What Is the Radius from Diameter Calculator?
This calculator finds the radius of a circle when you know its diameter. The radius is the distance from the center of a circle to any point on its edge, while the diameter is the full distance across the circle through the center. Because the diameter always passes through the center, it is exactly twice the radius — so the radius is simply half the diameter.
How to Use It
Enter the diameter of your circle in any unit (centimeters, inches, meters, etc.) and the calculator instantly returns the radius in the same unit. There is no unit conversion involved: if your diameter is in inches, your radius is in inches.
The Formula Explained
The relationship between radius and diameter is one of the most fundamental in geometry:
$$r = \frac{d}{2}$$
Here r is the radius and d is the diameter. Dividing the diameter by two gives the radius because the diameter is composed of two radii laid end to end through the center.
Worked Example
Suppose a circular table has a diameter of 120 cm. To find the radius, divide by 2: $$r = \frac{120}{2} = 60 \text{ cm}$$ So the table's radius is 60 centimeters, meaning the center is 60 cm from any edge.
FAQ
Is the radius always half the diameter? Yes — for any circle, the radius is exactly half the diameter, with no exceptions.
What unit is the result in? The radius is returned in the same unit as the diameter you entered. The formula is unit-independent.
How do I find the diameter from the radius? Reverse the formula: multiply the radius by 2, since \(d = 2r\).
