Lens and field-of-view calculator

From focal length to angle

For an ordinary (rectilinear) lens the angle of view follows from the sensor width s and the focal length f:

α = 2 · atan(s / (2 · f))

and the scene width at a distance d is s · d / f. Turn it round and the focal length that fits a scene w wide at distance d is f = s · d / w. The same focal length gives a narrower view on a smaller sensor: by this formula a 2.8 mm lens takes in about 88° on a 1/2.8" sensor and about 81° on a 1/3". Datasheets for 2.8 mm cameras often quote 100° or more, because short lenses are built with barrel distortion that widens the view past the pinhole figure.

Sensor formats are not sizes

A "1/2.8-inch" sensor is not 1/2.8 of an inch across: the name is inherited from the vidicon tubes of the 1950s, and the active width is about 5.4 mm. The calculator uses the published widths for the common formats. For the exact angle of a particular camera use its datasheet figure, which the camera database carries for every model that publishes one, at both ends of a zoom.

Wide lenses bend away from the pinhole model: past about 110° the real angle is usually wider than this formula says, and fisheyes follow a different projection altogether. Lenses and field of view explains the trade between a wide view and the detail in it.