field-of-view

As I continue to build out the photographic knowledge base on the site with articles like Understanding Neutral Density Filter Names and Numbers, and Understanding Aperture, I thought I’d write a quick post about how to calculate field of view for a photographic lens.  Lenses are usually described by their focal length, expressed in mm, but how does this translate to field of view?

If you read lens specifications (yes, I’m that kind of guy) on manufacturer’s websites, they’ll often quote the field of view (F.O.V) of a lens as well as the focal length.  When they do this in photographic terms, they’re talking about horizontal field of view in degrees, and whilst any lens will also have both a vertical and a diagonal field of view, they are rarely talked about in relation to photographic lenses.

The larger the field of view, the wider the lens is and the more of a scene you are going to see with your camera.  Telephoto and super telephoto lenses have very small fields of view, just a few degrees, so they aren’t able to see very much of the scene in front of them, although the compensating virtue is that what they do see, is much larger in the frame.  A wide angle lens for landscape photography has a very small focal length, and therefore a large field of view that lets you record broad landscapes in a single shot.

Equation For Calculating Field of View

fiel-of-view

Simple geometry will give us the equation:

field of view (in degrees) = 2 ArcTan( sensor width / (2 X focal length)) * (180/π)

Note: If your calculator is working in radians, you need the (180/π) part at the end.  if your calculator is working in degrees, you do not need that bit! If you aren’t sure… it will become pretty obvious when you run the equation as results will be wildly wrong.

Common Focal Lengths and Their Corresponding FOVs

Full frame 35mm (36mm sensor width)

Focal LengthField of VIew
15mm (Fisheye)180.0
11mm117.1
14mm104.3
16mm96.7
24mm73.7
35mm54.4
50mm39.6
85mm23.9
100mm20.4
150mm13.7
200mm10.3
300mm6.9
400mm5.2
500mm4.1
600mm3.4
800mm2.6
1000mm2.1
1200mm1.7

Nikon DX APS-C (1.5x) (23.6mm sensor width)

Focal length (35mm)Equivalent focal lengthField of View
11mm16.594.0
14mm2180.3
16mm2472.8
24mm3652.4
35mm52.537.3
50mm7526.6
85mm127.515.8
100mm15013.5
150mm2259.0
200mm3006.8
300mm4504.5
400mm6003.4
500mm7502.7
600mm9002.3
800mm12001.7
1000mm15001.4
1200mm18001.1

 

Canon APS-C (1.6x) (22.3mm sensor width)

Focal length (35mm)Equivalent focal lengthField of View
11mm17.690.8
14mm22.477.1
16mm25.669.7
24mm38.449.8
35mm5635.3
50mm8025.1
85mm13614.9
100mm16012.7
150mm2408.5
200mm3206.4
300mm4804.3
400mm6403.2
500mm8002.6
600mm9602.1
800mm12801.6
1000mm16001.3
1200mm19201.1

 

Micro Four Thirds (2x) (22.3mm sensor width)

Focal length (35mm)Equivalent focal lengthField of View
11mm2278.6
14mm2865.5
16mm3258.7
24mm4841.1
35mm7028.8
50mm10020.4
85mm17012.1
100mm20010.3
150mm3006.9
200mm4005.2
300mm6003.4
400mm8002.6
500mm10002.1
600mm12001.7
800mm16001.3
1000mm20001.0
1200mm24000.9

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