# Arc Length of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

•  Length (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)

### Where:

 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 $$\large{ in }$$ $$\large{mm }$$ Tags: Length Equations