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— Calculators: Camera Field of View —

Rectlinear Lenses

Lens focal lengths for FX 35 mm cameras are different for DX cameras by a ratio of about 1 : 1.5. The diagonal of a FX camera is 43.3 mm (36 x 24 mm), the sensor of a DX is 23.7 x 15.6 mm and hence the diagonal 28.4 mm (Nikon, Canon and others may be slightly different).

The diagonal for FX cameras is assumed to be 43.27 mm and 28.37 mm for DX.

Formulae

α = FoV — Field of View or viewing angle in °,

d = diameter (width, height or diagonal) of receptor (e.g. CCD chip) in mm (36 mm for example below),

f = focal length of lens system in mm (55 mm for example below).

α = 2 • arctan (d / (2 • f ));
    e.g.: 2 • arctan(36 / (2 • 55)) = 2 • arctan(0.327) = 2 • 18.1 = 36.2°.

d = 2 • f • tan (α / 2);
    e.g.: 2 • 55 • tan(36.2 / 2) = 2 • 55 • tan(18.1) = 2 • 55 • 0.327 = 35.97 mm.

f = d / (2 • tan(α / 2));
    e.g.: f = 36 / (2 • tan(36.2 / 2)) = 36 / (2 • 0.326) = 36 / 0.654 = 55.04 mm.

Source: Die CCD Astrokamera für den Amateur (p.51) by Hans-Ruedi Wernli; Birkhäuser 1995; ISBN 3-7643-5218-3.

Focal Length to View Angle Converter for Full-Frame Fisheye Lenses

For the lens focal length for FX cameras, the Nikon D600 camera is assumed for the calculation. The diagonal of the sensor is 35.9 x 24.0 mm and hence the diagonal 43.2 mm. There are 6016 x 4016 pixels with a pixel size of 6.0 µm x 6.0 µm (8.5 µm diagonal).

For the lens focal length for DX cameras the Nikon D50 camera is assumed for the calculation. The diagonal of the sensor is 23.7 x 15.6 mm and hence the diagonal 28.4 mm. There are 3008 x 2000 pixels with a pixel size of 7.8 µm x 7.8 µm (11 µm diagonal).

Formulae

α = FoV — Field of View or viewing angle in °,

d = diameter (width, height or diagonal) of receptor (e.g. CCD chip) in mm (28.4 mm for example below),

f = focal length of lens system in mm (10 mm for example below); the result NaN means > 180°.

α = 4 • arcsin (d / (4 • f ));
    e.g.: 4 • arcsin(28.4 / (4 • 10)) = 4 • arcsin(0.71) = 4 • 45.2 = 180.9°.

d = 4 • f • sin (α / 4);
    e.g.: 4 • 10 • sin(180.9 / 4) = 4 • 10 • sin(45.2) = 4 • 10 • 0.71 = 28.4 mm.

f = d / (4 • sin(α / 4));
    e.g.: f = 28.4 / (4 • sin(180.9 / 4)) = 28.4 / (4 • 0.71) = 28.4 / 2.84 = 10 mm.