How To Convert A Foot To Square Feet

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.

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: A = L x W.

For example, imagine you have a carpet that's 4 feet long by 3 feet wide. What is its area in square feet? The calculation is simple: A = 4 x 3 = 12 square feet. 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: A = 40 x 20 = 800 square feet.

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. ​

1 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 yards x (3 feet/1 yard) = 27 feet.​ There are 12 inches in 1 foot, so to convert from inches to feet, divide by 12. For example: 36 inches x (1 foot/12 inches) = 3 feet.

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. ​

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 square yards x (9 square feet/1 square yard) = 108 square feet. One square foot is equal to 144 square inches, so to convert from square inches to square feet, divide by 144: 864 square inches x (1 square foot/144 square inches) = 6 square feet.

References

• Math Goodies: Area of a Rectangle
• Purple Math: Geometric Formula Review