Why is 30% off then 20% off not 50% off?

Because the second discount applies to the already-reduced price, not the original. 100 becomes 70, and 20% off 70 is 56, so the effective discount is 44%. Two discounts always come to less than their sum.

Does the order of the discounts matter?

Not to the final price: multiplication commutes, so 30% then 20% and 20% then 30% both give 56. It does matter when one of them is a flat amount off rather than a percentage, which is what the coupon stacking calculator handles.

Businesspricing

Successive Discount Calculator

"30% off, then 20% off" is not 50% off. It is 44%. This shows the effective discount and the difference from simply adding them.

Also called: discount on discount calculator, two discounts combined.

You pay

2,800

You pay 2,800. The discounts total 50% if you add them up, but successively they come to 44%. The second is applied to an already-reduced price.

Effective discount

44%

What adding them would suggest

50%

You save

2,200

How this is calculated

Method and background

How this is calculated

Each discount applies to whatever is left after the previous one, so the factors multiply rather than the percentages adding. Two 50% discounts leave 25% of the price, not zero, which is why no chain of percentage discounts can ever make something free.

final = price * (1-d1) * (1-d2) * (1-d3)

d_i: Each discount as a decimal

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

30% then 20% is 44%, not 50%

Original price: 5,000
First discount (%): 30
Then a further (%): 20
And a further (%): 0

You pay2,800

arithmetic identity: 1 - 0.7x0.8

Open this example

two 50% discounts leave a quarter

Original price: 1,000
First discount (%): 50
Then a further (%): 50
And a further (%): 0

You pay250

boundary: percentages can never reach zero

Open this example

no discounts

Original price: 5,000
First discount (%): 0
Then a further (%): 0
And a further (%): 0

You pay5,000

degenerate case

Open this example

Frequently asked questions

Why is 30% off then 20% off not 50% off?: Because the second discount applies to the already-reduced price, not the original. 100 becomes 70, and 20% off 70 is 56, so the effective discount is 44%. Two discounts always come to less than their sum.
Does the order of the discounts matter?: Not to the final price: multiplication commutes, so 30% then 20% and 20% then 30% both give 56. It does matter when one of them is a flat amount off rather than a percentage, which is what the coupon stacking calculator handles.