Discount Calculator
Percent off, sale price, or the discount a price already represents: the discount calculator does all three, plus what two stacked discounts really come to.
Sale price
- Original price
- $120.00
- Discount $36.00 off.
- 30%
- You pay $120.00 x 0.7000.
- 70% of the original
- Volume needed to break even on this discount On a 40% margin, a 30% discount cuts the margin to 14.3% and needs 300% more units to make the same profit.
- depends on margin
| Off | You save | You pay |
|---|---|---|
| 10% | $12.00 | $108.00 |
| 15% | $18.00 | $102.00 |
| 20% | $24.00 | $96.00 |
| 25% | $30.00 | $90.00 |
| 30% | $36.00 | $84.00 |
| 40% | $48.00 | $72.00 |
| 50% | $60.00 | $60.00 |
| 60% | $72.00 | $48.00 |
| 70% | $84.00 | $36.00 |
How the Discount Calculator works
A discount is a multiplication, and treating it as one removes most of the ways to get it wrong. 30% off means you pay 70%, so the sale price is the original times 0.70, which is all a percent off calculator does. A $120 item at 30% off is $84. Finding 30% and subtracting it gives the same answer in two steps and is where arithmetic slips happen.
Reversed, the same relationship answers the other two questions. A $120 item selling for $84 is discounted by (120 - 84) / 120 = 30%, and the original price is the sale price divided by the multiplier.
Stacked discounts multiply, because the second applies to the already-reduced price. The gap against adding them grows with the size of the discounts: 50% plus an extra 50% is 75% off, not free. Since multiplication commutes, a store applying the larger discount first is not doing you a favor, and one applying the smaller first is not cheating you. A percentage-off coupon applied before tax and a fixed-dollar coupon applied after it are different amounts of money.
From the seller's side the arithmetic is more alarming than it looks, which is worth knowing as a buyer too. A 20% discount on a product with a 40% margin does not remove 20% of the profit. The $120 item costing $72 made $48; at $96 it makes $24. Half the profit, for a fifth off the price. Breaking even on that discount needs twice the unit volume. At thinner margins it is worse: a 20% discount on a 25% margin leaves 6.25% and needs five times the volume. This is why permanent discounting destroys businesses that could survive the same revenue at full price, and why "everything must go" sales are frequently exactly what they say.
One last piece of consumer arithmetic. A "buy one get one free" is 50% off two items, which is only a 50% discount if you wanted two. Buy two get one free is 33.3% off three. And anything expressed as "up to" is a statement about the best case in the store, not about the item in your hand.
Discount Calculator FAQ
How do I calculate a percent off?
Multiply by one minus the discount. 30% off means paying 70%, so a $120 item is 120 x 0.70 = $84. Going backwards, divide: an $84 price that is 30% off was 84 / 0.70 = $120. Adding 30% back to $84 gives $109.20 and is the wrong operation.
Is 30% off plus an extra 20% off the same as 50% off?
No. It is 44% off. The second discount applies to the already-reduced price, so the multipliers compose: 0.70 x 0.80 = 0.56. On $120 that is $67.20 rather than $60. Stacked discounts always come to less than the sum of their percentages.
Does the order of two discounts matter?
No. Multiplication commutes, so 30% then 20% gives exactly the same price as 20% then 30%. Order does matter for discounts against taxes and fixed-dollar coupons, where a percentage applied before or after a flat amount gives different results.
Is sales tax charged before or after a discount?
After. Tax applies to what you actually pay. A $120 item at 30% off with 8% sales tax is $84 plus $6.72 of tax, so $90.72. The discount reduces the tax along with the price.