# Re: Field of view

Discussion in 'Digital Photography' started by David J Taylor, Mar 8, 2009.

1. ### David J TaylorGuest

Alfred Molon wrote:
> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?

Tangent is your friend here. IIRC:

FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)

FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)

FoV (diag) = 2 * ArcTan (sensor-semi-diagonal / focal-length)

Ignore crop factor, and use the actual active area dimensions of the
sensor.

David

David J Taylor, Mar 8, 2009

2. ### Don StaufferGuest

David J Taylor wrote:
> Alfred Molon wrote:
>> What is the formula for calculating horizontal and vertical field of
>> view out of focal length, crop factor and aspect ratio of the sensor?

>
> Tangent is your friend here. IIRC:
>
> FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)
>
> FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)
>
> FoV (diag) = 2 * ArcTan (sensor-semi-diagonal / focal-length)
>
> Ignore crop factor, and use the actual active area dimensions of the
> sensor.
>
> David

However, if you do not have the actual dimensions, they are 24mm divided
by the crop factor, and 36mm divided by the crop factor. Those are the
full height and width, you then need to divide by two to get the
semi-(values).

Don Stauffer, Mar 8, 2009

3. ### David J TaylorGuest

Don Stauffer wrote:
> David J Taylor wrote:
>> Alfred Molon wrote:
>>> What is the formula for calculating horizontal and vertical field of
>>> view out of focal length, crop factor and aspect ratio of the
>>> sensor?

>>
>> Tangent is your friend here. IIRC:
>>
>> FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)
>>
>> FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)
>>
>> FoV (diag) = 2 * ArcTan (sensor-semi-diagonal / focal-length)
>>
>> Ignore crop factor, and use the actual active area dimensions of the
>> sensor.
>>
>> David

>
>
> However, if you do not have the actual dimensions, they are 24mm
> divided by the crop factor, and 36mm divided by the crop factor. Those
> are the full height and width, you then need to divide by two
> to get the semi-(values).

Thanks, Don. My reservation is that the usually quoted crop factors are
not all that accurate!

Cheers,
David

David J Taylor, Mar 8, 2009
4. ### David J TaylorGuest

Alfred Molon wrote:
[]
> Long live the arctan ;-)
>
> Let's calculate an example.
>
> APS-C sized sensor 23.5 x 15.7 mm

[]
> At 300mm:
> Hor. fov = 4.5°
> Ver. fov = 3°

... and my Nikon 300mm says "5 degrees 20 minutes FoV" in the manual, which
is 5.333 degrees diagonal. Your calculation gives 5.4 degrees. Probably
within the limits of the approximations in the data.

Cheers,
David

David J Taylor, Mar 8, 2009
5. ### ASAARGuest

On Sun, 08 Mar 2009 16:21:48 GMT, David J Taylor wrote:

>> However, if you do not have the actual dimensions, they are 24mm
>> divided by the crop factor, and 36mm divided by the crop factor. Those
>> are the full height and width, you then need to divide by two
>> to get the semi-(values).

>
> Thanks, Don. My reservation is that the usually quoted crop factors are
> not all that accurate!

Nikon's is supposed to be pretty close to 1.52, but even if you
use 1.5 the calculated error may be less than the actual error when
focused closer than infinity with many zoom lenses. That's probably
no big deal if the concern about FOV is for landscapes when the lens
*is* focused near infinity. I assume that the 2x crop factor for
4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
and 1.3x crop factors are.

ASAAR, Mar 13, 2009
6. ### David J TaylorGuest

ASAAR wrote:
> On Sun, 08 Mar 2009 16:21:48 GMT, David J Taylor wrote:
>
>>> However, if you do not have the actual dimensions, they are 24mm
>>> divided by the crop factor, and 36mm divided by the crop factor.
>>> Those are the full height and width, you then need to divide by two
>>> to get the semi-(values).

>>
>> Thanks, Don. My reservation is that the usually quoted crop factors
>> are not all that accurate!

