1. What is the Central Angle Formula?

The central angle formula calculates the angle at the center of a circle between two radii that subtend a given arc. It is a fundamental concept in geometry and trigonometry, expressed as θ = arc length / radius.

2. How Does the Calculator Work?

The calculator uses the central angle formula:

Where:

• \( \theta \) — Central angle in radians
• Arc Length — Length of the arc subtended by the angle
• Radius — Radius of the circle

Explanation: The formula shows the direct relationship between arc length, radius, and the central angle in radians.

3. Importance of Central Angle Calculation

Details: Calculating central angles is essential in various fields including engineering, architecture, navigation, and computer graphics for determining circular measurements and designing curved structures.

4. Using the Calculator

Tips: Enter both arc length and radius in the same units. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is the result in radians instead of degrees?
A: The formula θ = arc/radius naturally gives the angle in radians, which is the standard unit for angular measurement in mathematics.

Q2: How do I convert radians to degrees?
A: Multiply the radian value by 180/π (approximately 57.2958) to convert to degrees.

Q3: Can I use different units for arc and radius?
A: No, both values must be in the same units for the formula to work correctly.

Q4: What if the arc length is greater than the circumference?
A: The formula still works mathematically, but angles greater than 2π radians (360°) represent multiple rotations around the circle.

Q5: Does this formula work for any circle size?
A: Yes, the formula is valid for circles of any size as long as both measurements are in the same units.