How to Find the Radius of a Circle in Mathematics

In mathematics, the radius of a circle is the distance from the origin, or center, of the circle to any point on the circle's circumference, or border. A circle's radius is an important identifying marker of that circle and works with the mathematical constant pi, or π, which is a non-terminating and non-repeating number that begins with 3.14, to calculate the circle's area and circumference. Finding a circle's radius can help you understand a circle's size and shape.

Instructions

1. Divide the diameter by 2. The diameter is a straight line that goes from one point on the circumference, through the origin of the circle and to its opposite point on the circumference. For example, if the diameter of a circle is 10, then its radius is 5.

2. Divide the circumference by 2π, which is 2 multiplied by the constant π. The equation for forming the circumference is 2πr, where r is the radius. For example, dividing the circumference 15.7 by 2π, or 6.28, equals 2.5. 2.5 is the radius of the circle. Dividing the circumference by only π results in the diameter's measurement.

3. Find the square root of the circle's area divided by π. The formula for a circle's area is πr^2. For example, if the circle's area is 28.26, dividing by π, or 3.14, results in 9. The square root of 9 is 3. Three is the radius of the circle.

References

• Math Goodies: Area of a Circle
• Wolfram Mathworld: Circumference