Unit Rates and Unit Prices: How to Find the Best Buy

Is a 24-ounce jar at $5.49 cheaper than a 16-ounce jar at $3.99? Without a calculator, it's hard to tell at a glance. The unit rate, the price for one unit of the product, turns the comparison into a simple matter of which number is smaller.

The formula

unit price = total price ÷ quantity

24 oz at $5.49: 5.49 ÷ 24 = $0.229 per ounce
16 oz at $3.99: 3.99 ÷ 16 = $0.249 per ounce

The larger jar is about 2 cents per ounce cheaper, roughly 8% less. Many stores print unit prices on shelf labels, but they don't always use the same unit for every brand, so it pays to know how to calculate them.

Unit rates beyond shopping

Speed: 210 miles in 3.5 hours is 60 miles per hour.
Pay: $780 for 40 hours is $19.50 per hour.
Fuel economy: 336 miles on 12 gallons is 28 miles per gallon.
Typing: 450 words in 6 minutes is 75 words per minute.

Using a proportion to compare

Another approach: work out what one item would cost at the other's size. If 16 oz cost $3.99, what would 24 oz cost at the same rate? 3.99/16 = x/24 gives x = $5.985. The 24-oz jar at $5.49 is cheaper. The proportion calculator solves this in one step.

Mixed units

Convert to a common unit before comparing. A 1-liter bottle at $2.79 versus a 64-fluid-ounce bottle at $4.29:

1 liter ≈ 33.8 fl oz, so $2.79 ÷ 33.8 = $0.083 per fl oz
$4.29 ÷ 64 = $0.067 per fl oz

The larger bottle wins. Common conversions: 1 lb = 16 oz, 1 kg ≈ 2.205 lb, 1 gallon = 128 fl oz, 1 liter ≈ 33.8 fl oz.

Multi-buy deals

"3 for $10" is $3.33 each. "Buy 2, get 1 free" on a $4.50 item is 3 for $9.00, or $3.00 each. Compare the effective unit price with the regular price of a larger package before deciding.

When the cheaper unit price isn't the best buy

Waste: a bulk bag of produce that spoils before you use it costs more per unit eaten.
Storage and cash flow: buying a year's supply ties up money and space.
Quality differences: a cheaper unit price for a weaker concentrate may need more product per use. Compare cost per use, not per ounce, for things like detergent.
Sale prices: sometimes the small size on sale beats the large size at regular price, so check every time.

Unit rates in construction

Materials quoted by different units need the same treatment. Gravel at $38 per ton and $52 per cubic yard can only be compared after converting with the stone's density; see tons vs. cubic yards. Bagged versus bulk mulch is the same idea, covered in bulk vs. bagged materials.

Quick practice

Which is cheaper: 5 lb of rice for $6.25 or 2 lb for $2.79? Unit prices are $1.25 and about $1.40 per pound, so the 5-lb bag is the better buy, if you'll use it.