>
> Nikon's is supposed to be pretty close to 1.52, but even if you
> use 1.5 the calculated error may be less than the actual error when
> focused closer than infinity with many zoom lenses. That's probably
> no big deal if the concern about FOV is for landscapes when the lens
> *is* focused near infinity. I assume that the 2x crop factor for
> 4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
> and 1.3x crop factors are.

Just why I said use the sensor dimensions rather than some nominal
"crop-factor". Ideally use the actual focal length of the lens, rather
than the sanitised marketing value (i.e. 28.4mm and not "28mm").

The change of focal length at finite subject distances is a very good
point. I wonder if graphs are published anywhere, or if it's something we
should expect to see in reviews?

David

David J Taylor, Mar 13, 2009
7. ### ASAARGuest

On Fri, 13 Mar 2009 08:17:26 GMT, David J Taylor wrote:

>> Nikon's is supposed to be pretty close to 1.52, but even if you
>> use 1.5 the calculated error may be less than the actual error when
>> focused closer than infinity with many zoom lenses. That's probably
>> no big deal if the concern about FOV is for landscapes when the lens
>> *is* focused near infinity. I assume that the 2x crop factor for
>> 4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
>> and 1.3x crop factors are.

>
> Just why I said use the sensor dimensions rather than some nominal
> "crop-factor".

That may be acceptable for you or me, but most people have no idea
what their camera sensor's dimensions are. Crop factor is far more
well known, even for the camera-semi-literate. Aston Kutscher (in
Nikon's DSLR commercials) looks like he wouldn't know FX from DX.
Waving the camera in the air, nowhere in particular, he says that
the camera is properly set because he's able to fire a quick AF-C
burst while holding it only in one hand. Bleah.

> Ideally use the actual focal length of the lens, rather than the
> sanitised marketing value (i.e. 28.4mm and not "28mm").

Does it matter with less than 100% accurate viewfinders? Most
cameras are used for taking pictures, not for surveying.

ASAAR, Mar 13, 2009
8. ### David J TaylorGuest

ASAAR wrote:
> On Fri, 13 Mar 2009 08:17:26 GMT, David J Taylor wrote:
>
>>> Nikon's is supposed to be pretty close to 1.52, but even if you
>>> use 1.5 the calculated error may be less than the actual error when
>>> focused closer than infinity with many zoom lenses. That's probably
>>> no big deal if the concern about FOV is for landscapes when the lens
>>> *is* focused near infinity. I assume that the 2x crop factor for
>>> 4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
>>> and 1.3x crop factors are.

>>
>> Just why I said use the sensor dimensions rather than some nominal
>> "crop-factor".

>
> That may be acceptable for you or me, but most people have no idea
> what their camera sensor's dimensions are. Crop factor is far more
> well known, even for the camera-semi-literate. Aston Kutscher (in
> Nikon's DSLR commercials) looks like he wouldn't know FX from DX.
> Waving the camera in the air, nowhere in particular, he says that
> the camera is properly set because he's able to fire a quick AF-C
> burst while holding it only in one hand. Bleah.
>
>
>> Ideally use the actual focal length of the lens, rather than the
>> sanitised marketing value (i.e. 28.4mm and not "28mm").

>
> Does it matter with less than 100% accurate viewfinders? Most
> cameras are used for taking pictures, not for surveying.

I rather suspect that anyone who wants to calculate the FoV has more idea
than "most people". I am grateful that we do not get the same advertising
as you, it would likely put me off buying /anything/! For the sensor
sizes, DP Review is one sourse:

http://www.dpreview.com/reviews/nikond60/page2.asp

where the D60 is given as 23.6 x 15.8 mm, so it's not that difficult to
find out. It's what appears on the final image, not in the viewfinder
which matters.

Anyway, the formulae are there for those who want them. Whether the data
on the lenses is, is another matter.

Cheers,
David

David J Taylor, Mar 13, 2009
9. ### David J TaylorGuest

David J Taylor wrote:
[]
> For the sensor sizes, DP Review is one sourse:

Argh: s/sourse/source/

David

David J Taylor, Mar 13, 2009
10. ### ASAARGuest

On Fri, 13 Mar 2009 10:49:51 GMT, David J Taylor wrote:

>> Does it matter with less than 100% accurate viewfinders? Most
>> cameras are used for taking pictures, not for surveying.

