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

 - RF Cafe

 - RF Cafe

 - RF Cafe

 - RF Cafe

 

Circumference of an Ellipse - RF CafeEllipse

 - RF Cafe (approx)

 - RF Cafe

Circumference of an Annulus - RF CafeSector of an Annulus

  - RF Cafe

 - RF Cafe

     - RF Cafe

     - RF Cafe

Sector and Segment - RF CafeSector and Segment

 - RF Cafe

 - RF Cafe

 - RF Cafe

 - RF Cafe

 - RF Cafe

   - RF Cafe

 - RF Cafe

 - RF Cafe

 - RF Cafe

                     - RF Cafe

Parabolic Segment - RF CafeParabolic Segment

K (right segment)  - RF Cafe

 - RF Cafe

3D Parabolic Segment - RF CafeK (oblique segment)  - RF Cafe, 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