# Lens focal length calculator

This page is useful to calculate the required lens focal length to take a picture of an object of size yo at a distance xo in order to generate an image of size yi on the film (or the CCD/C-MOS imager). The film plane is located at a distance xi.

Of course, distances xo and xi are measured from the lens front and rear principal points respectively. Too often, unfortunately, these points are not specified by the lens manufacturer: it's hard to guess their position, since they can be anywhere inside or outside the lens. If you use a commercial camera with a compatible lens on it the distance xi is already adjusted to allow a perfect focus and you don't have to worry. Anyway, the rear principal point is always one focal length ahead the film plane when the lens is focused at infinity.

The location of the front principal point cannot be neglected when doing macro photography. If you don't know its exact position, you will probably be able to measure it: hold the lens in your hand, manual focus at infinity and while aiming at a very distant light with the back of the lens (the side of the thread or bayonet) try to make a sharp image of it on a piece of paper placed in front of the lens. The front principal point is one focal length ahead (toward the lens) the paper. This usually works for tele lenses but unfortunately many wide angles do not generate any sharp image when reversed this way (the image is actually formed inside the lens).

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 Object size: yo = mm Image size: yi = mm Object distance: xo = m Magnification: M = Focal length: f = mm Angle of view: w = ° Bellows factor: B = Image distance: xi = m

The formulas used assume that the lens is able to focus at the required distance (xi is not taken into account in the calculations). If this is not the case it may be possible to get a sharp image by slightly moving the lens away from the film. Focusing the lens at a closer distance than infinity will loose some light and make the aperture of the lens appear smaller. Just multiply the f/# number by the bellows factor to find the correct lens aperture.

Please remark that usually imagers or films are rectangular, meaning that if you use the calculator for determining the field of view, you will get three different values if you calculate for the height, width or diagonal. The table below reports the dimensions of the most common imagers and films.

 Imager size Height [mm] Width [mm] Diagonal [mm] 1/4" 2.7 3.6 4.5 1/3" 3.6 4.8 6.0 1/2" 4.8 6.4 8.0 2/3" 6.6 8.8 11.0 1" 9.6 12.8 16.0 Digital SLR 14.8 22.2 26.7 24 x 36 24.0 36.0 43.3

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