When you first learned to calculate two-dimensional area, you probably practiced with squares and rectangles, using the simple formula length × width. There's a simple formula for determining the area of a circle in square feet too but, instead of length or width, you need to know the radius of the round area.
TL;DR (Too Long; Didn't Read)
The formula for area of a circle is A = πr2, where A is the area and r is the radius of the circle or round area.
Radius and Diameter
Instead of measuring circles – or really, any round shape – in terms of length and width, you measure them by their radius or diameter. The radius describes the straight line distance from the center point of the circle to any point on the circle itself. Double the radius to get the diameter, or to put it another way, the diameter refers to the straight line distance all the way from any point on the circle, through the midpoint of the circle and then out to the far side of the circle.
So if you're given the diameter of the circle, you can simply divide that by two to get the radius. For example, if you're told that a circle has a diameter of 10 feet, then the radius is:
There's one more measurement you might need to know for round areas: circumference. The circumference tells you the distance all the way around the edge of the round area and, just like the diameter, there's a close relationship between the radius and the circumference. If you know the circumference of a circle, you divide by 2π to find the radius. So if you were told that a circle has a circumference of 314 feet, you'd calculate:
So 50 feet is the radius of that circle.
Calculating the Area of a Circle
Now that you understand the relationships between the different ways of measuring a circle – and how to extract the radius from each of them – it's time to actually calculate the circle's area, using the formula
A represents the area of the circle, and r is its radius.
Substitute the Radius Into the Formula
Simplify the Equation
Substitute the length of your circle's radius into the formula. Remember: if you want your answer to be in square feet, then the radius must be measured in feet, too. Imagine you have a circle of radius 20 feet. Substituting 20 for r in the formula gives you:
Simplify the right side of the equation. Most teachers will let you substitute 3.14 for the value of pi, which gives you:
Which then simplifies to:
This is the area of your circle.