Chord Length
Chord Length
\[c = 2r\sin\left(\frac{\theta}{2}\right)\]
Variables
c = chord length (m)
r = radius (m)
theta = central angle (rad)
Description
What is this formula?
This formula calculates the length of a chord in a circle using the radius and the central angle measured in radians.
When to use it
Use this formula when the straight-line distance between two points on a circle needs to be determined from the circle geometry.
Example
If the radius is 6 m and the central angle is 1.2 rad:
c = 2 × 6 × sin(1.2/2) = 6.776 m
Applications
- Geometry and trigonometry
- Engineering design
- Structural calculations
- CAD and drafting
- Circular component analysis
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