Discount Calculator

What this calculator answers

A sale tag leaves you with one of three questions: what you pay after the discounts, what percent off the deal really is, or what the item cost before the markdown. Stacked discounts are applied one after another, the way stores ring them up, so the combined percent off comes out right, and sales tax can be added at the end.

How to use it

• Find: choose Final price (the default: the sale price, with tax if you add it), % off or Original. The boxes change to match.
• Original price: the price before any discount, in dollars. Shorthand works: $120 is 120 and 1.2k is 1,200.
• Sale price (for % off and Original): the price after the discounts, before tax.
• Discounts: each row is a percent off (% off) or a dollar amount off ($ off). Type 40 for 40%, not 0.4. Press Add discount for an extra markdown or a coupon, up to five. They apply in the order listed, top to bottom.
• Sales tax rate (optional): your combined state and local rate, for example 8. Leave it blank for no tax. Once a rate is filled in, Tax charged on asks whether tax is charged after or before the discounts.
• Round each step to the cent, like a receipt: rounds every discount, running price and the tax to the cent, as a receipt shows them, instead of rounding only what is displayed.

Results update as you type. The Try buttons fill in the stacked deal and the reverse question worked through below. To compare offers, such as 30% off against a $25 coupon, keep the first with Save for comparison, switch the discount and save again; the table then shows how much the second price differs from the first.

How to calculate a discount

A percent discount is the rate times the price it applies to, and the sale price is what is left:

$$\text{discount} = P \times d$$ $$S = P - P \times d = P\,(1 - d)$$

• $P$ is the price before the discount, in dollars.
• $d$ is the percent off as a decimal (40% is 0.40).
• $S$ is the sale price.

A dollar discount is subtracted as it is: $S = P - D$, where $D$ is the amount off.

Worked example: $120 at 40% off

1. Rate as a decimal: 40 ÷ 100 = 0.40.
2. Discount: $120 × 0.40 = $48.00.
3. Sale price: $120 − $48.00 = $72.00, which is 60% of the original price.

The shortcut is to multiply by what is left: 40% off means paying 60%, and $120 × 0.60 = $72.00.

Stacked discounts: why 40% off plus 15% off isn’t 55% off

A second discount comes off the price left by the first, not off the original, so the percents can’t simply be added. Continuing the example with an extra 15% off:

1. Extra discount: $72.00 × 0.15 = $10.80.
2. New price: $72.00 − $10.80 = $61.20.

Together the two discounts leave 0.60 × 0.85 = 0.51 of the price, so they take 49% off, not 55%. On $120 that is $58.80 off instead of $66.00. For any number of percent discounts:

$$C = 1 - (1 - d_1)\cdots(1 - d_n)$$

Here $C$ is the combined percent off and $d_1$ to $d_n$ are the separate percents, all as decimals. Multiplication gives the same product in any order, so percent discounts alone can be applied in any order. Two 50% discounts take 75% off, not the whole price.

“Extra % off prices as marked” explained

When a sign offers an extra percent off the marked price and the marked price is already reduced, the extra percent comes off the reduced price: the discounts stack. Enter the first markdown and the extra percent as two rows, as above. If the tag shows only the reduced price, enter that as the original price with the extra discount alone; the result is the same.

Dollar coupons: why the order matters

With both percents and dollar amounts, the order changes the price. A dollar coupon taken after the percents saves its full face value. Taken first, it shrinks the price the percents apply to, so the percents take less.

The $4.90 gap is the coupon times the combined percent off: $10 × 0.49. Percents first and dollar coupons last gives the lowest price of any order, but the store decides the order at checkout. Whenever your discounts mix the two kinds, the result shows the price both ways.

A dollar coupon larger than the price left takes it to $0.00 and no further. A $25 coupon on a $20 item leaves $0.00 to pay and $5.00 of the coupon unused; the calculator says so rather than showing a negative price or a 125% discount.

Sales tax with a discount: before or after?

For a store’s own discount or coupon, tax is normally figured on the reduced price; California’s rules, for example, treat a retailer coupon as a true price reduction. In the example, the $10 coupon brings the price to $51.20, and 8% sales tax on it is $51.20 × 0.08 = $4.096, which rounds to $4.10, for a total of $55.30.

