Unless you are a current or future scientist, a construction worker or a surveyor, you can probably go about your daily business without worrying too much about measuring the area of things. You might overhear that the pressure is such-and-such "per square inch," or that a certain kind of carpet costs a given amount "per square foot," but not stop to consider the matter — pardon the pun — at length.
It is handy, however, to be able to work with common length units (e.g., inches, feet, yards, centimeters and meters) and work between them while moving from the single dimension of length to two-dimensional area. To convert inches to square feet, first recognize that you have different units in play and assess exactly what you're hoping to do or learn with your conversion.
What Are Inches and Feet, Anyway?
An inch was originally defined centuries ago in Europe as the width of an adult male's thumb, but this became the width of three pieces of barleycorn placed side by side. The foot's origins are what you would probably expect — the approximate length of a man's foot. The Romans first introduced the 12-inch foot to England in the first century CE.
Today, an inch is, ironically enough, defined precisely in terms of metric units, translating to 25.4 millimeters (mm). Correspondingly, a foot is now defined as 12 times 25.4 mm = 304.8 mm exactly.
Length in Two Dimensions: Area
Different two-dimensional shapes have different formulas for area, which is the size of a closed region of a plane (an idealized flat surface). The formula for the area of a rectangle is length times width, usually expressed as (l × w). The formulas for other regular shapes, such as circles and various kinds of triangles, are more complex, but just as reliable.
Length in Three Dimensions: Volume
In the case of extending your measurement by one more dimension, you add depth, height or some third direction that is mutually perpendicular to the other two. The multiplication of these three parameters gives the volume of the three-dimensional enclosed space.
The formula for a rectangular box, for example, is length times width times height, or (l × w × h). Formulas for spheres, pyramids, cones and more have shepherded many a geometry student through quizzes and exams.
How to Convert Inches to Square Feet
If you have a rectangular surface and know the width and the length in inches, you can find the area in square feet in a couple of different ways.
The first is to find the area in square inches and convert this directly to square feet. This is done by dividing by 144. The reason is because 1 ft = 12 in, (1 ft)2 = (12 in)2 = 144 in2. A second way is to convert both the length and the width to feet by dividing each by 12, and then multiply these together to attain the same result.
Example: Given a table 48 in. long and 30 in. wide, what is its area in square feet?
(48)(30) = 1,440 in2 1,440 in2/(144 in2/ft2) = 10 ft2
(48 in/[12 in/ft])(30 in/[12 in/ft]) = (4)(2.5) ft2 = 10 ft2
In general, method 1 is better when working with relatively low numbers. For example, a swatch of fabric 4 inches wide and 10 inches long is 40 square inches; dividing this into 144 gives 0.273 ft2. Using method 2 in this case would result in the multiplication of two decimal numbers with a value less than 1.0 to achieve the same answer.
- You can also leave your measurements in inches, multiply length by width to get square inches, then divide that by 12 to get square feet. The answer will be the same. In the example, 120 x 40 = 480 and then 480/12 = 40.
- You must have two measurements, such as length and width, to measure square feet or square inches. If you have only length, you cannot square it.
About the Author
Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.
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