Divide the price by the quantity, with both in the same unit, and compare the results. A 750 g package for $2.85 works out to $3.80 per kilogram, and a 1 kg package for $3.60 works out to $3.60. Even though the second one costs more at the register, it is the cheaper one per kilogram.
US shelf tags usually show price per ounce, pound or fluid ounce; the method is identical: $3.80/kg is about $1.72/lb, and $3.60/kg is about $1.63/lb.
To do the division automatically, the rule of three calculator solves the proportion with any reference quantity. This guide shows the order of the steps and the cases where the comparison gets tricky.
| Sold by | Divide the price by | Example |
|---|---|---|
| Weight | The kilograms in the package | $2.85 ÷ 0.75 kg = $3.80/kg |
| Volume | The liters in the package | $1.80 ÷ 2 L = $0.90/L |
| Pieces | The number of pieces | $4.50 ÷ 6 = $0.75 per piece |
| Buy 2 get 1 free | The pieces you take home | 2 × $1.20 ÷ 3 = $0.80 per piece |
In all four rows the divisor is what you buy, measured in the unit of the result.
You divide because the price grows in proportion to the quantity: twice the product costs twice as much. That is why the quotient of price and quantity is a constant, the price of one unit, and comparing offers means comparing constants. The guide to ratio, proportion and fraction explains why this ratio keeps its units, unlike a fraction of a whole. If you want to see the same reasoning with other quantities, the proportions page collects the cases.
Converting grams to kilograms and milliliters to liters
Pick the unit shown on the price tag, usually the kilogram or the liter, and convert the package quantity before dividing. A gram is 1/1000 of a kilogram and a milliliter is 1/1000 of a liter, so 250 g is 1/4 kg, 500 g is 1/2 kg, 330 mL is 33/100 L and 1.5 L is 3/2 L. If both offers use grams or both use milliliters, you can divide in that unit and still compare, because the order does not change.
Volume works the same way. A 2 L bottle at $1.80 works out to 1.80 ÷ 2 = $0.90/L, and a 500 mL bottle at $0.50 works out to 0.50 ÷ 0.5 = $1.00/L. The 2-liter bottle wins. If you write 500 instead of 0.5 L, the result comes out 1000 times smaller.
Worked example: 750 g for $2.85 against 1 kg for $3.60
Two packages of the same product: one of 750 g costs $2.85 and one of 1 kg costs $3.60. Which is cheaper per kilogram?
- Convert grams to kilograms. 750 g = 750/1000 kg = 3/4 kg = 0.75 kg.
- Divide the first price. 2.85 ÷ 0.75 = 285/75 = 19/5 = $3.80/kg.
- Divide the second. 3.60 ÷ 1 = 18/5 = $3.60/kg.
- Compare. 19/5 is greater than 18/5, so the 750 g package costs more per kilogram.
Result: the 1 kg package wins, at $0.20 less per kilogram.
Check: 3.80 × 0.75 = 2.85 and 3.60 × 1 = 3.60, the prices on the tags.
Comparing multipacks: 6 for $4.50 against 10 for $7.00
With products you count, such as batteries, cans or yogurts, the divisor is the number of pieces. The 6-pack costs 4.50 ÷ 6 = 3/4 = $0.75 per piece and the 10-pack costs 7.00 ÷ 10 = 7/10 = $0.70. The 10-pack is cheaper per piece, by $0.05 (3/4 − 7/10 = 1/20 of a dollar).
If the pieces are not the same size, count the total quantity that matters. A pack with more, smaller units can work out worse than one with fewer, bigger units, and then the right divisor is the total weight, volume or number of sheets. To compare three or more offers, work out the unit price of each and sort them from lowest to highest with the order fractions tool.
Buy 2 get 1 free and second item half off
A promotion is a way of changing the divisor or the numerator, and it is solved with the same quotient. With buy 2 get 1 free you pay for 2 items and take home 3, so each one costs 2/3 of the price. With a $1.20 product, that works out to 2 × 1.20 ÷ 3 = $0.80 per item. With the second item half off you pay 1.20 + 0.60 = $1.80 for two, which is $0.90 per item.
Buy 2 get 1 free improves the unit price only if you take all three items and will use them. The guide to successive discounts has the calculation for chained percentages, and in percentages you can convert each saving to a percent.
When the lowest unit price is not the best buy
The unit price compares prices, not needs. A large package can cost less per kilogram and still be a worse buy if part of the product spoils before you use it, because what you throw away is paid for too. Storage space, the money you spend all at once, and the fact that two products with the same name are not always the same quality also matter.
The comparison also assumes that the price is proportional to the quantity. A fixed cost, such as shipping, or price tiers by volume break that proportion, and then the unit price is no longer a constant.
Sources
- Unit rates as a ratio of a price to a quantity: see the guide to ratio, proportion and fraction and the rule of three calculator.