Radius Calculator
Use our radius calculator to calculate the radius of a circle given its diameter, circumference, or area.
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How to Calculate the Radius of a Circle
A circle is a symmetrical, round, two-dimensional shape with each point along the edge being equidistant from its center point.
The size of a circle is defined by several key properties: the radius, diameter, circumference, and area.
The radius is the distance from the center point of the circle to the outer edge.
The diameter is the longest distance from one edge to the other that passes through the center point.
The circumference is the length around the circle’s outer edge. This is the same as the perimeter of the circle.
The area is the total space inside the circle.
Given any of these properties, you can calculate the radius of the circle using a formula.
How to Calculate the Radius Given the Diameter
The diameter of a circle is equal to twice the length of the radius.
So, you can use the following formula to calculate the radius when given the diameter:
r = d/2
Thus, the radius of a circle r is equal to the diameter d divided by 2.
For example, let’s calculate the radius for a circle with a diameter of 6.
r = 6/2 = 3
So, this circle has a radius of 3.
You can also find this answer using our circle calculator.
How to Calculate the Radius Given the Circumference
You can calculate the radius of a circle if you know its circumference using a similar formula.
The formula to calculate the radius given the circumference is:
r = C/2π
The radius r is equal to the circumference C divided by 2 times pi.
For example, let’s calculate the radius of a circle with a circumference of 14.
4 = 14/2π = 2.23
The radius of this circle is equal to 2.23.
You can use our circumference calculator to find the circumference of a circle, given the radius.
How to Calculate the Radius Given the Area
Just like the previous conversions, you can use a formula to calculate the radius if you know the area of a circle.
The formula to calculate the radius given the area of a circle is:
r = √(A ÷ π)
The radius r of a circle is equal to the square root of the area A divided by pi.
For example, let’s calculate the radius of a circle with an area of 12.
r = √(12 ÷ π) = 1.95
The radius of this circle is 1.95.
You can also use our circle area calculator to find the area of a circle, given the radius.