Shopping math guide
How to compare unit prices and discounts
A larger package, brighter sale label, or higher percentage discount is not automatically the better purchase. A fair comparison starts by putting both offers on the same basis.
· About 8 minutes
Start with price per equal unit
Unit price is the package price divided by the amount in the package. A $6 box containing 20 items costs $0.30 per item. An $8 box containing 20 of the same item costs $0.40 per item. When quality and terms are otherwise equal, the first option costs 25 percent less per item than the second because the $0.10 difference is divided by the higher $0.40 price.
The units must match before dividing. Do not compare dollars per pound with dollars per ounce, or dollars per liter with dollars per fluid ounce. Convert one quantity so both packages use the same weight, volume, length, count, or usable serving definition. Package labels sometimes round their displayed unit prices, so using the full price and quantity can produce a slightly different result.
Decide what the quantity really represents
A count is straightforward only when the individual pieces are comparable. Ten large bags are not necessarily equivalent to ten small bags. Paper products may advertise rolls, sheets, sheet area, or an “equivalent roll” defined by the manufacturer. Concentrated cleaners can require comparison by prepared volume or recommended dose rather than bottle volume.
Choose a quantity that reflects what you actually consume. If two products have different strength, coverage, durability, or serving size, cost per package unit may not describe cost per use. Write down the basis explicitly—for example, cost per 100 grams, per standard dose, or per square meter covered—so the comparison can be checked.
Reduce multi-buy offers to one package
For an offer such as three packages for $12, divide the offer price by three before comparing package prices, or combine all three package quantities and divide $12 by the total quantity. Both methods produce the same unit price when every package has the same size.
“Buy one, get one free” is effectively a 50 percent reduction only when you receive two identical items, would otherwise pay full price for both, and can use both. “Buy two, get one free” gives three items for the price of two, which is a one-third reduction from the three-item regular total—not a 50 percent reduction.
Apply consecutive discounts in order
Successive percentage discounts multiply rather than add. A 20 percent discount followed by another 10 percent discount leaves 80 percent × 90 percent = 72 percent of the original price. The combined discount is therefore 28 percent, not 30 percent.
A fixed coupon and a percentage discount can give different answers depending on order. Retailer terms determine whether the coupon is subtracted before or after the percentage reduction and whether either discount changes the taxable amount. Use the actual checkout sequence instead of assuming every promotion stacks.
Separate the shelf price from the total cost
Shipping, taxes, deposits, membership fees, minimum-order charges, and required accessories can change the comparison. Add costs that apply specifically to an option, then divide the resulting total by its usable quantity. If a membership serves many purchases, allocating the full fee to one item would also be misleading; the relevant cost depends on why the membership was purchased and how it is used.
Cash-back rewards and rebates introduce timing and conditions. A mail-in rebate is not the same as an instant reduction if it may expire, requires documentation, or arrives later. Compare both the amount paid now and the expected net cost when that distinction affects the decision.
Account for waste and storage
The lowest unit price is useful only for quantity you can use. If half of a large food package spoils, its effective cost per consumed unit doubles. Bulk purchases may also require freezer space, containers, transport, or additional cash today.
Estimate the usable fraction when waste is predictable. Divide the package price by the amount likely to be used, not merely the amount purchased. This adjustment is an estimate, so avoid reporting it with unrealistic precision.
Use percentages with a stated baseline
“Option A is 25 percent cheaper than option B” and “option B is 33.33 percent more expensive than option A” can both describe unit prices of $0.30 and $0.40. The percentages differ because their baselines differ. State which price is the reference so the comparison is not ambiguous.
Use the Unit Price Calculator for two like-for-like package prices, the Discount Calculator for a sale price and optional tax, and the Percentage Calculator when you need to inspect the baseline directly.
Make the final decision broader than the arithmetic
Unit price does not measure quality, safety, ingredients, warranty, return terms, labor conditions, environmental impact, convenience, or personal preference. It is one input to a purchase decision, not a complete verdict. Confirm package descriptions and promotion terms at checkout because labels and availability can change.
The examples are general shopping arithmetic, not financial, tax, nutrition, or product advice. Prices, taxes, promotion rules, package definitions, and consumer protections vary by seller and location.