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 and Area
Ellipse
(approx)
Sector of an Annulus
Sector and Segment
Parabolic Segment
K (right segment)
K (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.
(approx)
Sector of an Annulus
Sector and Segment
Parabolic Segment
K (oblique segment) 
, where T is the area of the triangle