The radius of a circle -- expressed as r -- measures the distance from the circle's center to its edge. A few simple equations based on a circle's other qualities can help you find the radius.
Radius from Diameter
It can be difficult to accurately pinpoint the center point of a circle. In this case, it's easier to find the circle's diameter and use it to calculate the radius. The diameter -- expressed as d -- measures the distance across the circle. You can measure the diameter with a ruler by placing one corner on the edge of the circle and measuring to the opposite side of the circle. For example, if you were measuring the diameter of a clock, you would measure from the "12" to the "6."
The diameter of a circle is equal to two times the radius:
d = 2r
So, if you've found that a clock's diameter is 8 inches, you can find the radius by dividing by two.
8 in. = 2r 8 in./2 = r 4 in. = r
So the radius of a clock with a diameter of 8 inches is 4 inches.
You can find the radius of a circle from either its area or its circumference -- the distance around the edge of the circle. To do either of these calculations, you will need to use the number π.
π, or pi, is equal to the circumference of a circle divided by its diameter. However, you don't have to worry about this definition when doing your calculations. π always has the same value, 3.14. Note that π can be extended to an endless series of decimal places -- numbers to the right of the decimal point. For example, π extended to 10 places would be 3.1415926535. However, unless your calculations use other numbers with a large number of decimal places, 3.14 is a good enough approximation.
Radius from Circumference
Circumference -- expressed as C -- is the distance around the edge of a circle. You can find a circle's circumference by doubling its radius and multiplying by π:
C = 2πr
Given a circle's circumference, you can find its radius by dividing by 2π:
C/2π = r
If you were given a circle with a circumference of 15, you would calculate radius by dividing 15 by 2π:
15 in./(2 x 3.14) = r 15 in./(6.28) = r 2.38 in. = r
So a circle with a circumference of 15 inches is shown to have a radius of 2.38 inches.
Radius from Area
Area -- expressed as A -- is a measurement of the space inside a circle. A circle's area is equal to π multiplied by its radius squared.
A = π x r^2 A = π x r x r
To find a circle's radius from its area, you first divide its area by π, and then take the square root of the quotient.
√(A/π) = r
Unless the area of the circle is a multiple of π, you will need a calculator to find the radius using this equation. For example, if you were given a circle with an area of 48 square inches, you would first divide 48 by π, getting 15.28 square inches. You would then take the square root of 15.28, which is 3.9 inches:
√(48 sq in./π) = r √(15.28 sq. in.) = r 3.9 in. = r
So the radius of the circle is 3.9 inches.