The short answer
$100 at 20% off is $80, saving $20. Stack a second 10% discount on top and the final price is $72, not $70 — a 28% effective discount, because the second cut applies to the already-reduced price. A Buy 2 Get 1 Free deal on $10 items works out to $20 for 3 items — a 33.33% effective discount, or $6.67 per item.
Key takeaways
- $100 at 20% off = $80 sale price, $20 saved.
- Stacking 20% off then 10% off on $100 lands at $72 — a 28% effective discount, not 30%.
- Buy 2 Get 1 Free on $10 items: $20 for 3 items, a 33.33% effective discount at $6.67 per item.
- Paid $80 after 20% off? The original price was $80 ÷ 0.80 = $100.
The core sale-price formula
Sale Price = Original Price × (1 − discount rate)
= $100 × (1 − 0.20) = $80
The reverse direction uses division instead: Original Price = Sale Price ÷ (1 − discount rate), so $80 paid after a 20% discount means Original = $80 ÷ 0.80 = $100. Both directions describe the same relationship — just solved for a different unknown.
Why stacked discounts fall short of the sum
Each additional coupon or discount applies to the current, already-discounted price — not the original. On a $100 item with 20% off followed by 10% off:
After 20% off: $100 × 0.80 = $80
After 10% off that: $80 × 0.90 = $72
Effective discount: ($100 − $72) ÷ $100 = 28%
That 2-percentage-point gap between 30% (naive sum) and 28% (actual) grows as more discounts stack, since each one shrinks against a smaller base than the last. The order the discounts are applied in doesn't change the final total — 10% then 20% reaches the same $72 as 20% then 10%.
Buy-X-Get-Y: finding the real percentage off
A "Buy 2 Get 1 Free" sign never shows a percentage, but it's a discount like any other once converted to the same terms. At $10 per item:
Regular price for 3 items: $10 × 3 = $30
Deal price: $10 × 2 (paid) + $10 × 1 × 0% (free) = $20
Effective discount: ($30 − $20) ÷ $30 = 33.33% ($6.67 per item)
That 33.33% is worth comparing directly against any straight percent-off offer on the same items — sometimes a flat 30% off beats "Buy 2 Get 1 Free," sometimes it doesn't, and the only way to know is running both through the same math rather than trusting whichever sign looks like the bigger deal.
Related calculators
- Discount Calculator — a similar tool focused specifically on sale price and stacked discounts.
- Sales Tax Calculator — add tax back on top of your final discounted price.
- VAT Calculator — figure value-added tax instead of a discount for shoppers outside the US.