Working distance

Sensor optical format

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Input

Sensor width

S_w

Sensor height

S_h

Field of view (width)

FOV_w

Focal length

f

Required working distance

WD

Magnification

\beta

Field of view (height)

FOV_h

Calculated with the thin lens model, which treats the lens as having no thickness ( $\displaystyle WD = f\left(1+\frac{FOV_w}{S_w}\right)$ ).
Distortion and vignetting are not taken into account.
Optical formats such as 1/2" are nominal names; the real dimensions vary between makers and sensor generations. For a strict calculation, take the actual figures from the data sheet and enter them under Custom.