>
> I rather suspect that anyone who wants to calculate the FoV has more idea
> than "most people". I am grateful that we do not get the same advertising
> as you, it would likely put me off buying /anything/! For the sensor
> sizes, DP Review is one sourse:
>
> http://www.dpreview.com/reviews/nikond60/page2.asp
>
> where the D60 is given as 23.6 x 15.8 mm, so it's not that difficult to
> find out. It's what appears on the final image, not in the viewfinder
> which matters.

We seem to be talking past each other. Sure, those that are
*really* interested in photography are likely to be able to find
sensor dimensions with little effort. Your last sentence above
seems little more than a non sequitur truism. If what you see in
the viewfinder is less than what you get (for most DSLRs), and isn't
a concern, then why be concerned about the inaccuracy of using 1.5
as the crop factor for Nikon's DSLRs? It also promises a little
less than you actually get, and the difference is trivially small.
The advantage of using crop factors is that they only require simple
math. Telling photographers that they should use arctangents
instead violates the KISS principle but might be useful in that it's
likely to convince many to avoid asking you for further help.

ASAAR, Mar 13, 2009
11. ### J. ClarkeGuest

Alfred Molon wrote:
> In article <8Zqul.6383\$>, David J
> Taylor says...
>> David J Taylor wrote:
>> []
>>> For the sensor sizes, DP Review is one sourse:

>>
>> Argh: s/sourse/source/

>
> Never mind. Today a colleague "corrected" one of my slides in a ppt
> presentation. He replaced "licence" with "lisence", not just on one
> page, but on several pages. I sent him a link to an online dictionary.

What's truly sad is that Google has more than 4 million hits on "lisence".

J. Clarke, Mar 13, 2009
12. ### David J TaylorGuest

ASAAR wrote:
[]
> We seem to be talking past each other. Sure, those that are
> *really* interested in photography are likely to be able to find
> sensor dimensions with little effort. Your last sentence above
> seems little more than a non sequitur truism. If what you see in
> the viewfinder is less than what you get (for most DSLRs), and isn't
> a concern, then why be concerned about the inaccuracy of using 1.5
> as the crop factor for Nikon's DSLRs? It also promises a little
> less than you actually get, and the difference is trivially small.
> The advantage of using crop factors is that they only require simple
> math. Telling photographers that they should use arctangents
> instead violates the KISS principle but might be useful in that it's
> likely to convince many to avoid asking you for further help.

My feeling is that someone who wants to calculate the FoV wants an exact,
and not an approximate, answer. Calculation was the OP's requirement.

David

David J Taylor, Mar 13, 2009
13. ### ASAARGuest

On Fri, 13 Mar 2009 23:26:24 GMT, Spinmeister David J Taylor wrote:

>> We seem to be talking past each other. Sure, those that are
>> *really* interested in photography are likely to be able to find
>> sensor dimensions with little effort. Your last sentence above
>> seems little more than a non sequitur truism. If what you see in
>> the viewfinder is less than what you get (for most DSLRs), and isn't
>> a concern, then why be concerned about the inaccuracy of using 1.5
>> as the crop factor for Nikon's DSLRs? It also promises a little
>> less than you actually get, and the difference is trivially small.
>> The advantage of using crop factors is that they only require simple
>> math. Telling photographers that they should use arctangents
>> instead violates the KISS principle but might be useful in that it's
>> likely to convince many to avoid asking you for further help.

>
> My feeling is that someone who wants to calculate the FoV wants an exact,
> and not an approximate, answer. Calculation was the OP's requirement.

That "feeling" is only that, omniscience need not intrude, and it
should be pointed out that not only does using crop factors also
involve calculations, the OP's exact request was :

> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?

which specifically asked for a formula using the crop factor, which
if the one for 4/3 sensors is used wouldn't have the greater
inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
that the OP didn't really mean to phrase his question in terms of
crop factors? My "feeling" is that you will again attempt to
sidestep the issue, but it would be nice if I'm mistaken.

