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Geometry - Arcs & Circles

Here are formulas for some of the most commonly used arcs and circles. Equations for area and circumference are provided.








  K = area
  R = radius
  D = diameter
  C = circumference
  θ = central angle (radians)



Circumference of a Circle - RF CafeCircumference and Area





 

Circumference of an Ellipse - RF CafeEllipse

(approx)

Circumference of an Annulus - RF CafeSector of an Annulus

 

   
   
Sector and Segment - RF CafeSector and Segment






 



                   
Parabolic Segment - RF CafeParabolic Segment

K (right segment)


3D Parabolic Segment - RF CafeK (oblique segment) , where T is the area of the triangle
with the base along the chord of the segment and with
opposite vertex at the point on the parabola at which the
tangent to the parabola is parallel to the chord of the segment.


Source: CRC Standard Math Tables, 1987