The radius of a circle is one of its defining characteristics, but its length is not always known. The radius is the length from the circle's center to any point on its circumference. The properties of a circle can all be used to calculate the linear footage in a radius. These properties include the circle's diameter, circumference and area, as well as the length of its arcs, or segments of the circumference, and the area of its sectors, or partitions of the circle. Its properties also include the magical constant π or pi, which can be approximated as 3.14.
Divide the length of the diameter in half to find the footage of the radius. For example, if the diameter is 10, the radius is 5.
Divide the circumference by 2π to find the radius. For example, the circumference is 60 feet. Dividing 60 by 2π equals 9.549. The radius is 9.549 feet.
Divide the area of the circle by π, and then calculate the square root to find the radius. For example, the area of the circle is 100 square feet. Dividing by π equals 31.839. The square root of 31.839 is 5.649 feet.
Divide the arc length by the angle in radians to find the radius. If the arc length is 2 feet and the angle is π/4, the radius is 2.546 feet.
Multiply the area of a sector by 2, divide it by the measurement of the sector's angle and then calculate the square root of that number to find the radius. For example, if the sector's area is 25 square feet and the angle is π, then multiplying 25 by 2 equals 50. Dividing 50 by π equals 15.915, and the square root of 15.915 equals 3.989. The radius is 3.989 feet.
- circle frame image by Aleksey Bakaleev from Fotolia.com