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
Radius Calculation Results
Circle Components Diagram
Circle Formulas
Radius Formulas
Other Properties
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
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.
Frequently Asked Questions
What is the radius of a 6-foot circle?
If you mean a circle with circumference = 6 feet:
- Given: Circumference (c) = 6 ft
- Formula: r = c / (2π)
- Calculation: r = 6 / (2 × π) = 3/π ft
- 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).