Home / United States / Math Classes / Formulas / Customary Units of Length Conversion Formulas

Length is defined as the measurement of a line between two points from one end to the other. Standard units of measurement can be used to quantify their values. In this section we will learn about customary units of length such as yard, mile, foot and inches....Read MoreRead Less

We can convert one unit to another by dividing or multiplying the unit to be converted by a numerical factor. By this conversion, we can get the same value in different types of units. The most general units of distance are inches, feet, yards and miles. To express certain distances, appropriate units are used. The distance between two states or countries can be expressed in miles and not feet but to measure the height of a person, one can use feet and inches.

Standard conversions are given below –

1 foot = 12 inches

1 yard = 3 feet

1 mile = 1,760 yards

Now, let’s understand how to convert one customary unit to another unit.

So, to convert from a larger unit to a smaller unit we need to multiply the numerical factor. Therefore,

1 mile = 1,760 yards = 5,280 feet = 63,360 inches

Conversely, to convert from a smaller unit to a larger unit we need to divide it by the numerical factor. Therefore,

1 inch \(=\frac{1}{12}\) foot \(=\frac{1}{36}\) yards \(=\frac{1}{63,360}\) miles

**Example 1:** Find the number of yards in 4 miles.

**Solution:**

We know that there are 1760 yards in 1 mile.

So the number of yards in 4 miles will be; 4 × 1760 = 7040

**Hence, there are 7,040 yards in 4 miles.**

**Example 2:** Convert 2 yards into inches.

**Solution:**

We know that there are 3 feet in 1 yard.

The number of feet in 2 yards = 2 x 3

= 6 feet

Since, there are 12 inches in 1 foot.

The number of inches in 6 feet = 12 × 6

= 72 inches

Hence, there are 72 inches in 2 yards.

**Example 3:** Convert 7 miles into feet.

**Solution:**

We know that there are 1,760 yards in 1 mile.

Number of yards in 7 miles = 7 × 1,760

= 12,320 yards

Also, 1 yard = 3 feet

Number of feet in 12,320 yards = 12,320 × 3

= 36,960 feet

**Hence, there are 36,960 feet in 7 miles.**

**Example 4:** Suppose John has \(3\frac{1}{2}\) feet of string and he needed 24 inches of string to make a garland. Does John have enough string to make the garland?

**Solution:**

Given, John has \(3\frac{1}{2}\) feet of string.

We know that 1 foot = 12 inches

So, number of inches in \(=3\frac{1}{2}\) foot \(=12\times 3\frac{1}{2}\)

\(=12\times \frac{7}{2}\)

= 6 × 7

= 42 inches

Now. We can see that he has 42 inches and he needs only 24 inches to make garland.

**So, we can say that John has enough string to make the garland.**

**Example 5:** David has a laptop that is 10 inches tall. If David sets the laptop on a 2 feet tall stand, how far from the floor will the top of the laptop be (in inches).

**Solution:**

Given, height of the laptop = 10 inches

Height of the stand = 2 feet

Since, we know that 1 foot = 12 inches

So, 2 foot = 12 × 2 = 24 inches

Now, distance from the floor to the top of the laptop

= height of the stand + height of the laptop

= 24 + 10

= 34 inches

**Hence, the top of the laptop is 34 inches far from the floor.**

Frequently Asked Questions

The relation between inch and foot is that 1 foot is equal to 12 inches.

The customary units of length are as follows: yards, inches, feet and miles.

According to the standard conversion factors, 1 mile is 1,760 yards, so the number in miles can be multiplied by 1,760 to obtain the required answer in yards.

Metric units of length include meter, centimeter, kilometer and so on.

The relation between yard and feet is that 1 yard is equal to 3 feet.