CalcMate

Discount Calculator

Work out what you pay after a percent-off discount, see the dollars you save, and turn an original and sale price back into the discount percentage. Stacked discounts are combined the way stores actually apply them.

Sale price$80.00
You save$20.00
Effective discount off the original price20%

The discount is calculated on the original price.

Formula and calculation

sale price=price×(1−d1)×(1−d2)×…savings=price−sale priceeffective discount=savingsprice×100\begin{gathered}\text{sale price} = \text{price} \times (1 - d_1) \times (1 - d_2) \times \ldots\\ \text{savings} = \text{price} - \text{sale price}\\ \text{effective discount} = \dfrac{\text{savings}}{\text{price}} \times 100\end{gathered}
d₁, d₂ … are the stacked discounts as decimals (20% = 0.2). Every step multiplies the price by what is left after that discount, which is why stacked discounts are never quite as big as the sum of the percentages.

Worked example

A $100 item marked 20% off, with an extra 10% off at the register: the sale price is $72.00 and you save $28.00 in total. The two discounts stack to an effective 28% — not the 30% the two percentages appear to add up to.

Why stacked discounts multiply

Stores apply percent-off offers one after another, and each one is calculated on the price that is left at that moment. Take $100 with 20% off first: the price drops to $80, so the extra 10% is 10% of $80 — just $8 — leaving $72. The saving is $28, or 28% of the original price. The same logic covers coupons on sale items, loyalty discounts and two-for-one markdowns. Dollar-off coupons are different: they subtract a fixed amount, so they combine by simple subtraction instead.

What the results mean

Sale price
What you pay after every discount is applied. Each discount works on the price left by the previous one.
You save
The dollars taken off the original price. With stacked discounts this is always less than the plain sum of the percentages would suggest.
Effective discount
The single percent that takes you from the original price to the sale price — the number to use when comparing deals. Stacked 20% and 10% discounts give 28%, not 30%.

Frequently asked questions

How do I work out a percent off by hand?

Multiply the price by the discount and subtract it: 25% off $80 is 80 × 0.25 = $20 off, so you pay $60. Equivalently, multiply by what is left: 80 × 0.75 = $60.

Do stacked discounts add up?

No — they multiply, because each discount is calculated on the already-reduced price. An extra 10% off after 20% off takes only $8 off a $100 item, so the total is 28% off, not 30%. Two 50% discounts leave you paying 25% of the original, not zero.

How do I find the discount percent from two prices?

Divide the savings by the original price: a $72 sale price on a $100 item saves $28, and 28 ÷ 100 = 28% off. Switch the calculator to the two-prices mode and it does that step for you.

Does the order of stacked discounts matter?

No. Because every step is a multiplication, 20% then 10% gives the same $72 on a $100 item as 10% then 20%. Only the set of discounts matters, not their order — what changes the answer is when a discount applies to the original price instead of the reduced one.