Discount Calculator

A percent-off discount multiplies the original price by (1 − discount/100). A 25% discount on a $80 item leaves you paying $80 × 0.75 = $60. The savings is the inverse: $80 × 0.25 = $20. This is the same arithmetic regardless of the size of the discount — 5% off, 50% off, 75% off all use the same formula.

A common mistake is to treat the discount and the sales tax as if they cancel out. A 10% discount followed by a 10% tax does not return you to the original price: $100 × 0.9 × 1.10 = $99. The $1 difference is the tax that wasn't collected on the discounted portion.

When a sale advertises 'up to X% off,' the headline rate usually applies only to a small set of items. Always check the actual discount on the items you intend to buy — the average discount across a sale rack is often far lower than the maximum advertised.

Stacked discounts multiply, they do not add. A 30% off coupon plus an extra 20% off promotion is not 50% off — it's 0.70 × 0.80 = 0.56, so 44% off. The order in which the discounts are applied does not change the final price as long as both are pure percentage discounts.

When a fixed-dollar coupon is combined with a percentage discount, the order does matter. A $10 coupon then 20% off a $100 item: ($100 − $10) × 0.80 = $72. The reverse — 20% off then $10 off: $100 × 0.80 − $10 = $70. Most retailers apply percentage discounts before fixed-dollar coupons, but always check the receipt.

BOGO offers convert cleanly into a percentage. Buy one get one free = 50% off the total when you buy two. BOGO 50% off = 25% off the total. BOGO at 30% off = 15% off the total. This makes BOGO easy to compare against a straight percent-off coupon.

The standard sequence is: subtotal → apply discounts → apply sales tax on the discounted subtotal → add tip on the pre-tax subtotal (if any). Sales tax is almost always calculated on the post-discount price, which means a coupon also reduces the tax you owe.

Restaurant gratuities are calculated on the pre-tax subtotal in most US states, though some restaurants and POS systems default to the post-tax total. The difference on a $100 check at 8% tax and a 20% tip is $1.60 — small per meal, meaningful over a year.

For credit-card cashback, the rebate applies to the final amount you actually pay (post-discount, post-tax, post-tip). Rewards never compound the way the underlying discount does — a 2% cashback on a 25% discount is not 27% off.

If you know the original price and the sale price but not the headline discount percentage, the formula is: discount % = (original − sale) ÷ original × 100. An item that dropped from $120 to $84 is (120 − 84) ÷ 120 = 30% off. This is useful for verifying retailer claims when the original price isn't obviously displayed, or for comparing two stores selling the same item at different list-and-discount combinations.

Be wary of inflated original prices. Some retailers list a 'manufacturer's suggested retail price' (MSRP) that no store actually charges, then advertise a percentage 'off' that MSRP. The Federal Trade Commission has guidelines against fictitious pricing, but enforcement is uneven — always compare to recent street prices at competing retailers, not the MSRP.

When evaluating clearance markdowns, the marginal discount matters more than the cumulative. An item that went from $100 → $70 → $50 is 50% off the original, but only 28.6% off the most recent price. If you're deciding whether to wait for further markdowns, the second number is the better gauge of how much more room there is to drop.

Loss-leader pricing exploits the assumption that higher percentage off = better value. A 70%-off impulse purchase you wouldn't otherwise make costs more than skipping the item at full price. Multiply (final price after discount) × (probability you'll actually use it) and compare to the true alternative — usually $0.

Bulk discounts can have negative per-unit value for perishables and seasonal goods. A 30%-off 5-pack of an item you'll use twice a year is more expensive per actual unit consumed than buying one at full price, with the added storage cost and waste from expiration.

Subscription discounts that auto-renew at full price after the promotional window are the most common 'expensive discount.' The first-year savings frequently get more than recovered in years 2 and 3 unless you actively renegotiate or cancel. Set a calendar reminder for the day before the discount expires.