Radius Calculator

How to Calculate Circle Radius

The radius of a circle is a fundamental measurement in geometry. It's the distance from the center of the circle to any point on its circumference. Understanding how to calculate the radius from other circle properties is crucial in many fields, including mathematics, physics, and engineering.

Circle Formulas

The key formulas for calculating circle properties are:

• Diameter (d) = 2r
• Circumference (C) = 2πr
• Area (A) = πr²

Where r is the radius of the circle and π (pi) is approximately 3.14159.

Calculation Steps

1. Identify the given property of the circle (diameter, circumference, or area).
2. Use the appropriate formula to calculate the radius:
   • If diameter is given: r = d / 2
   • If circumference is given: r = C / (2π)
   • If area is given: r = √(A / π)
3. Once the radius is known, you can calculate all other properties using the formulas above.
4. Round the results to an appropriate number of decimal places if necessary.

Example Calculation

Let's calculate the radius and other properties of a circle with a circumference of 31.4 units:

1. Given: Circumference (C) = 31.4 units
2. Calculate radius: r = C / (2π) = 31.4 / (2 × 3.14159) ≈ 5 units
3. Calculate diameter: d = 2r = 2 × 5 = 10 units
4. Calculate area: A = πr² = π × 5² ≈ 78.54 square units

Visual Representation

This diagram illustrates a circle with its radius (r) in red and diameter (d) in green. The circle itself is drawn in blue. The radius extends from the center to any point on the circle's circumference, while the diameter spans the entire width of the circle, passing through the center.