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:
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.
How to Calculate Square Miles
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:
Now, plug in the known values with the associated units.
Multiplying the length times the width you get:
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.
Multiplying it together you get:
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.
To do this, square both sides:
Which means that:
Now, you have a conversion factor for taking the area you found in square feet and converting it into square miles.
Multiplying these together you find that:
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.
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:
Multiply them together, and you get:
Both methods give the same answer.
Area always equals length multiplied by width. Make sure to keep track of units.
- Always keep units in your calculations. This will ensure that you use the conversion ratios the right way.
About the Author
Riti Gupta holds a Honors Bachelors degree in Biochemistry from the University of Oregon and a PhD in biology from Johns Hopkins University. She has an interest in astrobiology and manned spaceflight. She has over 10 years of biology research experience in academia. She currently teaches classes in biochemistry, biology, biophysics, astrobiology, as well as high school AP Biology and Chemistry test prep.