1. What is the Radius Formula?

The radius formula calculates the distance from the center of a circle to its edge when you know the circumference. It's derived from the basic circumference formula.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius (length units)
• \( C \) — Circumference (length units)
• \( \pi \) — Pi (approximately 3.14159)

Explanation: The formula divides the circumference by 2π to find the radius, since circumference equals 2πr.

3. Importance of Radius Calculation

Details: Knowing the radius is essential for many geometric calculations including area, arc length, and sector area of circles.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if I have the diameter instead of circumference?
A: The radius is simply half of the diameter (r = d/2). No need to calculate circumference first.

Q2: What units should I use?
A: Any consistent length units can be used (meters, feet, etc.). The result will be in the same units as your input.

Q3: How precise is π in this calculation?
A: The calculator uses π to 15 decimal places (3.141592653589793) for maximum precision.

Q4: Can I use this for spheres?
A: Yes, the formula works for the radius of a sphere when you know its circumference (great circle).

Q5: What's the difference between radius and diameter?
A: The diameter is twice the radius (d = 2r), representing the full width of the circle through its center.