How to Convert a Foot to Square Feet

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As a linear measurement, the foot gauges distance in just one dimension. For example, if you're measuring a box, you could measure its length, width or height in feet – but only one of those at once. Square feet, on the other hand, express the area created by measuring two dimensions at once. To keep things simple, those dimensions are usually called length and width – but you can use the concept of area to measure any flat surface, no matter how it's angled or oriented. If you know the linear measurements for any two adjacent sides of a surface, the calculation for finding its area is very simple.

TL;DR (Too Long; Didn't Read)

To convert from linear feet to square feet, multiply length × width.

Calculating Ft to Sq Ft

Before you start calculating square footage, make sure your linear dimensions – that is, the length and width of whatever you're measuring – are expressed in feet. Once that's done, it's time to apply the simple mathematical formula for area:

length × width

Example: Imagine you have a carpet that's 4 feet long by 3 feet wide. What is its area in square feet? Calculate:

4 feet × 3 feet = 12 ft2

So your carpet's area is 12 square feet, also written as feet squared or simply ft2.

Another example: Imagine that you're fertilizing a lawn that measures 40 feet by 20 feet. Calculating the area will tell you how much fertilizer to buy:

40 feet × 20 feet = 800 ft2

Tips

  • Did you notice that in both examples, you keep the unit of measure (feet) in the left side of the equation? There are two reasons for doing that. First, the units you use on the left side of the equation tell you which units to put on the right side of the equation, so having them written out makes it easier to double-check your work. And second, if you're working this sort of problem in school, you'll probably lose points if you forget to write down the units of measure.

Converting From Other Units of Measure

Now that you've mastered the simple area calculation from feet to square feet, you can, in essence, be your own linear foot calculator to transform linear measurements into measurements of area. But what if the dimensions you're given to work with aren't in feet?

No problem: You can use simple conversion factors to convert those measurements from other units into feet. It's usually easiest to perform those conversions before you do the math to go from linear dimensions into square dimensions. The two conversions you're most likely to find yourself making are yards and inches.

Yards

One yard equals 3 feet. So if you're given linear measurements in yards, multiply each measurement by 3 to get its equivalent in feet. For example:

9 yd × 3 ft/yd = 27 feet

Inches

There are 12 inches in 1 foot, so to convert from inches to feet, divide by 12. For example:

36 in ÷ 12 in/ft = 3 ft

Converting From Other Square Units

Here's one last angle to consider: What if you're given area measurements that are already in two dimensions, but they're not measured in feet? For example, maybe you have a small area rug that measures 864 in2, or you've been told that a room measures 12 yd2, and you want to know what the equivalent is in square feet.

Once again, all you need is the right conversion factor to convert the measurements from yards to feet or inches to feet – but it's very important to recall that square dimensions have different conversion factors than linear dimensions.

Yards

One linear yard is equal to 3 linear feet – but 1 square yard is equal to 9 square feet. So to convert from square yards to square feet, multiply by 9:

12 yd2 × 9 ft2/yd2 = 108ft2

Inches

One square foot is equal to 144 square inches, so to convert from square inches to square feet, divide by 144:

864 in2 ÷ 144 in2/ft2 = 6 ft2

References

About the Author

Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.

Photo Credits

  • BACKGROUND OF RECTANGLES image by SHANICIA JACKSON from Fotolia.com

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