How the Double Discount Calculator works
A double discount (also called a stacked or successive discount) is what happens when a price is cut twice in a row — a storewide sale plus a coupon, or a markdown plus a clearance tag. The second discount does not apply to the original price; it applies to the price that is already reduced. That single fact is why two discounts never simply add together.
The formula
For an original price P, a first discount rate d1, and a second discount rate d2 (both expressed as decimals, e.g. 30% = 0.30), the final price is:
Final Price = P × (1 − d1) × (1 − d2)
The total amount saved is simply the original price minus the final price, and the effective combined discount rate — the single percentage that would have produced the same final price in one step — is 1 − (1 − d1) × (1 − d2), expressed as a percentage.
Worked example
Take a $100 item marked 30% off, with an extra 20% off applied at checkout. The first discount brings the price to $100 × 0.70 = $70. The second discount applies to that $70, not the original $100, bringing it to $70 × 0.80 = $56. Total savings are $44, which works out to an effective combined discount of 44% — not the 50% you would get by simply adding 30% and 20%.
Why the discounts don't just add up
Adding percentages would only be correct if both discounts applied to the original price independently. Because the second discount is taken off an already-lower number, it removes a smaller dollar amount than it would have on the full price, so the combined effect is always a little less than the sum of the two rates. The gap between the "naive" sum (d1 + d2) and the true effective rate grows as the discounts get larger.
Order doesn't matter
Because multiplication is commutative, P × (1 − d1) × (1 − d2) gives the same result as P × (1 − d2) × (1 − d1). Whether the storewide sale or the coupon is applied first, the $100 item above still lands at $56. What changes the total is the number and size of the discounts, never the sequence they are entered in.