**Introduction**

The process of associating numbers with physical quantities and phenomena is what we call a system of measurement. We need to measure a lot of things in our real life such as the weight of a bag, the capacity of a jar, length of a table. etc. The word “measurement” is derived from the Greek word “metron,” which means a limited proportion. There are two different systems of measurement in place that are commonly in use –

**Metric system** – It is the international decimal system of weights and measures, based on the metre for length and the kilogram for mass that was adopted in France in 1795 and is now used officially in almost all countries.

**US Standard Units** – The United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being formalized in 1832. Although U.S. customary units have been defined in terms of metric units since the 19th century, the United States is one of only three countries, others being Myanmar and Liberia that, as of 2022, have not officially adopted the metric system as the primary means of weights and measures. US Standard Volume is a part of the US standard units. Let us learn more about it.

**What is US Standard Volume?**

We know that volume is a three-dimensional quantity. It is the amount of capacity/space a substance contains, or the space it can hold. How is volume measured in the US standard system of units? Depending upon the volume to be measured, there are five main units for measuring capacity in the U.S. customary measurement system. These units are – fluid ounce, cup, pint, quart and gallon. Let us learn about each one of them.

**Fluid Ounces**

The fluid ounce is the smallest unit of measurement for volume in the US customary measurement system. The term “ ounce “ has been derived from the Latin word “ uncia “ which means “ twelfth part “. It is important to understand here that, the unit ounce is also used as a measure of weight. Hence, when referring to the unit for capacity it is necessary to use the complete word “ fluid ounce ”. This differentiates the use between an ounce as a measure of weight and ounce as a measure of capacity. 1 fluid ounce is approximately equal to 2 tablespoons. If we compare fluid ounce with the counterpart in the imperial system, one unit of a fluid ounce is approximately 29.5735297 ml. using the U.S. Customary system while it is just approximately 28 ml. using the Imperial system. The abbreviation for fluid ounce is fl. oz. Let us summarise the difference between an ounce and a fluid ounce.

**Difference between ounce and fluid ounce**

The following are the differences between ounce and fluid ounce –

Ounce | Fluid Ounce |

Ounce is a unit for measuring weight | Fluid ounce is a unit for measuring capacity |

One “oz.” is approximately 28.3495231 grams using the international avoirdupois system | One fl. oz. is equal to 29.5735297 ml. using the U.S. Customary system. |

One pound is equal to 16 ounces | one pint is equal to 16 fluid ounces |

The abbreviation for ounce is “ oz “ | The abbreviation for fluid ounce “ fl. oz “ |

Now, let us learn about the next unit, i.e. cups.

**Cups**

Cup is the next unit in the US customary system of measurement for volumes. 1 unit of a cup is equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.

**Pints**

Pint is the next unit in the US customary system of measurement for volumes. 1 unit of a pint is equal to 16 fluid ounces or 2 cups.

**Quarts**

Quart is the next unit in the US customary system of measurement for volumes. 1 unit of quart is equal to 32 fluid ounces or 2 pints or 4 cups.

**Gallons**

Gallon is the next unit in the US customary system of measurement for volumes. 1 unit of a gallon is equal to 128 fluid ounces or 4 quarts. Gallon is the largest liquid measurement.

**How are these units used in everyday life?**

Depending upon the volume of different objects we use these units for measurements in objects of daily use. Some of these examples are –

- The amount of liquid medicine is often measured in fluid ounces.
- The capacity of a standard measuring cup is one cup.
- The capacity of a carton of ice cream is often measured in pints.
- Milk is often sold in Quarts in the supermarket.
- When you fill up your car with gasoline, the price of gas is often listed in dollars per gallon.
- A water bottle may contain about 1 pint of liquid.
- A large shampoo bottle contains about 1 quart of liquid.
- A juice box contains about 1 cup of liquid.

Now that we have learnt the basic definitions of the units used in the US customary system of measurement for volumes, let us now understand the conversion factors of these five units.

