A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely enclose the other, and the centers of curvatures are on opposite sides of the lens. If the centers of curvature are on the same side, a lune results.
The area of a general asymmetric lens obtained from circles of radii 
and 
and offset 
can be found from the formula for circle-circle intersection, namely
 |  |  |
(1)
|
 |  |  |
(2)
|
Similarly, the height of such a lens is
 |  |  |
(3)
|
 |  |  |
(4)
|
A symmetric lens is lens formed by the intersection of two equal disk. The area of a symmetric lens obtained from circles with radii 
and offset 
is given by
 |
(5)
|
and the height by
 |
(6)
|
Two historical symmetric lenses are distinguished by their center offsets. The vesica piscis, which is the same figure as the Babylonian
ox-eye, has 
and bounding arcs that are each
one third of a circle. The grain
figure has 
and bounding arcs that are each one quarter of a circle,
so it is narrower than the vesica piscis.
A lens-shaped region also arises in the study of Bessel functions, is very important in the theory of Kapteyn series and the study of Kepler's equation, and is intimately related to the so-called Laplace limit.
In Season 4 episode "Power" of the television crime drama NUMB3RS, physicist Larry Fleinhardt discusses the religious symbology of the vesica piscis when main character Charles Eppes mentions he is constructing a Venn diagram.