ASAAR, Mar 14, 2009
14. ### David J TaylorGuest

ASAAR wrote:
[]
>> What is the formula for calculating horizontal and vertical field of
>> view out of focal length, crop factor and aspect ratio of the sensor?

>
> which specifically asked for a formula using the crop factor, which
> if the one for 4/3 sensors is used wouldn't have the greater
> inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
> that the OP didn't really mean to phrase his question in terms of
> crop factors? My "feeling" is that you will again attempt to
> sidestep the issue, but it would be nice if I'm mistaken.

To know the "crop factor" exactly, you need to know the exact size of the
sensor. I don't see what your problem is with that.

If you insist on muddying the issue with 4/3 sensors, then you have two
"crop factors", one for vertical and one for horizontal.

horizontal: 36/18 = 2

vertical: 24/13.5 = 1.777....

Easier to use 18 x 13.5mm, isn't it?

David

David J Taylor, Mar 14, 2009
15. ### ASAARGuest

On Sat, 14 Mar 2009 08:03:16 GMT, The incorrigible David J Taylor,
wrote:

> ASAAR wrote:
> []
>>> What is the formula for calculating horizontal and vertical field of
>>> view out of focal length, crop factor and aspect ratio of the sensor?

>>
>> which specifically asked for a formula using the crop factor, which
>> if the one for 4/3 sensors is used wouldn't have the greater
>> inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
>> that the OP didn't really mean to phrase his question in terms of
>> crop factors? My "feeling" is that you will again attempt to
>> sidestep the issue, but it would be nice if I'm mistaken.

>
> To know the "crop factor" exactly, you need to know the exact size of the
> sensor. I don't see what your problem is with that.

You've reverted to the classic David. This has never been about
knowing the crop factor "exactly". The "usually quoted crop
factors" (your words) are more than good enough for most people,
most of the time. You'll argue all day rather than be reasonable,
if it means you'd have to back down from unreasonable positions.
Since you've accused me of having a "problem", it's only fair to
note that the problem here isn't what you think it is. But then,
when have you ever acknowledged your own "problems"?

> If you insist on muddying the issue with 4/3 sensors, then you have two
> "crop factors", one for vertical and one for horizontal.
>
> horizontal: 36/18 = 2
>
> vertical: 24/13.5 = 1.777....
>
> Easier to use 18 x 13.5mm, isn't it?

Speak of muddying the waters . . . This is a good example of the
lengths you'll go to avoid being reasonable. Based on your way of
thinking, all of the photographers (and DPReview, et. al.) that
recognize the 4/3 system's generally accepted crop factor must have
problems of their own, and have no good reason to speak of crop
factors for 4/3 cameras because their image's dimensions don't share
the same 3:2 ratio. How foolish the photographic world must be when
they dare speak of crop factors for so many of the P&S cameras, such
as one of Panasonic's that lets you choose from among 4:3, 3:2 and
16:9 ratios. You'll probably want to expand on this to show why
it's so overwhelmingly important to be able to know the several crop
factors and FOVs for each of these different formats, but I and most
people don't really care. That's your problem, not ours.

ASAAR, Mar 14, 2009
16. ### David J TaylorGuest

ASAAR wrote:
[]
> You've reverted to the classic David. This has never been about
> knowing the crop factor "exactly". The "usually quoted crop
> factors" (your words) are more than good enough for most people,
> most of the time. You'll argue all day rather than be reasonable,
> if it means you'd have to back down from unreasonable positions.
> Since you've accused me of having a "problem", it's only fair to
> note that the problem here isn't what you think it is. But then,
> when have you ever acknowledged your own "problems"?

[]
> Speak of muddying the waters . . . This is a good example of the
> lengths you'll go to avoid being reasonable. Based on your way of
> thinking, all of the photographers (and DPReview, et. al.) that
> recognize the 4/3 system's generally accepted crop factor must have
> problems of their own, and have no good reason to speak of crop
> factors for 4/3 cameras because their image's dimensions don't share
> the same 3:2 ratio. How foolish the photographic world must be when
> they dare speak of crop factors for so many of the P&S cameras, such
> as one of Panasonic's that lets you choose from among 4:3, 3:2 and
> 16:9 ratios. You'll probably want to expand on this to show why
> it's so overwhelmingly important to be able to know the several crop
> factors and FOVs for each of these different formats, but I and most
> people don't really care. That's your problem, not ours.

