`d = 2*r*sin(a/(2r))`

Enter a value for all fields

The Chord from Arc Length and Radius calculator computes the length of a chord (d) on a circle based on the radius (r) of the circle and the length of the arc (a).  

INSTRUCTIONS:  Choose units and enter the following:

• (a) Length of Arc
• (r) Radius of Circle

Chord of a Circle (d): The calculator compute the length of the chord (d) in meters.  However, this can be automatically converted to other length units via the pull-down menu.  The calculator also returns the inner angle (θ) in degrees.

The Math

The formula for the length of a chord is:

   d = 2•r•sin (a/2r)

where:

• d is the length of the chord
• r is the radius of the circle
• a is the arc length

The length of the chord (d) is the distance between two points on a circle. 

1. θ= a / r
2. sin (θ/2) = ½ d/r
3. d = 2•r•sin (θ/2)
4. d = 2•r•sin (a/2r)

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