How To Calculate Square Miles

If you need to calculate a large area, like the approximate area of a city, state or lake, it is likely that you will want to use units such as miles or kilometers, not inches or centimeters.

The basic formula for calculating area is:

\(Area = length\times width\)

It is important to keep in mind the units associated with each of these variables.

First, length and width are straight lines. If you started at one end of the line, you could walk to the other end. That means that both length and width are linear values. The unit associated with length and width is any linear measure of distance like miles, kilometers, feet, etc.

Area, on the other hand, is found by multiplying two linear measures together. That means you take some number of miles and multiply it by another number of miles. This means that instead of having the unit of just miles, the area will have a unit of miles squared. This is because anything when multiplied by itself is the same as that thing being squared.

You are given that the length of a state park is 10 miles. The width of this same park is 21 miles. What is the area of the park? You can use the formula given above as shown below:

\(Area = length\times width\)

Now, plug in the known values with the associated units.

\(Area = 10\enspace miles\times 21\enspace miles\)

Multiplying the length times the width you get:

\(Area = 210\enspace miles^2\enspace or\enspace 210\enspace square\enspace miles\)

Now, you know that the area of the state park is 210 square miles.

What about if you know that the area of an American football field is 360 feet long and 160 feet wide. How would you calculate the area of the football field in square feet? And in square miles?

To find the area in square feet, you can apply the area formula in the same way that you did above.

\(Area = 360\enspace feet\times 160\enspace feet\)

Multiplying it together you get:

\(Area = 57600\enspace feet^2\)

So you know the area of the field is 57,600 square feet. But how many square miles is that?

There are two ways you can go about this:

Method 1: You can directly convert the area in square feet to square miles

Method 2: You can first convert the length and width into miles and then multiply them together to find the area

In both of these situations, the most important piece of information is how many feet there are in a mile. There are 5,280 feet in 1 mile.

To solve it first using Method 1, you will need to know how many square feet there are in 1 square mile.

\(5280\enspace feet = 1\enspace mile\)

To do this, square both sides:

\(5280^2\enspace feet^2 = 1^2\enspace mile^2\)

Which means that:

\(27878400\enspace feet^2 = 1\enspace mile^2\)

Now, you have a conversion factor for taking the area you found in square feet and converting it into square miles.

\(Area = 57600\enspace feet^2\Biggl(\dfrac{1\enspace mile^2}{27878400\enspace feet^2}\Biggl)\)

Multiplying these together you find that:

\(Area = 0.002\enspace mile^2\)

Using Method 1, you find that a football field has a 0.002 square mile area.

Now, using Method 2 should give the same area. Here is how:

Instead of multiplying the length and width together to find the area, you first need to convert the feet into miles. To do that, you will need to use the conversion factor between feet and miles.

\(length = 360\enspace feet\Biggl(\dfrac{1\enspace mile}{5280\enspace feet}\Biggr)\)

Which equals:

\(length = 0.068\miles\)

Doing the same thing for the width gives you 0.03 miles.

Now, you can use the area formula to find the area in square miles:

\(Area = 0.068\enspace mile\times 0.03\enspace mile\)

Multiply them together, and you get:

\(Area = 0.002\enspace mile^2\)

Both methods give the same answer.