How this works
A percentage discount knocks a flat fraction off the original price. The maths is straightforward: a 30% discount on a $59.99 item leaves you paying 70% of that, or about $42, saving roughly $18. Where it gets confusing is when retailers stack discounts — "extra 20% off sale prices" applied to a 30% sale doesn't total 50% off. The two cuts compound: the second 20% comes off the already-reduced price, so the true effective discount is 1 − 0.7 × 0.8 = 44%, not 50%. The calculator handles single discounts and one optional stacked discount, showing the final price, the amount saved, and (when stacking) the real effective rate so you don't fall for misleading signage.
The formula
discount% is the headline number on the price tag (e.g. 30 means 30%). When two discounts apply, d1 is the first reduction (typically the sale price) and d2 is the second (coupon, member discount). The effective rate is always lower than the naive sum of the two; for two equal discounts of d, it equals 2d − d²/100.
Example calculation
- Original price: $59.99. Discount: 30%.
- Sale price: 59.99 × (1 − 0.30) = 59.99 × 0.70 = $41.99.
- You save: 59.99 − 41.99 = $18.00.
- Add a 20% coupon (stacked): 41.99 × 0.80 = $33.59. True effective discount = 1 − 0.7 × 0.8 = 44%, not 50%.
Frequently asked questions
Why is "20% off + 20% off" not the same as 40% off?
Because the second discount is applied to the already-reduced price, not to the original. After the first 20% off, you pay 80% of the original. The second 20% off comes off that 80%, leaving 80% × 80% = 64% — so the effective discount is 36%, not 40%. The shortcut formula for two equal stacked discounts of d% is 2d − d²/100. For 20% + 20% that gives 40 − 4 = 36% — confirming the calculation.
Does the order of stacked discounts matter?
For the final price, no — multiplication is commutative, so 30% then 20% gives the same number as 20% then 30%. But it can matter for whether a coupon is even valid: many "% off" coupons explicitly exclude sale items, in which case applying the coupon "first" (full price) wouldn't be allowed. And for taxable purchases, jurisdictions sometimes specify whether sales tax is computed before or after coupons, which can shift the bottom line by a small amount even though the discount itself is order-independent.
How do I figure out the original price from a sale price?
Divide, don't add. If a $42 item is marked as "30% off", the original was 42 ÷ (1 − 0.30) = 42 ÷ 0.70 = $60. Don't fall into the trap of adding 30% back to $42 (which gives $54.60, the wrong number). The mistake comes from confusing "30% of original" with "30% of sale price" — they're different amounts because the original is bigger.
Where does sales tax fit in?
Most countries display tax-inclusive prices, so the discount applies to the price as shown and the calculator's answer is what you actually pay. The big exception is the US, where listed prices are pre-tax: in that case, apply the discount first, then add sales tax to the discounted figure (state law typically requires this). If you want a one-step number that includes tax, multiply the calculator's sale price by (1 + tax_rate/100).