Why is 30% off plus an extra 20% off not 50% off?

Because the second discount applies to the already-reduced price, not the original. Thirty percent off 120 dollars gives 84; twenty percent off 84 gives 67.20. A straight 50 percent discount would have given 60. The stacked offer is worth 44 percent, not 50, and the gap widens as the individual discounts get larger.

Does the order of two stacked discounts matter?

No. Multiplication is commutative, so applying 30 percent then 20 percent gives exactly the same result as 20 percent then 30 percent. Where order does matter is between discounts and coupons with fixed dollar amounts, which is why stores are specific about the sequence in their terms.

Is tax calculated before or after the discount?

After. Sales tax applies to what you actually pay, so a discount reduces the tax as well as the price. This calculator applies tax to the post-discount amount, which is how it works at the register.

How do I work out the original price from a sale price?

Divide rather than subtract. If an item is 67.20 after 44 percent off, the original was 67.20 divided by 0.56, which is 120. Adding 44 percent back to the sale price would give the wrong answer, because the percentage refers to a different base.

Is a percentage discount always better than a dollar amount?

It depends on the price. Twenty percent off beats 20 dollars off on anything over 100 dollars, and loses below it. On a 60 dollar item, 20 dollars off is worth a third. Working out the crossover point is usually quicker than it feels: it is simply the fixed amount divided by the percentage.

What does the real discount figure mean?

It is the single discount that would produce the same final price as the two stacked ones. It exists so you can compare a stacked offer against a competitor’s straight discount without doing the arithmetic yourself.

Discount Calculator: Sale Price and Stacked Deals

How to use this calculator

Enter the original price.
Enter the discount percentage.
Add an extra discount if the offer stacks one on top of another.
Add your sales tax rate if you want the register total.

The “real discount” figure is the one worth looking at: it is the single discount equivalent to whatever combination you entered.

How the calculation works

A discount is a multiplication, not a subtraction:

after first  = price × (1 − d₁/100)
after second = after first × (1 − d₂/100)

The second discount applies to the already reduced price. This is why stacked discounts never add up to what they look like.

Tax is then applied to what you actually pay:

final = after second × (1 + tax/100)

A worked example

A $120 jacket, 30% off, with an extra 20% off at the register, plus 8.25% sales tax.

30% off 120        = 120 × 0.70 = 84.00
extra 20% off 84   =  84 × 0.80 = 67.20
tax on 67.20       = 67.20 × 0.0825 = 5.54


Original price	$120.00
Price after discounts	$67.20
You save	$52.80
Real discount	44%
Sales tax	$5.54
You pay	$72.74

The offer reads as “30% + 20% = 50% off”, but a genuine 50 percent discount would have given $60, not $67.20. The stacked offer is worth 44 percent — the store keeps $7.20 that the mental arithmetic gave away.

Why the gap exists

The second discount is calculated on $84, not $120. Twenty percent of $84 is $16.80, while twenty percent of $120 would have been $24. The missing $7.20 is exactly the difference.

The shortfall grows with the size of the discounts:

Stacked offer	Looks like	Actually is
10% + 10%	20%	19%
25% + 25%	50%	43.75%
30% + 20%	50%	44%
50% + 50%	100%	75%

Two 50 percent discounts can never make something free, which is the clearest illustration of the principle.

Common mistakes to avoid

Adding stacked percentages together. As above. Multiply the remainders instead: 70% × 80% = 56% of the original price remains, so 44 percent came off.

Assuming order matters. It does not, for percentage discounts. Thirty percent then 20 percent gives exactly the same result as 20 percent then 30 percent, because multiplication is commutative. Order does matter when a fixed-dollar coupon is involved, which is why stores are specific about sequencing in their terms.

Working the original price back out by adding the percentage. If an item is $67.20 after 44 percent off, the original is $67.20 ÷ 0.56 = $120. Adding 44 percent to $67.20 gives $96.77, which is wrong, because the percentage refers to the original price and not the sale price.

Assuming a percentage always beats a dollar amount. Twenty percent off beats $20 off on anything over $100, and loses below it. The crossover point is simply the fixed amount divided by the percentage.

Comparing the discount instead of the price. A 60 percent discount off an inflated “was” price can easily be more expensive than 20 percent off a competitor’s honest one. The percentage is a description of the retailer’s pricing, not of the value you receive.

A note on reference prices

Discounts are quoted against a “was” price whose meaning varies considerably. Many jurisdictions require that price to have been genuinely charged for a minimum period, and enforcement is inconsistent. Where a permanent sale runs all year, the reference price is closer to marketing than to a price anyone paid. The only reliable comparison is the actual amount you hand over, against the actual amount somewhere else would charge.

When this calculator is not the right tool

For adding or removing sales tax on its own, the sales tax calculator handles both directions. For general percentage work — increases, shares, changes — the percentage calculator covers all three at once. And for buy-one-get-one offers, the effective discount depends on whether you wanted two of the item, which no calculator can answer for you.

Discount Calculator