# Arc Length of a Circle

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.
• 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

$$L \;=\; \Delta \; r$$     (when $$\; \Delta \;$$ is in radians)

$$L \;=\; \Delta \; ( \pi \;/\; 180 ) \; r$$     (when $$\; \Delta \;$$ is in degrees)

Symbol English Metric
$$L$$ = length $$in$$ $$mm$$
$$\Delta$$ = angle $$deg$$ $$rad$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

Tags: Circle