Discount

How a Sale Price Is Calculated

A sale price is the original price minus the discount percentage applied to it. Enter the original price and the discount percentage from a sale, coupon, or markdown, and this calculator shows exactly how much you save and what you’ll actually pay. It’s the same math a cashier’s register does automatically at checkout, made visible before you get there.

Three related questions are covered:

• Percent off — the common case above, with an optional second discount for stacked promotions (a coupon on top of a sale price).
• Fixed amount off — when the discount is a flat dollar amount (“$15 off”) rather than a percentage.
• Reverse — work backward from what you actually paid and the discount percent applied, to find the original price — useful for expense reports or just satisfying curiosity about a receipt.

An optional sales tax field (for the percent-off and fixed-off modes) shows the actual out-the-door total after the discount.

The Formula

Every quantity is color-coded and carried through consistently:

$$\vC{\text{Amount Saved}} = \vA{\text{Original Price}} \times \left(\frac{\vB{\text{Discount Percent}}}{100}\right)$$ $$\vD{\text{Sale Price}} = \vA{\text{Original Price}} - \vC{\text{Amount Saved}}$$

A 100% discount means the amount saved equals the original price, making the sale price $0 — useful as a sanity check, since a discount can never take more than 100% off a price.

Fixed amount off is simpler still: $\vD{\text{Sale Price}} = \vA{\text{Original Price}} - \vE{\text{Amount Off}}$, capped at $0 — a coupon larger than the price just makes the item free, not a negative price.

Reversing a percent-off discount solves the sale-price formula backward:

$$\vA{\text{Original Price}} = \frac{\vD{\text{Sale Price}}}{1 - (\vB{\text{Discount Percent}} \div 100)}$$

Worked Example

A jacket originally priced at $80 is 25% off.

1. Amount Saved: $\vA{80} \times (\vB{25} \div 100) = \vC{20}$.
2. Sale Price: $\vA{80} - \vC{20} = \vD{60}$.

The jacket costs $60, and you save $20. If two discounts apply — say an additional 10% off at checkout — apply them one at a time rather than adding the percentages together: 10% off the new $60 price saves another $6, for a final price of $54, not the $52 you’d get by (incorrectly) treating it as a flat 35% off the original $80.

Key Factors to Consider

• Sales tax is typically calculated on the discounted price, not the original price. Most jurisdictions tax the actual amount paid after a discount is applied, not the pre-discount sticker price — this calculator’s optional tax field applies the rate to the sale price, matching how most retail transactions actually work.
• Stacked discounts always save less than simply adding the percentages together. Two 20% discounts applied one after another save 36% total, not 40%, since the second discount applies to an already-reduced price — this compounding effect means stacked percentage discounts are always less generous than their sum would suggest.
• A “buy one get one” or similar promotion isn’t a straightforward percent-off calculation. Some promotions (BOGO, tiered discounts, minimum-purchase thresholds) don’t reduce to a single effective discount percentage in the way this calculator assumes — those need their own separate math based on the specific promotion’s actual terms.
• The reverse mode is useful for verifying a receipt or expense report, but assumes you know the exact discount percentage applied. If a receipt doesn’t state the discount percentage explicitly, working backward from just the sale price alone isn’t possible without that missing piece of information.

Common Mistakes

• Adding stacked discount percentages together instead of applying them sequentially. Two 20% discounts don’t combine into 40% off — the second discount applies to the already-reduced price, so the true combined savings is always a bit less than the sum of the two percentages suggests.
• Applying sales tax to the original price instead of the discounted price. Most retailers tax what a customer actually pays after a discount, not the pre-discount sticker price — using the original price overstates the final total.
• Assuming a fixed-amount coupon works the same as a percentage discount at every price point. A $15-off coupon is a much bigger relative discount on a $30 item than on a $300 item, unlike a percentage discount, which stays proportionally the same regardless of price.

Useful to Know

A percent-off discount and a percentage markup are mirror images of each other, but they’re not simple opposites — a 20% discount followed by a 20% markup doesn’t return you to the original price, because each percentage is calculated against a different base (the original price for the discount, the already-reduced price for the markup). This is the same compounding effect that makes stacked discounts save less than their sum suggests.