Discount Calculator
Free discount calculator: enter any two of list price, sale price, and discount percent to find the third, plus the amount you save.
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The three discount formulas
Every discount question relates three values: the list price (L, the original price), the sale price (S, the discounted price), and the discount percent (D). Know any two and the calculator finds the third, plus the amount you saved.
| You know | You find | Formula |
|---|---|---|
| List price, discount % | Sale price | S = L × (1 − D/100) |
| List price, sale price | Discount % | D = (L − S) / L × 100 |
| Sale price, discount % | List price | L = S / (1 − D/100) |
Amount saved is L − S in every case.
1. Find the sale price
Example — a $120 jacket, 75% off.
- Convert 75% to a decimal:
75 ÷ 100 = 0.75. - Multiply the list price by that rate:
0.75 × 120 = 90. - Subtract:
120 − 90 = 30.
Sale price is $30. You save $90.
2. Find the discount percent
Example — a $120 item on sale for $90.
- Find the amount saved:
120 − 90 = 30. - Divide by the list price:
30 ÷ 120 = 0.25. - Multiply by 100:
0.25 × 100 = 25%.
Discount is 25%. You save $30.
3. Find the list price
Example — a $40 sale price, marked 20% off.
- Convert the remaining percent to a decimal:
100% − 20% = 80% = 0.80. - Divide the sale price by it:
40 ÷ 0.80 = 50.
Original list price is $50. You save $10.
Tip: Finding the list price requires dividing by
(1 − D/100), not adding the percent back on. Adding 20% to a $40 sale price gives $48, not the correct $50 — the discount was taken off a larger number, so undoing it takes more than a flat percent add-back.Real-world example with a messy number
A lava lamp is marked down from $165.99 to $89.63. What percent discount is that?
You saved $76.36 — about a 46% discount.
Discount vs. Percentage Decrease
Tip: Finding a discount percent from a list price and a sale price is the exact same formula as Percentage Decrease, with "starting value" = list price and "final value" = sale price. Discount Calculator is built specifically for shopping — it also solves the two reverse directions (sale price, list price) that a generic percentage-decrease calculator doesn't.
Reach for this calculator whenever a price tag, a coupon, or a receipt gives you two of the three numbers and you need the third.
Common mistakes
- Adding the percent back on instead of dividing. Recovering the list price from a sale price needs
sale ÷ (1 − D/100), notsale × (1 + D/100). The discount percent was taken off the original price, not the sale price, so the two operations aren't inverses. - Multiplying by the raw percent instead of the decimal rate. 25% off $120 is
120 × 0.25 = 30saved, not120 × 25. - Mixing up which price is "list" and which is "sale." The list price is always the larger, pre-discount number; the sale price is what's actually paid.
Where discount math shows up
- Shopping — comparing a percent-off sign to the actual dollar savings.
- Coupons and promo codes — checking that a code applied the advertised percentage.
- Budgeting — working backward from a receipt to see what something cost before a sale.
Frequently asked questions
- How do I calculate the sale price after a discount?
- Multiply the list price by 1 minus the discount rate. For a $120 item at 25% off, 120 × (1 − 0.25) = 120 × 0.75 = $90.
- How do I find what percent discount was applied?
- Divide the amount saved by the list price, then multiply by 100. A $120 item on sale for $90 saved $30, and 30 ÷ 120 × 100 = 25%.
- How do I find the original list price from a sale price and a discount percent?
- Divide the sale price by 1 minus the discount rate — never divide by 1 plus the discount, and never just add the percent back on. A $40 sale price at 20% off means the original price was 40 ÷ 0.80 = $50.
- Why can't the discount be 100% when solving for the list price?
- A 100% discount makes the sale price $0, and dividing by 1 minus 100% means dividing by zero. Any list price would make the sale price $0, so the original amount is mathematically undefined from that information alone.
- How much do I save on a $165.99 item marked down to $89.63?
- You save $76.36, which works out to about 46% off — 76.36 ÷ 165.99 × 100 ≈ 46.00%.
- What's the difference between this and the Percentage Decrease calculator?
- Finding the discount percent from a list price and a sale price uses the exact same formula as Percentage Decrease, with the list price as the starting value and the sale price as the final value. This calculator adds the two reverse directions on top — solving for the sale price or the list price instead.
- Does the discount percent apply before or after tax?
- This calculator works entirely with the numbers you enter — it doesn't know about tax. Enter the pre-tax list and sale prices if you want a discount percent that ignores tax.