**Conversion Factors of the five customary units of measurement of capacity**

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

Unit Equivalent | Conversion Factor ( Heavier to Lighter units of measurement ) | Conversion Factor ( Lighter to Heavier units of measurement ) |

1 cup = 8 fluid ounces | 1 cup / 8 fluid ounces | 8 fluid ounces / 1 cup |

1 pint = 2 cups | 1 pint / 2 cups | 2 cups / 1 pint |

1 quart = 2 pints | 1 quart / 2 pints | 2 pints / 1 quart |

1 quart = 4 cups | 1 quart / 4 cups | 4 cups / 1 quart |

1 gallon = 4 quarts | 1 gallon / 4 quarts | 4 quarts / 1 gallon |

1 gallon = 16 cups | 1 gallon / 16 cups | 16 cups / 1 gallon |

This relationship can be summarise as

Cup | Pint | Quart | Gallon |

16 | 8 | 4 | 1 |

4 | 2 | 1 | 1 / 4 |

2 | 1 | 1 / 2 | 1 / 8 |

1 | 1 / 2 | 1 / 4 | 1 / 16 |

The above table clearly defines the relationship between the five customary units that are used to measure capacity in the US customary system of measurement. However, it is not always possible to convert one unit to another using the formulas. Some standard conversions have been derived using the above formulas that are used in everyday practice which makes the conversions faster and efficient. Let us understand this conversion table.

**Liquid Volume Conversion Chart**

The following table shows the conversion values from one unit to another according to the US customary system of measurement for capacity –

Unit Equivalent | Unit Equivalent | Metric Equivalent | Metric Unit ( Simplified ) | |||

1 table spoon | = | 3 teaspoons | = | 14.78777 millilitres | = | 15 millilitres |

1 fluid ounce | = | 2 tablespoons | = | 29.57353 millilitres | = | 30 millilitres |

1 cup | = | 8 fluid ounces | = | 236.58824 millilitres | = | 237 millilitres |

1 pint | = | 2 cups | = | 473.17648 millilitres | = | 473 millilitres |

1 pint | = | 16 fluid ounces | = | 473.17648 millilitres | = | 473 millilitres |

1 quart | = | 2 pints | = | 946.35296 millilitres | = | 946 millilitres |

1 gallon | = | 4 quarts | = | 3.7854 litres | = | 3.8 litres |

1 gallon | = | 128 fluid ounces | = | 3.7854 litres | = | 3.8 litres |

**Converting larger units to smaller units**

To convert larger units to smaller units we multiply the number of larger units by the green conversion factor for the appropriate smaller units. The following relationships between units are used for this purpose –

**1 pint = 2 cups**

**1 quart = 4 cups**

**1 quart = 2 pints**

**1 gallon = 4 quarts**

Let us understand it using an example.

**Example**

Convert 4 gallons into quarts.

**Solution**

We are required to convert 4 gallons into quarts. For this conversion, we must first recall the relation between a gallon and a quart. We have learnt above that

1 gallon = 4 quarts

Now, using the above relation, we can easily find the value of 4 gallons with respect to quarts. We will have,

1 gallon = 4 quarts

Therefore,

4 gallons = 4 x 4 quarts = 16 quarts

**Hence, 4 gallons = 16 quarts**

Let us consider another example.

**Example**

Convert 8 pints into cups.

**Solution**

We are required to convert 8 pints into cups. For this conversion, we must first recall the relation between a pint and a cup. We have learnt above that

1 pint = 2 cups

Now, using the above relation, we can easily find the value of 8 pints with respect to cups. We will have,

1 pint = 2 cups

Therefore,

8 pints = 8 x 2 cups = 16 cups

**Hence, 8 pints = 16 cups**

Now, let us learn how to convert smaller units into larger units

**Converting smaller units to larger units**

To convert smaller units to larger units we divide the number of smaller units by the purple conversion factor for the appropriate larger units.

The following relationships between units are used for this purpose –

1 cup = 1 / 2 pint

1 pint = 1 / 2 quart

1 quart = 1 / 4 gallon

Let us understand it using an example.

**Example**

Convert 12 pints into quarts.

**Solution**

We are required to convert 12 pints into quarts. For this conversion, we must first recall the relation between a pint and a quart. We have learnt above that

1 pint = 1 / 2 quart

Now, using the above relation, we can easily find the value of 8 pints with respect to cups. We will have,

1 pint = 1 / 2 quart

Therefore,

12 pints = 12 / 2 quarts = 6 quarts

**Hence, 12 pints = 6 quarts**

Let us consider another example.

**Example**

Convert 20 quarts into gallons.

