Chord Length from Arc Length and Radius

The Chord Length 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 in meters.  The calculator also returns the inner angle (θ) in degrees. However, these can be automatically converted to compatible units via the pull-down menu.  

CORRECTION NOTICE

The chord lengths returned in this calculator have been correct all along. However, the inner angle returned (θ) was half the correct value.  Thanks to a user's feedback, this has been corrected.

The Math / Science

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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