1. What is the Arc Radius Formula?

The arc radius formula calculates the radius of a circle when you know the arc length and the central angle. This relationship is fundamental in circle geometry and is expressed as r = s/θ, where r is the radius, s is the arc length, and θ is the central angle in radians.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius of the circle
• \( s \) — Arc length
• \( \theta \) — Central angle in radians

Explanation: The formula directly relates the radius to the arc length and the angle subtended by the arc at the center of the circle.

3. Importance of Radius Calculation

Details: Calculating radius from arc length and angle is essential in various fields including engineering, architecture, physics, and computer graphics where circular measurements are needed.

4. Using the Calculator

Tips: Enter the arc length and angle in radians. Both values must be positive numbers. The angle must be in radians (not degrees) for the formula to work correctly.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees instead of radians?
A: You'll need to convert degrees to radians first. Multiply degrees by π/180 to convert to radians.

Q2: Can this formula be used for any circle?
A: Yes, this formula works for any perfect circle, regardless of size.

Q3: What units should I use?
A: The units for radius will be the same as the units used for arc length. The angle must always be in radians.

Q4: What if the angle is zero?
A: If the angle is zero, the arc length would also be zero, making the calculation undefined. Both values must be positive.

Q5: Can this formula be rearranged to find arc length or angle?
A: Yes, the formula can be rearranged as s = rθ to find arc length, or θ = s/r to find the angle.