US Customary Units

The United States is one of the few countries that still relies on its own system of measurement for everyday use. Whether you are reading a recipe, measuring lumber, or checking your weight at the doctor’s office, you will encounter US customary units. Understanding how these units relate to each other is essential for everyday math.

Length

US customary length units build on each other. Here are the key relationships:

To convert from a larger unit to a smaller unit, multiply. To convert from a smaller unit to a larger unit, divide.

$\text{larger unit} \times \text{conversion factor} = \text{smaller unit}$

$\text{smaller unit} \div \text{conversion factor} = \text{larger unit}$

Weight

US customary weight units use ounces, pounds, and tons:

Capacity (Volume)

Capacity measures how much liquid a container holds:

A helpful way to remember: Gallon contains 4 Quarts, each Quart contains 2 Pints, each Pint contains 2 Cups.

Worked Examples

Example 1: Converting Feet to Inches

Convert 7 feet to inches.

Since 1 foot = 12 inches, multiply:

$7 \text{ ft} \times 12 = 84 \text{ in}$

7 feet = 84 inches.

Example 2: Converting Ounces to Pounds

Convert 96 ounces to pounds.

Since 1 pound = 16 ounces, divide:

$96 \text{ oz} \div 16 = 6 \text{ lb}$

96 ounces = 6 pounds.

Example 3: Converting Cups to Gallons

A punch recipe calls for 24 cups of liquid. How many gallons is that?

Since 1 gallon = 16 cups, divide:

$24 \text{ c} \div 16 = 1.5 \text{ gal}$

24 cups = 1.5 gallons, or 1 gallon and 2 quarts.

Example 4: Converting Miles to Yards

A cross-country course is 3 miles long. How many yards is that?

Since 1 mile = 1,760 yards, multiply:

$3 \text{ mi} \times 1{,}760 = 5{,}280 \text{ yd}$

3 miles = 5,280 yards.

Example 5: Mixed Unit Conversion

A package weighs 5 pounds 8 ounces. What is the total weight in ounces?

First convert the pounds to ounces, then add the remaining ounces:

$5 \text{ lb} \times 16 = 80 \text{ oz}$

$80 \text{ oz} + 8 \text{ oz} = 88 \text{ oz}$

5 pounds 8 ounces = 88 ounces.

Practice Problems

Test your understanding with these problems. Work each one out before revealing the answer.

Key Takeaways

• US customary units use different conversion factors for length, weight, and capacity — there is no single pattern like the metric system.
• Multiply when converting from larger units to smaller units (feet to inches).
• Divide when converting from smaller units to larger units (ounces to pounds).
• Memorize the key relationships: 12 inches per foot, 3 feet per yard, 5,280 feet per mile, 16 ounces per pound, 2,000 pounds per ton, and the cup-pint-quart-gallon chain.
• Mixed-unit problems require converting one part before combining.

Return to Arithmetic for more foundational math topics.