Calculating angular and dimensional FOV with crop factor
Hi all,
I have a question regarding DX sensor and lens crop factor to calculate the angular and dimensional field of view (for horizontal and vertical only) of photos taken at specific focal lengths and distances. There seems to be a number of conversation on Nikonians and the web about the crop factor, in particular, and there are several good online calculators.
The problem is that I need to be able to calculate the FOV data offline for my research, which is often in remote locations. I have found the mathematical formulas, but none account for crop factor and for the life of me I cannot get my results to match up with any of the online calculators and it is driving me nuts. I hope one of ya'll will be able to help me out.
For reference, I am using my Nikon D300s and AFS DX NIKKOR 18200mm f/3.55.6G ED VR II. The sensor size of the D300s is 23.6 mm x 15.8 mm.
The formula to calculate angular FOV that I have is:
angle = 2arctan(image size / (2 x focal length))
At 18 mm focal length: the horiz FOV = 2arctan(23.6 mm / (2 * 18)) = 66.5 decimal degrees
the vertical FOV = 2arctan(15.8 mm / (2 * 18)) = 47.4 degrees
But, these values do not match up with the online calculators like tawbaware.com. As best as I can tell I am not accounting for the sensor crop factor, though I thought it was not needed if I was using a DX sensor and DX lens?
Can someone please tell me if my math is correct (maybe the online calculators are wrong) or tell me where to account for the crop factor in the formulas so that I get accurate results.
Thanks so much,
Erich
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#1. "RE: Calculating angular and dimensional FOV with crop factor"  In response to Reply # 0
Thu 20Dec12 03:25 PMThe formula you quote is the one I have used in the past, and your arithmetic appears to be correct also.
Your calulated values are pretty close (within 0.5 degree) to the values contained in this table in our Resources section. Any difference may be due to using a slightly different size for the DX frame dimensions  Nikon's DX DSLR's do vary from model to model by 0.10.2mm.
What figures are you getting from the online calculator(s)?
The "crop factor" is taken account of in your calculation, because you plug in the actual sensor dimension into the formula. You don't need to do anything else.
Another factor to be aware of  if you need ultimate precision  is that most lenses differ a little in focal length from the named numbers.Brian
Welsh Nikonian
#2. "RE: Calculating angular and dimensional FOV with crop factor"  In response to Reply # 1
efisher16 Registered since 05th Sep 2010Thu 20Dec12 04:12 PM  edited Thu 20Dec12 04:17 PM by efisher16Hi Brian,
Thanks for such a quick response. I've typed up a quick comparison chart of My calculations (A), Tawbaware (B), and the values listed on the Nikonians page (C). Please note, that I recently read that the Tawbaware calculations had an error in them at some point, but they do conform with several other online calculators that I have found so I think that error has been fixed.
__________A_______B_______C______AB_____AC
Horiz_____66.5____66______67.4____0.5____0.9
Vert______47.4____46.9____47.9____0.5____0.5
Diag______76.5____77.4____77.4____0.9___0.9
As you can see the error listed on the far right (A minus B and A minus C) are within 1 degree. For practical purposes this is ok because at 1 meter distance (i.e. distance from target to focal plane indicator) 1 degree only translates into 1.7 cm error.
This work is all part of some new research I am working on, and I will eventually publish the results. I simply want to cross all my t's and dot all of my i's...like ensuring I don't forget to account for something like crop factor...so that the information I publish is as accurate and reliable as possible!
Again, thanks so much,
Erich
Attachment#1 ( file)
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