About

Retailers often use psychological pricing strategies like Buy One, Get One Free (BOGO) or Buy 2, Get 1 50% Off to increase average transaction value. While these deals look attractive, the actual effective discount is often lower than it appears. This tool calculates the mathematical reality of these promotions, helping you determine the true cost per unit and total savings.

Whether you are a shopper analyzing a sale or a business owner setting prices, this calculator handles both Uniform Carts (all items same price) and Mixed Carts (items of varying prices), applying the industry-standard Greedy Algorithm (sorting high-to-low) to maximize customer savings automatically.

Formulas

The Effective Discount (E) is calculated by comparing the total amount paid against the total market value of the goods.

E = V_total − C_paidV_total × 100

Where:

V_total = Sum of all item original prices (Market Value)
C_paid = Actual cost after applying BOGO logic

Reference Data

Deal Type	Formula Structure	Effective Discount (Ideal)
Buy 1 Get 1 Free	Pay for 1, Get 2	50%
Buy 1 Get 1 50% Off	Pay 100% + 50%, Get 2	25%
Buy 2 Get 1 Free	Pay for 2, Get 3	33.33%
Buy 2 Get 1 $1	Pay 2x + $1, Get 3	Varies (approx 30-33%)
3 for 2	Pay for 2, Get 3	33.33%
Buy 1 Get 2 Free	Pay for 1, Get 3	66.66%

Frequently Asked Questions

For mixed items, the calculator uses the standard "Customer Advantage" sorting method. It sorts all items from most expensive to least expensive. It then groups them according to the "Buy X, Get Y" rule. The first X items in every group are charged full price, and the next Y items are discounted. This simulates how most modern Point-of-Sale (POS) systems work to maximize the deal for the buyer.

If all items have the same price, the effective discount percentage is Y / (X + Y). For example, in a Buy 2 Get 1 Free deal, you get 1 free item out of 3 total. The calculation is 1 / 3 = 33.33% discount.

Mathematically, sales tax does not change the discount *percentage* because it is applied to the final subtotal. However, it affects the final "out of pocket" cost. This tool calculates tax on the discounted amount, which is standard in most jurisdictions (though some regions require tax on the pre-discount value; this tool assumes the standard post-discount taxation).

Buy 1 Get 1 50% Off is effectively a 25% discount on the total pair (buying 2 items). Therefore, a flat 30% discount on everything is a better deal than BOGO 50%.