Manufacturer coupons can be different, because the manufacturer repays the store. In California the reimbursement counts as part of the store’s receipts, and the store may charge sales tax on it. If your receipt shows tax on the full price, set Tax charged on to Before discounts: the tax in the example becomes $120 × 0.08 = $9.60 and the total $60.80. Rules differ by state; your state’s tax agency publishes its own.

This page takes one combined rate. To enter state and local rates separately, mark some items tax-free or take tax back out of a total, use Continue in the Sales Tax Calculator under the result: it opens with your price after discounts and your rate filled in.

How to calculate the discount percentage between two prices

Subtract the sale price from the original, then divide by the original:

$$d = \frac{P - S}{P}$$

For $120 marked down to $61.20: ($120 − $61.20) ÷ $120 = $58.80 ÷ $120 = 0.49, so 49% off. Divide by the original price, not the sale price: $58.80 ÷ $61.20 gives 96.08%, which is not the discount.

If the second price is higher than the first, the change is a price increase, not a negative discount, and the result is labeled that way. From $80 to $90 is a 12.5% increase.

How to find the original price before a discount

Divide the sale price by the share that was paid, $1 - d$:

$$P = \frac{S}{1 - d}$$

A $72.00 sale price after 40% off came from $72.00 ÷ 0.60 = $120.00. Adding 40% back gives the wrong answer, $72.00 × 1.40 = $100.80, because the 40% was taken from the larger original price.

With several discounts, undo them last to first: add back dollar coupons and divide out percents. For $61.20 after 40% and then 15% off, $61.20 ÷ 0.85 = $72.00, then $72.00 ÷ 0.60 = $120.00. A 100% discount can’t be undone, since every price ends at $0.00, so the calculator asks for less.

Rounding: why a receipt can be a cent off

A receipt shows each discount in whole cents, so it rounds at every step; a formula rounds only at the end. The two usually agree, but not always. Take $24.99 with 15% off and then another 15% off:

When the two methods give different cents, the result says so, and Round each step to the cent switches to the receipt method. Half a cent or more rounds up, the normal rule for sales tax.

Quick percent-off table for your price

Under each sale-price result is a table of the same price at 10%, 15%, 20%, 25%, 30%, 40%, 50%, 60% and 70% off, with your own percent marked. For $120, 25% off is $90.00 and 70% off is $36.00. With several discounts, the table varies the first percent discount and keeps the rest as entered. It downloads as a CSV file.

Reading the result

• Sale price, or Price with tax when you enter a tax rate, is the headline: what you pay.
• You save is the original price minus the sale price. With several discounts, the tile shows each one’s part: $48.00 + $10.80 + $10.00 in the example.
• Percent off is the true combined discount on the original price, dollar coupons included: $68.80 ÷ $120 = 57.33% for the full example.
• Price step by step lists every discount, and the tax, with the price before and after, like a receipt.
• Notes appear when they matter: why stacked percents don’t add up, how a coupon’s position changes the price, and when receipt rounding would give a different cent.

Assumptions and limitations

• Discounts apply to one price, an item or a basket total, in the order listed. Multi-buy deals are not built in (the questions below show how to enter one), and neither are minimum-spend conditions or limits on combining offers; check the store’s terms.
• A percent off is only as meaningful as the price it starts from. Federal Trade Commission guidance treats a “was” price as a fair comparison only when the item was genuinely offered at it for a reasonably substantial period, so an inflated former price makes a discount look bigger than it is.
• Sales tax is one rate on the whole price. Items taxed at different rates and fees are not handled; the sales tax calculator can leave tax-free items out of a basket.
• The result is an educational estimate, not tax or legal advice.

Common mistakes

• Adding stacked percents. 40% off and then 15% off is 49% off, not 55%.
• Dividing by the sale price. Percent off is the saving divided by the original price.
• Adding the percent back to find the original. Divide by the share paid instead: $72 ÷ 0.60, not $72 × 1.40.
• Typing a percent as a decimal. The percent boxes are in percent, so 0.15 means 0.15%. A value of 0.2 or less brings up a “Did you mean” note under the box.
• Using a total that includes tax. Take the tax out before finding the percent off (see the questions below).
• Assuming a coupon’s position doesn’t matter. With a dollar coupon in the mix, it does.