ASAAR,

I've actually had to use the formulae I quoted to work out FoV, and I'm
quite happy to do so. No problem. If others want to use less accurate
ways, that's fine if the results are good enough for their purpose. I
have no problems with this.

I also tended to think in 35mm focal lengths (although when I started 35mm
was "wide", not it's 28 or even 24), and that can be a helpful way of
comparing lenses and systems, to a first approximation. Today I tend to
think more: "Is the 18-200mm enough or do I need the range of my 16mm and
300mm"? You might like to consider how a 24mm lens on a 4:3 and a 28mm
lens on a 16:9 aspect ratio sensor compare....

David

David J Taylor, Mar 15, 2009
17. ### ASAARGuest

On Sun, 15 Mar 2009 09:29:05 GMT, David J Taylor wrote:

>> Speak of muddying the waters . . . This is a good example of the
>> lengths you'll go to avoid being reasonable. Based on your way of
>> thinking, all of the photographers (and DPReview, et. al.) that
>> recognize the 4/3 system's generally accepted crop factor must have
>> problems of their own, and have no good reason to speak of crop
>> factors for 4/3 cameras because their image's dimensions don't share
>> the same 3:2 ratio. How foolish the photographic world must be when
>> they dare speak of crop factors for so many of the P&S cameras, such
>> as one of Panasonic's that lets you choose from among 4:3, 3:2 and
>> 16:9 ratios. You'll probably want to expand on this to show why
>> it's so overwhelmingly important to be able to know the several crop
>> factors and FOVs for each of these different formats, but I and most
>> people don't really care. That's your problem, not ours.

> . . .
>
> I've actually had to use the formulae I quoted to work out FoV, and I'm
> quite happy to do so. No problem. If others want to use less accurate
> ways, that's fine if the results are good enough for their purpose. I
> have no problems with this.

I'm sure that you have used those formulas, but really, what kind
of accuracy is really needed by casual photographers, as opposed to
engineers or those doing scientific research. How many digits of
precision did you require. How many do you think the OP needed? Of
course you can't yet know the answer to that yet, and while you
could use this to justify your "solution", so could someone else
assume that double precision float might be warranted. It's often
noticed that when some in these newsgroups write, in effect "your
reasonable solution isn't good enough, mine is better . . ." it's
often done not to help answer and OP's question so much as it is to
strut one's superior knowledge in front of others. The ng is too
often used as a vanity forum.

> I also tended to think in 35mm focal lengths (although when I started 35mm
> was "wide", not it's 28 or even 24), and that can be a helpful way of
> comparing lenses and systems, to a first approximation. Today I tend to
> think more: "Is the 18-200mm enough or do I need the range of my 16mm and
> 300mm"?

Yes, that's also how I see it. And when others answered the OP,
using the terms he requested (crop factor included), it would have
been helpful and more accurate than this "first approximation".

> You might like to consider how a 24mm lens on a 4:3 and a 28mm
> lens on a 16:9 aspect ratio sensor compare....

Umm ... are you suggesting that you know something that I don't,
or that I might not have considered? See "superior knowledge",
above. When discussing FOV earlier you mentioned only two of the
sensor's dimensions. You might like to also consider its diagonal,
as some occasionally do.

