1. What is the Radius of a Circle?

The radius of a circle is the distance from the center of the circle to any point on its edge. It's a fundamental measurement in geometry that relates to other circle measurements like circumference, diameter, and area.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius of the circle
• \( C \) — Circumference of the circle
• \( \pi \) — Pi (approximately 3.14159)

Explanation: The radius can be found by dividing the circumference by 2π, since the circumference formula is \( C = 2\pi r \).

3. Importance of Radius Calculation

Details: Knowing the radius is essential for many geometric calculations including finding area (\( \pi r^2 \)), diameter (\( 2r \)), and for solving problems in physics, engineering, and design that involve circular shapes.

4. Using the Calculator

Tips: Enter the circumference in any length units (cm, inches, meters, etc.). The result will be in the same units. The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this with diameter instead of circumference?
A: Yes, but you would need to first calculate circumference from diameter (\( C = \pi d \)) or use the simpler formula \( r = d/2 \).

Q2: What if I know the area instead?
A: The radius can be calculated from area using \( r = \sqrt{A/\pi} \).

Q3: How precise is this calculation?
A: The calculation is mathematically exact. Precision depends on your input value's accuracy and π approximation (calculator uses high precision).

Q4: What are common units for radius?
A: Any length unit can be used (meters, centimeters, inches, feet, etc.). The result will be in the same units as your input.

Q5: Can this be used for spheres?
A: Yes, the formula works for the radius of a sphere when you know its circumference (great circle).