Arc Length Calculator
This calculator helps you determine the length of an arc, a segment of a circle's circumference, based on its radius and central angle. It's a valuable tool for students, educators, and professionals in fields like engineering and architecture.
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Data Source and Methodology
All calculations are strictly based on the standard formula for arc length calculation. For detailed information, see Wikipedia - Arc (geometry).
The Formula Explained
The formula used is: \( L = r \times \frac{\theta \pi}{180} \)
Glossary of Terms
- Radius (r): The distance from the center of the circle to any point on its circumference.
- Central Angle (θ): The angle subtended by the arc at the center of the circle, measured in degrees.
- Arc Length (L): The distance along the curved line making up the arc.
How It Works: A Practical Example
To calculate the arc length, input the circle's radius and the central angle. For example, if the radius is 10 units and the angle is 60 degrees, the arc length is \( L = 10 \times \frac{60 \times \pi}{180} \approx 10.47 \) units.
Frequently Asked Questions (FAQ)
What is an arc?
An arc is a portion of the circumference of a circle.
How do I find the radius if I have the diameter?
The radius is half of the diameter. For instance, if the diameter is 10, the radius is 5.
Can the angle be more than 360 degrees?
No, the central angle for a full circle is 360 degrees; hence, it cannot exceed this.
What units should I use?
You can use any consistent units for radius and arc length. The calculator will output in the same units.
What is the relationship between arc length and circumference?
Arc length is a fraction of the circle's circumference, determined by the ratio of the angle to 360 degrees.