ASAAR, Mar 15, 2009
18. ### David J TaylorGuest

ASAAR wrote:
> On Sun, 15 Mar 2009 09:29:05 GMT, David J Taylor wrote:
>
>>> Speak of muddying the waters . . . This is a good example of the
>>> lengths you'll go to avoid being reasonable. Based on your way of
>>> thinking, all of the photographers (and DPReview, et. al.) that
>>> recognize the 4/3 system's generally accepted crop factor must have
>>> problems of their own, and have no good reason to speak of crop
>>> factors for 4/3 cameras because their image's dimensions don't share
>>> the same 3:2 ratio. How foolish the photographic world must be when
>>> they dare speak of crop factors for so many of the P&S cameras, such
>>> as one of Panasonic's that lets you choose from among 4:3, 3:2 and
>>> 16:9 ratios. You'll probably want to expand on this to show why
>>> it's so overwhelmingly important to be able to know the several crop
>>> factors and FOVs for each of these different formats, but I and most
>>> people don't really care. That's your problem, not ours.

>> . . .
>>
>> I've actually had to use the formulae I quoted to work out FoV, and
>> I'm quite happy to do so. No problem. If others want to use less
>> accurate ways, that's fine if the results are good enough for their
>> purpose. I have no problems with this.

>
> I'm sure that you have used those formulas, but really, what kind
> of accuracy is really needed by casual photographers, as opposed to
> engineers or those doing scientific research. How many digits of
> precision did you require. How many do you think the OP needed? Of
> course you can't yet know the answer to that yet, and while you
> could use this to justify your "solution", so could someone else
> assume that double precision float might be warranted. It's often
> noticed that when some in these newsgroups write, in effect "your
> reasonable solution isn't good enough, mine is better . . ." it's
> often done not to help answer and OP's question so much as it is to
> strut one's superior knowledge in front of others. The ng is too
> often used as a vanity forum.
>
>
>> I also tended to think in 35mm focal lengths (although when I
>> started 35mm was "wide", not it's 28 or even 24), and that can be a
>> helpful way of comparing lenses and systems, to a first
>> approximation. Today I tend to think more: "Is the 18-200mm enough
>> or do I need the range of my 16mm and 300mm"?

>
> Yes, that's also how I see it. And when others answered the OP,
> using the terms he requested (crop factor included), it would have
> been helpful and more accurate than this "first approximation".
>
>> You might like to consider how a 24mm lens on a 4:3 and a 28mm
>> lens on a 16:9 aspect ratio sensor compare....

>
> Umm ... are you suggesting that you know something that I don't,
> or that I might not have considered? See "superior knowledge",
> above. When discussing FOV earlier you mentioned only two of the
> sensor's dimensions. You might like to also consider its diagonal,
> as some occasionally do.

All I'm saying is that sometimes vertical FoV matters, sometimes
horizontal FoV, depending what you are trying to photograph. The
different aspect ratio will also affect the appearance of the final image.

David

David J Taylor, Mar 15, 2009
19. ### ASAARGuest

On Sun, 15 Mar 2009 14:58:00 GMT, David J Taylor wrote:

>>> You might like to consider how a 24mm lens on a 4:3 and a 28mm
>>> lens on a 16:9 aspect ratio sensor compare....

>>
>> Umm ... are you suggesting that you know something that I don't,
>> or that I might not have considered? See "superior knowledge",
>> above. When discussing FOV earlier you mentioned only two of the
>> sensor's dimensions. You might like to also consider its diagonal,
>> as some occasionally do.

>
> All I'm saying is that sometimes vertical FoV matters, sometimes
> horizontal FoV, depending what you are trying to photograph. The
> different aspect ratio will also affect the appearance of the final image.

Yes, sometimes it does and more often than not, landscape
photographers are more interested in the horizontal FOV and
architectural photographers may be more evenly split. And all I was
saying (well, we both were saying more) was that this wasn't
sufficient reason to disparage calculations using crop factors,
especially when there was no good reason to assume extreme accuracy
was desired by the OP as shown by his modest request. After all,
you didn't just say "This is another way to calculate FOV that may
be preferable if you need great accuracy", you said instead,
suggesting more omniscience than was warranted, "Ignore crop factor,
and use the actual active area dimensions of the sensor.".

ASAAR, Mar 15, 2009
20. ### ASAARGuest

On Sun, 15 Mar 2009 19:36:14 +0100, Alfred Molon wrote:

> Sorry, what exactly is the problem in using the simple formulas which
> David kindly posted?

Nothing at all. Much gets by you as usual, Alfie*. To recap, you