How to compare discounts

“40% off plus an extra 20%” is not 60% off. “Buy one get one free” is not a 50% discount on two items unless you wanted both. Retail discount language is optimized to sound larger than the real savings, and the math that reveals the actual price is almost never shown on the sticker. This guide covers how to price out stacked discounts, BOGO deals, and percent-off-plus-coupon combinations so you can tell a real bargain from a rounded one.

The single-discount baseline

Easy case first. 30% off a $120 item: $120 × (1 − 0.30) = $84. You saved $36. Every other discount scenario is built from this primitive, applied more than once.

Stacked discounts don’t add — they compound

“40% off, plus an extra 20% at checkout” looks like 60%, feels like 60%, and is not 60%. Discounts stack multiplicatively, not additively.

Start with $100. 40% off → $60. Then 20% off that → $60 × 0.80 = $48. You paid $48, not $40. The effective discount is 1 − (0.60 × 0.80) = 1 − 0.48 = 52%.

General formula for stacked percent-off discounts: Effective discount = 1 − (1 − d₁)(1 − d₂)(1 − d₃)…. Order doesn’t matter mathematically — $100 × 0.80 × 0.60 is the same as $100 × 0.60 × 0.80 — but register systems often apply them in a specific order, so the displayed intermediate price depends on sequence even though the final total doesn’t.

Percent-off vs dollar-off — when to prefer which

$20 off a $50 item is a 40% discount. $20 off a $200 item is 10%. Dollar-off coupons are more valuable on cheaper items, percent-off more valuable on expensive ones. If a store lets you choose one, the breakeven is where dollar_off / sticker_price = percent_off. Below that, take the dollar-off; above, take the percent-off.

BOGO and quantity-based deals

“Buy one get one 50% off” on a $40 item: you pay $40 + $20 = $60 for two. Effective per-item price is $30, or 25% off each. Not 50%.

“Buy one get one free” on a $30 item: $30 for two = $15/each, a 50% effective discount — but only if you were going to buy two. If you only wanted one, the effective discount on what you needed is 0%; you just paid sticker.

“Buy 3 for $30” when the sticker is $12.99 each: normally $38.97, now $30, a 23% effective discount. This format is usually a weaker deal than it feels, because the sticker anchors high.

Pre-tax vs post-tax discount order

Most US sales tax is applied after discounts, not before. $100 item, 20% off, 8% sales tax: $100 × 0.80 = $80, then $80 × 1.08 = $86.40. A coupon reduces your tax bill proportionally.

Gift cards are the opposite — applied after tax, because they’re treated like payment, not like a price reduction. $100 item, 8% tax = $108, minus a $20 gift card = $88 out of pocket. You still paid the full tax on $100.

Clearance math — “final sale” still deserves math

An item marked “$89.99, now $49.99, take an additional 40% off” ends at $49.99 × 0.60 = $29.99. That’s a 67% effective discount off the original $89.99. Worth it if you wanted it at $60; not worth it if the impulse is driven by the percent-off itself.

The trap: anchoring. Stores set initial prices high specifically so later “70% off” looks heroic. The number to trust is the out-the-door price, not the percent off.

Price-per-unit comparisons

A 16 oz bottle at $4.49 vs a 24 oz at $5.99: per-oz prices are $0.281 and $0.250. The larger is 11% cheaper per oz. Grocery-store shelf tags often show this already; for online shopping it’s usually not displayed, so compute it yourself. The discount calculator includes a per-unit mode for exactly this comparison.

Subscription and bundle math

“Save 20% with annual billing” on a $10/mo service: $120 nominal, $96 with the discount — a $24/year saving. Real-world value of that saving depends on how likely you are to still use it in month 12. If service churn is 30%/year, the expected saving is $24 × 0.7 = $16.80 annualized, not the full $24.

Bundle pricing (“package 3 items for $50, individually $20 each”) is worth the bundle discount (17% here) only if you wanted all 3. Buying the third only because of the bundle is a 0% saving on things you wouldn’t have otherwise bought.

A 30-second discount audit

Before checkout: add up what’s in the cart at sticker. Write down your out-the-door price (after all discounts and tax). Divide to get the effective percent off. If it’s less than the advertised headline number, you’re paying for the marketing fog. If it matches, the deal is what it says.

The discount calculator handles stacked percent-off, dollar-off coupons, BOGO ratios, pre/post-tax ordering, and unit-price comparisons in one pass — pair it with the percentage calculator for quick sanity checks and the sales tax calculator when you’re shopping across multiple states.