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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 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.
