Central Angle from Arc Length
Central Angle from Arc Length
\[\theta = \frac{s}{r}\]
Variables
theta = central angle (rad)
s = arc length (m)
r = radius (m)
Description
What is this formula?
This formula calculates the central angle of a circle from the arc length and radius. The angle must be expressed in radians.
When to use it
Use this formula when the arc length and radius of a circle are known and the corresponding central angle needs to be determined.
Example
If the arc length is 8 m and the radius is 4 m:
θ = 8 / 4 = 2 rad
Applications
- Geometry and trigonometry
- Circular motion calculations
- Mechanical engineering
- CAD and technical drafting
- Curve and arc analysis
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