How To Calculate Square Feet From The Perimeter

Calculating the perimeter and area of geometric shapes like circles and squares is a skill you can use throughout your life. It comes in handy every time you build something, arrange something, or just try to figure out if one object will fit inside or alongside another. Often, it's much easier to measure perimeter than area of real-world objects. Once you know a couple of simple formulas, you can easily convert that perimeter to area using basic calculations.

A square is the easiest shape for calculating area based on perimeter, between each of its sides is 1/4 the length of the perimeter. If you want your answer to be in terms of square feet, make sure your measurements are either in feet or converted into feet before you begin the calculations.

1. Divide the Perimeter by 4

Calculate the length of one side of the square by dividing the perimeter by 4. So if the perimeter of the square is 32 feet, you have:

\(\frac{32 \text{ ft}}{4} = 8 \text{ ft}\)

Note that you carry the unit of measure – feet – along throughout your calculations.

2. Square the Length of One Side

Compute the area of the square by multiplying the length of one side by itself. So you have:

\(8 \text{ ft} × 8 \text{ ft} = 64 \text{ ft}^2\)

You can also calculate the area of a circle based on its perimeter. As always, if you want your result to be in square feet, you must first ensure that all your measurements are in feet.

1. Square the Circumference

Square the circumference of the circle or, to put it another way, multiply the circumference by itself. So if the circumference of your circle is 10 feet, you'd have:

\(10 \text{ ft} × 10 \text{ ft} = 100 \text{ ft}^2\)

Again, note how you carry the units of measure through the calculations. But even though the result of this step is in square feet, you're not done finding the area of your circle yet. You still need to finish the rest of the formula.

2. Divide by 4 × Pi

Divide the result from Step 1 by 4π. The result is the area of the circle in square feet. This gives you:

\(\frac{100 \text{ ft}^2 }{4 × 3.14} = 7.96 \text{ ft}^2\)