Radius of a Circle Calculator

Calculate the radius of a circle from circumference, area, or diameter with step-by-step solutions

Calculate Circle Radius

The perimeter of the circle

Quick Unit Reference

1 m = 100 cm = 1000 mm
1 ft = 12 in = 30.48 cm
1 yd = 3 ft = 91.44 cm

Radius Calculation Results

0.000000 cm
Radius
0 cm
Diameter
0.000000 cm
Circumference
C = 2πr
0.000000 cm²
Area
A = πr²

Circle Components Diagram

RadiusCenterCircumferenceArea = πr²
Center: Fixed point
Radius: Distance from center to edge
Diameter: Distance across circle
Circumference: Perimeter of circle

Circle Formulas

Radius Formulas

r = c / (2π)
r = √(A / π)
r = d / 2

Other Properties

C = 2πr
A = πr²
d = 2r

Example Calculations

From Circumference

Given: C = 31.42 cm

Formula: r = c / (2π)

Calculation: r = 31.42 / (2 × 3.14159)

Result: r = 5.00 cm

From Area

Given: A = 78.54 cm²

Formula: r = √(A / π)

Calculation: r = √(78.54 / 3.14159)

Result: r = 5.00 cm

Quick Tips

The radius is half the diameter

π ≈ 3.14159 (use more decimal places for precision)

All points on a circle are equidistant from the center

Unit circle has radius = 1

Understanding Circle Radius

What is the Radius of a Circle?

By definition, a circle is a 2-dimensional shape consisting of all the points lying at the same, fixed distance from a given point (the center). That distance is known as the radius of the circle.

Key Properties

  • The radius is the MVP in all circle formulas
  • All radii of the same circle have equal length
  • The radius determines all other circle properties
  • Measured from center to any point on the circumference

Circle Formula Relationships

From Circumference: r = c / (2π)
From Area: r = √(A / π)
From Diameter: r = d / 2

Real-World Applications

  • Architecture: Designing circular structures
  • Engineering: Calculating pipe dimensions
  • Sports: Field and court layouts
  • Manufacturing: Circular components

Unit Circle Special Case

A unit circle is a circle with radius = 1. It's commonly used in mathematics, especially when explaining trigonometric functions. The unit usually has no specific measurement assigned.

Unit Circle Properties: r = 1, d = 2, C = 2π ≈ 6.283, A = π ≈ 3.142

Frequently Asked Questions

What is the radius of a 6-foot circle?

If you mean a circle with circumference = 6 feet:

  1. Given: Circumference (c) = 6 ft
  2. Formula: r = c / (2π)
  3. Calculation: r = 6 / (2 × π) = 3/π ft
  4. Result: r ≈ 0.955 ft

How accurate should my radius calculation be?

The accuracy depends on your application. For most practical purposes, 3-4 decimal places are sufficient. For engineering applications, you might need more precision. Our calculator provides 6 decimal places for maximum accuracy.

Can I calculate radius from arc length?

Yes, if you know the arc length and the central angle. The formula is: r = arc length / angle (in radians). For a complete circle, the arc length equals the circumference, so r = circumference / (2π).