What Are the Imperial Units for Area?

This entry uses the imperial system of measurement. For the metric system, click here.

When you want to describe the size of a surface, you are talking about an area. Examples of this are the size of a floor, a piece of paper, or a wall. How many doormats can you fit on the floor of your living room? How many pieces of paper can you fit in the hallway? How many towels can you fit on the floor of your bedroom?

Because towels can come in many different sizes, it can be difficult to agree on how big a surface is if you measure it in the number of towels you can put on it. Which towel should you use? A bath towel or a kitchen towel? Because there isn’t any standard towel size, we agreed to use a square with one inch on each side. We call this square a square inch. Because we all agree on the length of an inch, we also agree on the size of the square inch.

Area is measured in square inch (in²), square foot (ft²) and square yard (yd²). A square inch is as large as a square where every side has a length of 1 inch.

You might have already learned that 1 foot is the same as 12 inches. But $1$ in² is not the same as $12$ ft². There’s actually room for 144 squares in $1$ ft². Take a look at the figure below. You can see that the blue square ($1$ in²) can fit 12 times into the white square. The white square can fit 12 times into the pink square, which has the size $1$ ft². That means that there is room for $12\cdot 12=144$ of the blue squares ($1$ in²) in the pink square of $1$ ft².

For measuring smaller surfaces, square inches is the most practical unit to use. If you want to measure larger surfaces, you can use square yards. As one yard is three feet, one square foot (ft²) is a square with sides equal to one third of a yard (a foot). You might think that one square yard has space for three square feet. But that’s not the case! You can fit 9 square feet in one square yard. You can see the reason for this in the figure below.

In the same way, one square inch (in²) is a square where each side has a length of $\frac{1}{36}$ of a yard (one inch). As there are $36$ in in a yard, you can fit a whole $36\cdot 36=1296$ square inches in a yard.

Similarly, one square yard (yd²) is a square where each side has a length of $\frac{1}{1760}$ of a mile (one yard). As there are $1760$ yd in a mile, you can fit a whole $1760\cdot 1760=3097600$ square yards in a mile!

When you need to measure the surface of really big surfaces, for example cities and countries, it can be smart to use larger units. In that case, the units square miles (mi²) or acre are often used. One square mile is equal to 640 acres. One acre is equal to $6272640$ square inches.

Notice how I write and calculate with units. I begin by writing down the expression. Next, I check the bubble figure to see what I have to divide or multiply by to get to the unit the exercise asks for. Then, I solve the exercise step by step. The trick is to swap the unit in the expression with this: The multiplication or division sign (depending on which way I’m moving in the bubble figure), the number the bubble figure shows me, and the corresponding unit. In that way, I can work my way through the bubble figure until I get where I need to go.