1. What is the Central Angle Formula?

The central angle formula calculates the angle (in radians) at the center of a circle that is subtended by a given arc. It is derived from the relationship between arc length, radius, and the central angle.

2. How Does the Calculator Work?

The calculator uses the central angle formula:

Where:

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

Explanation: The formula first calculates the radius by dividing the diameter by 2, then divides the arc length by this radius to find the central angle in radians.

3. Importance of Central Angle Calculation

Details: Calculating central angles is essential in geometry, engineering, architecture, and various fields involving circular measurements. It helps in designing circular structures, calculating sector areas, and solving trigonometric problems.

4. Using the Calculator

Tips: Enter both arc length and diameter in the same units. Values must be positive numbers. The result will be in radians.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this calculator with radius instead of diameter?
A: This specific calculator requires diameter. If you have the radius, you can multiply it by 2 to get the diameter.

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

Q3: What if my arc length is longer than the circumference?
A: The calculator will still work, but the result will represent an angle greater than 2π radians (360°), indicating more than one full rotation.

Q4: Are there limitations to this formula?
A: This formula assumes a perfect circle and works for all positive values of arc length and diameter.

Q5: Can I use this for elliptical shapes?
A: No, this formula is specific to circles. Ellipses require different calculations.