Calculating Focal length

PaulButler

PaulButler

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I'm having a brain fade at the moment and need some help. I am trying to calculate the focal length of the lenses used. I know the sensor/film size and I know the horizontal field of view ...

Now I know that calculating FoV can be achieved using this formula:

fov = 2 * arctan( s / (2 * f)) where s = sensor or film size (horizontal, vertical or diagonal it will calc the respective fov) and f = focal length of the lens used ... I cannot for the life of me remember how to resolve for f when I know fov ...

Help appreciated ...
 
arctan( s / (2*f)) = fov/2

s / (2*f) = tan (fov/2)

2*f = s / tan (fov/2)

f = s / (2*tan (fov/2))
 
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Just out of interest.. honest question.... Why ? as in what is the info used for ?

Just being nosey :)
 
KIPAX said:
Just out of interest.. honest question.... Why ? as in what is the info used for ?

Just being nosey :)
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Its a data analysis exercise, partly driven because so many images have been cropped and in some cases heavily, so I got curious ...
 
PaulButler said:
Its a data analysis exercise, partly driven because so many images have been cropped and in some cases heavily, so I got curious ...
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Gotcha.

So if you see an image like this, and you know that the wingspan of a yellow-billed kite is typically about 150cm, you'd estimate that the horizontal field of view is probably about 150-200cm, and the magic formula would tell you that the focal length was around ... what?

541203_421215237903727_1979430169_n.jpg


I think you're missing something. You can determine the dimensional field of view from the image (around 150-200cm in this case) but the formula you were playing with uses the angular field of view, and I don't see how you can determine that from the image.

Unless what you're doing is completely different from what I expected, in which case I'm curious. What are the circumstances in which you can know the angular field of view but not the focal length?
 
I know the angular FoV ... not sure what your point is Stewart ... or are you deliberately being obtuse ?
 
I think PaulButler is trying to calculate effective focal length for a cropped image.

He knows initial FoV and sensor size and how much he cropped by, so effective FoV and size can be calculated from there. The only thing left is calculate the effective focal length, which is what the question was about.

Probably an attempt to decide which focal length to go for for a new lens? :D
 
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gunnar said:
I think PaulButler is trying to calculate effective focal length for a cropped image.

He knows initial FoV and sensor size and how much he cropped by, so effective FoV and size can be calculated from there. The only thing left is calculate the effective focal length, which is what the question was about.

Probably an attempt to decide which focal length to go for for a new lens? :D
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Not quite, re new lens. I have a lot of images that were shot on known sensor sizes and (making a few sensible assumptions) have been able to work out what the FoV was - many of these are cropped and no exif so (and also not all of them mine either) ... - I wanted to reverse that to the focal length. I was simply bored and was curious. :)

The new lens aspect is interesting but falls down because if the lenses used didn't cover the focal length wanted/needed I'd never know ...

GreenNinja67 said:
42
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It always is :)
 
PaulButler said:
I know the angular FoV ... not sure what your point is Stewart ... or are you deliberately being obtuse ?
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No, I'm not being obtuse. (At least, not deliberately or knowingly.) I genuinely don't know how you can tell what the angular FoV is.
 
StewartR said:
No, I'm not being obtuse. (At least, not deliberately or knowingly.) I genuinely don't know how you can tell what the angular FoV is.
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OK, fair enough. As I said I was bored and wanted to know what the cropped images could have been shot using ...
 
PaulButler said:
OK, fair enough. As I said I was bored and wanted to know what the cropped images could have been shot using ...
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But how did you know the angular field of view? I mean, the image I posted could have been taken with a 200mm lens at a range of about 15m, or a 400mm lens at a range of about 30m, or a 600mm lens at a range of about 45m ... how can you tell them apart? I'm genuinely curious.
 
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