Focal length or field of view: why the data sheet is the better source

The formula and the condition attached to it

On paper it is simple. The horizontal angle of view of an ideal lens follows from two figures: the width of the active sensor area and the focal length.

• Field of view = 2 × arctan(sensor width ÷ (2 × focal length))

The condition is in the small print: the lens has to be free of distortion. Surveillance lenses are not, and that is deliberate. A wide angle that covers more area than the formula allows sells better.

What a real data sheet says

The varifocal lens of a widely used dome camera names two operating points: 111° at 4.4 mm focal length and 47° at 9.3 mm. Work backwards from those pairs to the sensor width the formula assumes, and you get two different answers.

So the same optics on the same sensor would have to have two different sensors. There is a factor of 1.58 between the two values. That is not an arithmetic error, it is distortion: manufacturers state the field of view they measured, not the one the approximation produces.

A focal length calculated back from an angle is a claim, not a figure. At 47° on 1/2.8″ you get 6.21 mm. The data sheet says 9.3 mm.

What follows from this in practice

For pixel density only the angle counts anyway. So take the field of view from the data sheet when you plan, and use the focal length only where it too comes from the data sheet. When ordering, that is — because that is what a lens is chosen by.

That is exactly how the cctvfinder works: the horizontal field of view goes in, and the focal length stands beside it whenever the chosen model has one in its data sheet. Nothing is calculated backwards.