**Solution**

We are required to convert 20 quarts into gallons. For this conversion, we must first recall the relation between a quart and a gallon. We have learnt above that

1 quart = 1 / 4 gallon

Now, using the above relation, we can easily find the value of 8 pints with respect to cups. We will have,

1 quart = 1 / 4 gallon

Therefore,

20 quarts = 20 / 4 gallons = 5 gallons

**Hence, 20 quarts = 5 gallons**

**Solved Examples**

**Example 1** Alice mixed 2 cartons of orange juice, 3 bottles of soda water and 6 cans of cocktail fruits to make a fruit punch for the Christmas party. Each carton of juice is 1 gallon and 3 quarts. Each soda water bottle contains 6 quarts. The cans of cocktail fruit are 2 pints each. How much (measured in gallons) of fruit punch did Alice make?

**Solution** We have been given that Alice mixed 2 cartons of orange juice, 3 bottles of soda water and 6 cans of cocktail fruits to make a fruit punch for the Christmas party. Each carton of juice is 1 gallon and 3 quarts. Each soda water bottle contains 6 quarts. The cans of cocktail fruit are 2 pints each. We are required to find the fruit punch that Alice made in gallons. Let us summarise the information given to us. We have,

Orange juice used = 2 cartons

Number of Soda bottles = 3

Cocktail fruits = 6 cans

Now, we have also been given the capacity of cartons, bottles and cans. We have,

1 carton = 1 gallon + 3 quarts

1 bottle = 6 quarts

1 can of cocktail = 2 pints

Since, we are required to find the fruit punch that Alice made in gallons, therefore, it important that we first convert all the given measurements in pints which we can further convert into gallons. Let us do them one by one. We will have,

Orange juice used = 2 cartons

1 carton = 1 gallon + 3 quarts

Now, we know that 1 gallon = 4 quarts.

Therefore,

1 carton = 1 gallon + 3 quarts = 4 quarts + 3 quarts = 7 quarts

Also, 1 quart = 2 pints, therefore, 7 quarts = 7 x 2 = 14 pints

2 cartons = 14 x 2 pints = 28 pints

Hence, the capacity of orange juice = 28 pints …………… ( 1 )

Next, we have, Number of Soda bottles = 3

Now, 1 bottle = 6 quarts = 6 x 2 pints = 12 pints

Therefore, 3 soda bottles = 3 x 12 pints = 36 pints

Hence, capacity of soda bottles = 36 pints ………………. ( 2 )

Last, we have Cocktail fruits = 6 cans

Now, 1 can of cocktail = 2 pints, therefore

6 cans = 6 x 2 pints = 12 pints

Hence, capacity of cocktail fruits = 12 pints …………….. ( 3 )

From equation (1 ), ( 2 ) and ( 3 ), we have,

2 cartons of orange juice + 3 bottles of soda water + 6 cans of cocktail fruits =

28 pints + 36 pints + 12 pints = 76 pints

Now, that we have all values in pints, let us convert pints into the gallon. We know that 1 gallon = 8 pints. This means that 76 pints = 76 / 9 gallons = 9.5 gallons.

**Hence, Alice made 9.5 gallons of fruit punch.**

**Example 2** How many gallons is 32 fluid ounces?

**Solution** We are required to convert 32 fluid ounces into gallons. For this conversion, we will have to recall the relationship between a fluid ounce and a gallon. Note that one is the smallest unit while the other is the largest unit of capacity in the US customary system of measurement. We know that –

1 gallon = 128 fluid ounces

Therefore, sing the unitary method, we have

128 fluid ounces = 1 gallon

1 fluid ounce = 1 / 128 gallon

32 fluid ounces = 32 x ( 1 / 128 ) gallons

⇒ 32 fluid ounces = 1 / 4 gallons

Hence, 32 fluid ounces = 1 / 4 gallons.

**Key Facts and Summary**

- The process of associating numbers with physical quantities and phenomena is what we call a system of measurement.
- The Metric system is the international decimal system of weights and measures, based on the metre for length and the kilogram for mass.
- The United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being formalized in 1832.
- The fluid ounce is the smallest unit of measurement for volume in the US customary measurement system. The abbreviation for fluid ounce is fl. oz.
- An ounce is a unit for measuring weight while a Fluid ounce is a unit for measuring capacity.
- 1 unit of a cup is equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.
- 1 unit of a pint is equal to 16 fluid ounces or 2 cups.
- 1 unit of quart is equal to 32 fluid ounces or 2 pints or 4 cups.
- Gallon is the largest liquid measurement. 1 unit of a gallon is equal to 128 fluid ounces or 4 quarts.

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