1. What is Radius Calculation From Arc?

Radius calculation from arc length and angle is a fundamental geometric calculation that determines the radius of a circle when given the length of an arc and the central angle in radians.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius of the circle (m)
• \( \text{arc length} \) — Length of the arc (m)
• \( \theta \) — Central angle in radians

Explanation: This formula directly relates the radius to the arc length and the central angle, based on the definition of a radian.

3. Importance of Radius Calculation

Details: Calculating radius from arc measurements is essential in various fields including engineering, architecture, physics, and any application involving circular geometry and measurements.

4. Using the Calculator

Tips: Enter arc length in meters and angle in radians. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why must the angle be in radians?
A: The formula r = arc length/θ is derived from the definition of a radian, where 1 radian is the angle subtended by an arc equal in length to the radius.

Q2: What if my angle is in degrees?
A: Convert degrees to radians first using the formula: radians = degrees × π/180 before using this calculator.

Q3: Can this formula be used for any arc of a circle?
A: Yes, this formula works for any arc of a circle as long as you have the arc length and the corresponding central angle in radians.

Q4: What are common applications of this calculation?
A: This calculation is used in engineering designs, circular construction projects, manufacturing of circular components, and various physics calculations involving circular motion.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, but the practical accuracy depends on the precision of your arc length and angle measurements.