Arc Length of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle 17circle arc length 2Length (L)  -  Total length of any circular curve measured along the arc.
  • Angle (\(\Delta\))  -  Two rays sharing a common point.
  • Center (cp)  -  Having all points on the line circumference are at equal distance from the center point.
  • Chord (c)  -  Also called long chord (LC), is between any two points on a circular curve.
  • Circle  -  All points are at a fixed equal distance from a radius point (rp).
  • Circumference (C)  -  The outside of a circle or a complete circular arc.
  • Height (h)  -  Length of radius from radius center to midpoint of chord.
  • Height (h')  -  Length of radius from midpoint of chord to point on circular curve.
  • Major Arc  -  The longest of two arcs of a circle or ellipse.
  • Minor Arc  -  The shorter of two arcs of a circle or ellipse.
  • Radius (r)  -  Half the diameter of a circle.  A line segment between the center point and a point on a circle or sphere.
  • Radius Point (rp)  -  Radius center point of circular curve.
  • Sector is a fraction of the area of a circle with a radius on each side and an arc.
  • Segment is an interior part of a circle bound by a chord and an arc.
  • Tangent (T)  -  A line that touches a curve at just one point such that it is perpendicular to a radius line of the curve.


arc Length of a Circle  formulas

\(\large{ L =   \Delta \; r \;\; }\)  (when \(\; \Delta \;\) is in radians) 
\(\large{ L =  \Delta \;   \frac {  \pi } { 180 } \; r  \;\;  }\)  (when \(\; \Delta \;\) is in degrees) 


 Units English Metric
\(\large{ L }\) = length \(\large{ in }\) \(\large{ mm }\) 
\(\large{ \Delta }\) = angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{mm  }\)


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Tags: Length Equations