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This question already has an answer here:

I'm working on smartphone cameras. I want calculate Field Of View of different smartphone cameras using the formula : FOV = 2 arctan(SensorSize/2f) where:

  • f is the focal length

  • sensor size is the Height or Width or Diagonal of the sensor (in mm)

In doing some research, I've found that there is another parameter to take in consideration, which is the crop factor. When using the formula for FOV, should I apply the given f (focal length), or should I apply the effective focal length which is (focal length x crop factor)?

marked as duplicate by mattdm, chuqui, inkista, Hugo, TFuto Mar 6 '15 at 14:24

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You should use the actual focal length of the lens in question. When you include the sensor size into the equation FOV = 2 arctan(SensorSize/2f), you have already included the crop factor into your calculation.

That is because the so called crop factor is really nothing more than describing what field of view, in terms of a lens of a given focal length for a 35mm/FF sensor, will be given by a particular sized sensor. The reason a Canon APS-C sensor has a crop factor of 1.6x is because the linear dimensions of a Canon APS-C sensor are 1/1.6 the dimensions of a 36mm x 24mm full frame sensor. The same is true of a camera with a 2x crop factor: the 18mm x 12mm sensor has linear dimensions 1/2 that of a full frame sensor.

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Crop factor exists simply to convert real focal lengths to the focal length that would give a certain field of view on the "reference" format, 35mm film. So, yes, crop factor affects field of view, by definition.

So, for your purposes, there are two ways of looking at this.

  1. If you have the spec with the real focal length, use the real focal length and real sensor size to calculate field of view.
  2. If you have the spec with the "effective" focal length, that already has the crop factor applied, so you could either
    • A. Unconvert it — divide by the crop factor to go back to real focal length, and then see #1 above.
    • B. Use the converted value, but also use the 24mm×36mm height and with of 35mm film in your calculation.

I guess in case one you could also multiply both the focal length and the sensor size by the crop factor, but that would be kind of silly.

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Yes, the crop factor definitely affects the field of view, and applying the effective focal length should give you the result you need.

  • Including the sensor size already takes the "crop factor" into account. Applying it again would lead to incorrect results. – Michael C Mar 5 '15 at 22:11
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Another member of this Exchange (jdlugosz) recently posted this link as a comment to a question about Camera Phone Photography - http://dofsimulator.net/en/

It has a depth of field calculator that may help determine what you are looking for

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