20% off' is not 50% off, and the gap is bigger than most people assume.

Why stacked discounts are not additive

A single discount is straightforward:

Two discounts multiply rather than add, because the second applies to the already-reduced price:

Take £120 with 30 % off and then a further 20 %. The intuitive answer is 50 % off, or £60. The real answer: £120 × 0.70 = £84, then £84 × 0.80 = £67.20. That is a 44 % discount, not 50 %. The £7.20 gap is the stacking effect, and retailers are entirely aware of it.

Usefully, the order does not matter. Multiplication is commutative, so 20 % then 30 % gives exactly the same £67.20.

Reading a sale price honestly

• “Was” prices. A reference price only means something if the item was genuinely sold at it for a meaningful period. Many jurisdictions now require this, and enforcement is uneven.
• Percentage off a coupon versus off the item. “£20 off” is 40 % on a £50 item and 4 % on a £500 one. Convert everything to percentages before comparing.
• Buy one get one free is 50 % off only if you wanted two. If you wanted one, it is a 100 % price increase for a spare.
• Three for two is a 33.3 % discount, not 50 %: you pay for two and receive three, so you save one item in three.
• Tax timing. Where tax is added at checkout, the discount applies to the pre-tax price and tax is charged on the reduced amount — which is in your favour.

Working backwards

To find the original price from a known sale price and discount:

An item at £67.20 after 44 % off was £67.20 ÷ 0.56 = £120. This is the calculation to use when a shop advertises the discount and the final price but not the original, and it is a quick way to check whether the stated percentage is truthful.

To find what discount you were actually given: (original − sale) ÷ original × 100.