Everyday Life · General Mathematics
Discount Calculator
Calculate the sale price, discount amount, and savings percentage for any item given its original price and discount rate.
Calculator
Formula
P is the original (list) price, d is the discount percentage (0–100). The discount amount is P × (d / 100), and the sale price is the original price minus that discount amount.
Source: Standard retail arithmetic; consistent with consumer finance guidelines from the U.S. Consumer Financial Protection Bureau (CFPB).
How it works
A percentage discount works by reducing the original price by a proportional fraction. If an item costs $80 and carries a 25% discount, the markdown is calculated as 25 divided by 100, giving the decimal multiplier 0.25. Multiplying the original price by this decimal yields the dollar amount saved — in this case $20. The final sale price is simply what remains after that deduction: $80 − $20 = $60.
Mathematically, the sale price can be computed in a single step using the formula Sale Price = P × (1 − d/100), where P is the original price and d is the discount percentage. This is more efficient than computing the discount separately first and then subtracting, and it's the approach used internally by most point-of-sale systems worldwide. The same formula scales seamlessly from small percentages like 5% to large clearance markdowns of 70% or more.
Understanding discounts is also essential for comparing offers that bundle multiple markdowns. For example, a "20% off, then an additional 10% off" deal is not the same as a flat 30% discount. The compound discount is actually 1 − (0.80 × 0.90) = 28%, not 30%. Being comfortable with the basic discount formula helps you quickly spot which offer genuinely provides the deeper savings.
Worked example
Suppose a jacket has an original retail price of $120 and is on sale for 30% off.
Step 1 — Calculate the discount amount:
Discount Amount = $120 × (30 / 100) = $120 × 0.30 = $36.00
Step 2 — Calculate the sale price:
Sale Price = $120 − $36 = $84.00
Alternatively in one step:
Sale Price = $120 × (1 − 0.30) = $120 × 0.70 = $84.00
You pay $84.00 at the register and save $36.00 compared to the original price. If your state charges an 8% sales tax, the tax would be applied to the discounted price: $84.00 × 0.08 = $6.72, bringing the total to $90.72. This calculator outputs the pre-tax sale price; always add applicable taxes to determine your actual out-of-pocket cost.
Limitations & notes
This calculator assumes a straightforward single-percentage discount applied to a fixed original price. It does not account for stacked or sequential discounts (e.g., an additional coupon applied after an initial markdown), buy-one-get-one deals, quantity-based pricing tiers, or taxes. It also assumes the "original price" entered is the genuine retail price — inflated "original" prices used as a marketing anchor can make discounts appear more significant than they are in practice. Always verify the pre-discount price against historical data or competing retailers before assuming a listed sale represents true savings.
Frequently asked questions
How do I calculate the original price if I only know the sale price and discount percentage?
Rearrange the formula to solve for the original price: Original Price = Sale Price ÷ (1 − d/100). For example, if an item costs $63 after a 30% discount, the original price was $63 ÷ 0.70 = $90. This reverse-discount approach is useful when a tag shows only the sale price and you want to verify the stated savings.
Is a 20% discount followed by an additional 10% off the same as 30% off?
No — stacked discounts are multiplicative, not additive. A 20% discount leaves 80% of the price, and a subsequent 10% discount takes 10% off that reduced amount, leaving 72% of the original price. The combined effect is a 28% total discount, not 30%. You can calculate this as 1 − (0.80 × 0.90) = 0.28.
Does the discount apply before or after sales tax?
In most retail scenarios and per standard U.S. tax law, sales tax is calculated on the final discounted price, not the original price. So if an item is $100 with 25% off, you pay tax on $75. However, some promotional structures (like manufacturer rebates applied after purchase) may differ, so always check the retailer's terms.
What does '50% off' actually mean in terms of the multiplier applied to the price?
A 50% discount means you pay exactly half the original price, since the multiplier is (1 − 0.50) = 0.50. A 25% discount means you pay 75% of the original price (multiplier 0.75), and a 10% discount means you pay 90% (multiplier 0.90). Thinking in terms of the 'pay' multiplier rather than the 'save' percentage can make mental math faster at the checkout.
How can I quickly estimate a percentage discount in my head?
A reliable mental shortcut is to find 10% of the price first by moving the decimal one place left, then multiply to get the full discount. For a 30% discount on $85: 10% = $8.50, so 30% = $8.50 × 3 = $25.50, and the sale price is $85 − $25.50 = $59.50. For 5%, halve the 10% figure; for 15%, add the 10% and 5% results together.
Last updated: 2025-01-15 · Formula verified against primary sources.