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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).

> Enter Focal Length

Focal Length (mm) >  

                

  =  
Field of View (Diagonal) – dFoV

  FX (°): >  

  DX (°):>  

 
Field of View (Horizontal) – hFoV

  FX (°): >  

  DX (°):>  

     
Field of View (Vertical) – vFoV

  FX (°): >  

  DX (°):>  

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).

> Enter Fisheye Focal Length

Focal Length (mm) >  

                

  =  
Field of View (Diagonal) – dFoV

  FX (°):>  

  DX (°):>  

 
Field of View (Horizontal) – hFoV

  FX (°):>  

  DX (°):>  

     
Field of View (Vertical) – vFoV

  FX (°):>  

  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 (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.

 
  © 2004 - 2017 by Horo Wernli.