1.3: Capacity

Capacity is the amount of liquid (or other pourable substance) that an object can hold when it’s full. When a liquid, such as milk, is being described in gallons or quarts, this is a measure of capacity.

There are five main units for measuring capacity in the U.S. customary measurement system. The smallest unit of measurement is a fluid ounce. “Ounce” is also used as a measure of weight, so it is important to use the word “fluid” with ounce when you are talking about capacity. Sometimes the prefix “fluid” is not used when it is clear from the context that the measurement is capacity, not weight.

The other units of capacity in the customary system are the cup, pint, quart, and gallon. The table below describes each unit of capacity and provides an example to illustrate the size of the unit of measurement. You can use any of these five measurement units to describe the capacity of an object, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the capacity of a swimming pool in gallons and the capacity of an expensive perfume in fluid ounces.

The table below shows some of the most common equivalents and conversion factors for the five customary units of measurement of capacity.

Unit Equivalents	Conversion Factors (heavier to lighter units of measurement)	Conversion Factors (lighter to heavier units of measurement)
1 cup = 8 fluid ounces	\(\dfrac{1 \text { cup }}{8 \text { fluid ounces }}\)	\(\dfrac{8 \text { fluid ounces }}{1 \text { cup }}\)
1 pint = 2 cups	\(\dfrac{1 \text { pint }}{2 \text { cups }}\)	\(\dfrac{2 \text { cups }}{1 \text { pint }}\)
1 quart = 2 pints	\(\dfrac{1 \text { quart }}{2 \text { pints }}\)	\(\dfrac{2 \text { pints }}{1 \text { quart }}\)
1 quart = 4 cups	\(\dfrac{1 \text { gallon }}{4 \text { quarts }}\)	\(\dfrac{4 \text { cups }}{1 \text { quart }}\)
1 gallon = 4 quarts	\(\dfrac{1 \text { quart }}{4 \text { cups }}\)	\(\dfrac{4 \text { cups }}{1 \text { quart }}\)
1 gallon = 16 cups	\(\dfrac{1 \text { gallon }}{16 \text { cups }}\)	\(\dfrac{16 \text { cups }}{1 \text { gallon }}\)

As with converting units of length and weight, you can use the factor label method to convert from one unit of capacity to another.

Example \(\PageIndex{1}\)

Use the Factor Label Method to determine the number of pints in \(2 \dfrac{3}{4} \) gallons.

Solution

\(2 \dfrac{3}{4} \) gallons = ________ pints	Begin by reasoning about your answer. Since a gallon is larger than a pint, expect the answer in pints to be a number greater than\(2 \dfrac{3}{4} \) gallons.
\(\dfrac{11 \text { gallons }}{4} \cdot \dfrac{4 \text { quarts }}{1 \text { gallon }} \cdot \dfrac{2 \text { pints }}{1 \text { quart }}\) = ________ pints	The table above does not contain a conversion factor for gallons and pints, so you cannot convert it in one step.
\(\dfrac{11 \text { gallons }}{4} \cdot \dfrac{4 \text { guarts }}{1 \text { gallon }} \cdot \dfrac{2 \text { pints }}{1 \text { guart }}\) = ________ pints	However, you can use quarts as an intermediate unit, as shown here
\(\dfrac{11}{4} \cdot \dfrac{4}{1} \cdot \dfrac{2 \text { pints }}{1}\) = ________ pints	Set up the equation so that two sets of labels cancel—gallons and quarts.
\(\dfrac{11 \cdot 4 \cdot 2 \text { pints }}{4 \cdot 1 \cdot 1}\) = ________ pints
\(\dfrac{88 \text { pints }}{4}\) = 22 pints
\(2 \dfrac{3}{4} \) gallons is equivalent to 22 pints

Example \(\PageIndex{2}\)

Natasha is making lemonade to bring to the beach. She has two containers. One holds one gallon and the other holds 2 quarts. If she fills both containers, how many cups of lemonade will she have?

Solution

1 gallon + 2 quarts = _______ cups	This problem requires you to find the sum of the capacity of each container and then convert that sum to cups.
4 quarts + 2 quarts = 6 quarts	First, find the sum in quarts. 1 gallon is equal to 4 quarts
\(\dfrac{6 \text { quarts }}{1} \cdot \dfrac{2 \text { pints }}{1 \text { quart }} \cdot \dfrac{2 \text { cups }}{1 \text { pint }}\) = _______ cups	Since the problem asks for the capacity in cups, convert 6 quarts to cups.
\(\dfrac{6 \text { quarts }}{1} \cdot \dfrac{2 \text { pints }}{1 \text { quart }} \cdot \dfrac{2 \text { cups }}{1 \text { pint }}\) = _______ cups	Cancel units that appear in both the numerator and denominator.
\(6 \cdot 2 \cdot 2\) = 24 cups	Multiply.
Natasha will have 24 cups of lemonade.

You Try \(\PageIndex{1}\)

Alan is making chili. He is using a recipe that makes 24 cups of chili. He has a 5-quart pot and a 2-gallon pot and is trying to determine whether the chili will all fit in one of these pots. Which of the pots will fit the chili?

A) The chili will not fit into either of the pots.
B) The chili can fit into either pot.
C) The chili will fit into the 5-quart pot only.
D) The chili will fit into the 2-gallon pot only.

Answer

D) The chili will fit into the 2-gallon pot only.