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Radius of a Circle Calculator Show Work

Radius Formula:

\[ r = \frac{d}{2} \]

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1. What is Radius?

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is exactly half of the diameter of the circle.

2. How Does the Calculator Work?

The calculator uses the simple formula:

\[ r = \frac{d}{2} \]

Where:

Explanation: The diameter of a circle is always exactly twice its radius, so dividing the diameter by 2 gives the radius.

3. Importance of Radius Calculation

Details: The radius is fundamental in many circle calculations including circumference, area, and in 3D shapes like spheres. It's used in engineering, architecture, and various scientific calculations.

4. Using the Calculator

Tips: Simply enter the diameter of your circle in any length units (meters, inches, feet, etc.). The calculator will output the radius in the same units.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for spheres too?
A: Yes, the radius of a sphere is calculated the same way from its diameter.

Q2: What if I have circumference instead of diameter?
A: You can calculate radius from circumference using \( r = \frac{C}{2\pi} \).

Q3: What are common units for radius?
A: Any length units can be used (meters, centimeters, inches, feet, etc.).

Q4: How precise should my diameter measurement be?
A: For most practical purposes, 2-3 decimal places is sufficient.

Q5: Can radius be negative?
A: No, radius is always a positive value as it represents a physical distance.

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