1. What is the Radius Calculation Formula?

The radius calculation formula \( r = \frac{L}{2 \pi f} \) calculates the radius of a circle when given the arc length (L) and the fraction of the full circle (f) that the arc represents.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of the circle (m)
• \( L \) — Arc length (m)
• \( f \) — Fraction of the full circle (unitless)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the relationship between arc length, radius, and the central angle of a circle.

3. Importance of Radius Calculation

Details: Calculating radius from arc length is important in geometry, engineering, architecture, and various applications where circular measurements are needed but the full circle isn't available.

4. Using the Calculator

Tips: Enter arc length in meters and the fraction as a decimal value (e.g., 0.5 for half a circle). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if I have the angle in degrees instead of a fraction?
A: Convert the angle to a fraction by dividing by 360 (e.g., 90° = 90/360 = 0.25).

Q2: Can this formula be used for any circular arc?
A: Yes, this formula works for any circular arc as long as you know the arc length and what fraction of the full circle it represents.

Q3: What are common applications of this calculation?
A: This calculation is used in construction, manufacturing, navigation, and any field where circular measurements are important.

Q4: How accurate is this calculation?
A: The accuracy depends on the precision of your input measurements and the value of pi used in the calculation.

Q5: What if my arc length is in different units?
A: Convert your arc length to meters before calculation, or the result will be in the same units as your input.