Circle                                                             All points on the circumference of a circle                                                      are equidistant from its center.                                                         Radius: r                                                         Diameter: d d = 2r                                                         C = 2 Pi r = Pi d                                                         K = Pi r2 = Pi d2/4                                                        C = 2 sqrt(Pi K)                                                        K = C2/4 Pi = Cr/2                                                       Circumference: C                                                      Area: K

Arc of a Circle

A curved portion of a circle.

Length: s

Central angle:
alpha (in degrees)

s = r theta = r alpha Pi/180

Segment of a Circle

Either of the two regions into which a secant or a chord cuts a circle. (However, the formulas below assume that the segment is no larger than a semi-circle.)
Chord length: c
Height: h
Distance from center of circle to chord's midpoint: d
Central angle: theta (in radians), alpha (in degrees)
Area: K
Arc length: s

theta = 2 arccos(d/r) = 2 arctan(c/(2d)) = 2 arcsin(c/(2r))
h = r - d

c = 2 sqrt(r2-d2) = 2r sin(theta/2) = 2d tan(theta/2) = 2 sqrt[h(2r-h)]
d = sqrt(4r2-c2)/2 = r cos(theta/2) = c cot(theta/2)/2

K = r2[theta-sin(theta)]/2 = r2arccos([r-h]/r) - (r-h)sqrt(2rh-h2)
= r2arccos(d/r) - d sqrt(r2-d2)

theta = s/r
K = r2[s/r - sin(s/r)]/2

Sector of a Circle

The pie-shaped piece of a circle 'cut out' by two radii.

Central angle: