"50% off" sounds straightforward — half price, right? Sometimes. But discount math gets tangled fast: stacked discounts, MSRP inflation, BOGO offers, percentage markups vs markdowns, and "up to" qualifiers all add complexity. Here's the practical breakdown.
Simple discount math
Sale price = original × (1 − discount%).
- $100 with 25% off: $75.
- $100 with 50% off: $50.
- $100 with 75% off: $25.
Savings: original − sale price = original × discount%.
Stacked discounts (the trick)
"20% off, then an additional 10% off" is NOT 30% off. It's 28%.
Math: $100 × 0.80 × 0.90 = $72. Total savings 28%, not 30%.
Why: the 10% applies to the already-discounted price, not the original.
For three stacked discounts: 1 − (0.80 × 0.90 × 0.95) = 31.6% effective. Each subsequent discount has less effect.
BOGO discount math
"Buy one get one free": only effective if you buy two. Effective discount = 50% off the total. If you only need one, paying full price is the same as BOGO with one item.
"Buy one get one half off": 25% off the total when buying two.
"Buy two get one free": 33% off when buying three. Roughly equivalent to "33% off everything" if you buy in threes.
BOGO sales encourage you to buy more than you need. Sometimes worth it; sometimes wasteful.
The MSRP trap
MSRP (Manufacturer's Suggested Retail Price) is often inflated above what anyone actually charges. "$200 jacket on sale for $99 — 50% off!" sounds great but maybe nobody actually paid $200.
True savings = real selling price − sale price. Compare to typical street price, not MSRP.
Online tools like Honey, CamelCamelCamel (Amazon), and Keepa show price history. The "sale" might be the regular price.
The "up to" qualifier
"Up to 70% off" is a marketing weasel phrase. It means SOME items have that discount, often the slowest-moving stuff. Most items are discounted less.
Real average discount in "up to 70% off" sales is typically 20–40%. Calculate based on actual marked items.
Percentage markups vs markdowns
Subtle but important distinction:
- "$100 marked up 20%" = $120.
- "$120 marked down 20%" = $96 (not back to $100).
To restore from a 20% markdown, you need to mark up by 25%, not 20%. The math:
Markup needed = discount / (1 − discount). For 20% discount, need 0.20 / 0.80 = 25% markup back.
This is why retailers use very high MSRPs — they can show big "discounts" while still hitting target margins.
Coupon math
Coupons can be:
- Flat dollar: "$10 off" — straightforward.
- Percentage: "20% off" — calculate above.
- Combinations: "$50 off any order over $200" — only useful if you'd buy that much.
- Conditional: "free shipping on orders $50+" — encourages adding items.
Many coupons require minimum purchases or specific items. Read terms carefully.
Membership discount math
Costco, Sam's Club, BJ's charge $50–120/year for membership. Members save 5–20% on prices.
Break-even: $60 membership / 10% savings = $600/year of purchases. Below that, membership doesn't pay off.
Most members spend $1500+/year. Worth the membership for typical families.
Sales tax and discounts
Tax is typically applied AFTER the discount, not before. So:
- $100 × 0.80 (20% off) = $80 sale price.
- $80 × 1.085 (8.5% sales tax) = $86.80 final.
Full math: original × (1 − discount) × (1 + tax). Don't forget tax.
Online vs in-store
Same product can have different prices online vs in-store. Online often cheaper, but you pay shipping. Sometimes shipping is more than the savings.
"Buy online, pickup in store" combines benefits — sometimes you get the online price without shipping cost.
Promotional pricing strategies
"Loss leader": retailer sells one product below cost to attract customers. They make money on other items in the cart.
Anchoring: show high-priced "premium" option first. Makes the option you're trying to sell look reasonable.
Decoy effect: three options where the middle one is the target. Top option is too expensive, bottom too cheap, middle "just right."
Bundle discount: buying multiple items at a fixed total price. Often good if you actually use everything bundled.
Black Friday math
Black Friday discounts are real but inflated:
- Many "sale" prices match standard online prices.
- Doorbuster items have very limited stock.
- "Lowest price of the year" sometimes appears in October instead.
Use price tracking tools (CamelCamelCamel) before declaring a Black Friday "deal."
Retailer markup history
Standard apparel retailer:
- Cost: $20.
- List price: $80 (4× markup).
- Sale at 50% off: $40 (still 100% markup over cost).
- "Final markdown" 70% off: $24 (20% over cost).
So even at "70% off," the retailer is profitable. Their margin is thin but positive.
This is why deep discounts are sustainable — they're built into the original pricing structure.
True comparison shopping
To find real deals:
- Use price comparison sites (Google Shopping).
- Check price history (CamelCamelCamel for Amazon).
- Don't anchor on MSRP. Anchor on the lowest recent price.
- Check shipping and return policies.
- Verify warranty applies for sale items.
Calculate true savings
Our discount calculator handles the basic math. Use it to verify "50% off" claims, calculate stacked discounts, or work out "what discount equals what dollar amount."