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Crop Factor, Focal Length and Field of View
Posted By: Ole, 02-15-2010, 05:46 PM

Two of the most frequently asked questions are:

- what is the “crop factor”
- how does a full frame lens work when mounted on a DSLR with a 1.5 crop factor?

First, let's discuss focal length. We only discuss lenses with a positive focal length (converging lenses), i.e. such lenses as we use in photography.

When parallel light rays enter a lens, they will converge to a dot at a distance from the optical center of the lens. That distance is called the focal length, and the point where the light converges is the focal point. The focal length is usually denoted by the letter f.



From this definition we see that the focal length is a characteristic of a lens, it does not depend on the sensor size, and it does not change when the lens is mounted on differing camera bodies. As an example, an smc Pentax-A 50 mm lens is a 50 mm lens when mounted on a 24 x 36 mm "full frame" camera as well as when mounted on an APS-C body.

The focal length affects the field of view which the lens covers. A tele lens covers a narrow field of view (less of the subject gets recorded on the film/sensor) and has a longer focal length. A wide angle lens covers a wide field of view (more of the subject gets recorded on the film/sensor) and has a shorter focal length.



Now let's discuss crop factor and what happens when a lens is used on differently sized sensors.

The standard “full frame” format negative is 36mm on the longest side. The APS-C sensor which is used in Pentax DSLRS from the *istD series to the K series is 24mm on the longest side. The crop factor is 1.5, namely 36mm divided by 24mm.

Let's mount some lenses:



We mount the same lens with a focal length of f=50mm (say) on a full frame (24x36mm) camera (“A” above) and on an APS-C DSLR (“B” above).

We see that this same lens gives a narrower field of view on the APS-C DSLR than it does on the full frame camera (in actual numbers the horizontal field of view of a 50mm lens is 40 degrees on the 24x36mm format and just 27 degrees on the APS-C format (the illustration above is not to scale)).

If we want the same field of view on the APS-C DSLR as we have on the full frame camera then we need to use a lens with a shorter focal length on the APS-C DSLR (“C” above). We use the crop factor to determine the required focal length: f2 = f divided by the crop factor. In our example where we used a 50mm lens in illustration “A” we will need a 33mm lens (50 divided by 1.5) in illustration C.

In other words, a 50mm lens on a full frame sensor/film provides the same field of view as a 33mm lens on an APS-C sensor.

A handy table comparing Field of View across the many film/sensor formats in use in Pentax cameras is found here:

https://www.pentaxforums.com/forums/pentax-lens-articles/93714-field-view-tab...d-645-6x7.html

Last edited by Ole; 09-22-2011 at 08:06 PM.
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04-08-2010, 12:48 AM   #2
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Thank You, Ole for an insightful article.
Not many of Pentaxian are into technical details, but I do admire your knowledge on all things technical.

Cheers.
04-11-2010, 06:29 AM   #3
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This explains very well a concept that many have problems with. Now, if only every newbie finds and reads this article a lot of wasted verbiage would be averted!
04-12-2010, 02:21 AM   #4
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QuoteOriginally posted by rparmar Quote
This explains very well a concept that many have problems with. Now, if only every newbie finds and reads this article a lot of wasted verbiage would be averted!
Agreed.
If all newbies do read up in the forum on all matters related to their "problems" or "issues" they encountered, a lot of wasted verbiage would be averted. (this also include "yours truly").


Cheers.

05-24-2010, 03:58 AM   #5
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Thanks for the info, well explained.
I'm a newbie to DSLR and having read this article will no doubt allow me to avoid participating in what the members above have alluded to.
07-09-2010, 01:11 AM   #6
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A theoretical question. What if in case of APS-C sensor, we move the sensor closer to the lens, so that the whole frame is "filled" (see edited illustration in attachment)? Seems to me, everything should be the same as in case of FF sensor, or shouldn't it?
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07-09-2010, 10:27 AM   #7
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Georgis, you can't do that. The sensor plane needs to be where the lens is actually focusing!

Put another way, if you moved the focal plane you'd also need to change the effective focal length of the lens, putting you back to square one.
12-16-2010, 08:15 PM   #8
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Using FF and 35mm FL as the reference, here are the crop factors & "equivalent FF FLs" (for the same FOV):

MF (film) – Pentax 67N ("6x7"format – 6x7cm - actually 55x70mm 0.49x 17mm
MF (film) – Pentax 645N ("645" format – 6x4.5cm - actually 56x41.5mm) 0.62x 21.5mm
MF (digital) – Pentax 645D (44x33mm) 0.79x 27.5mm
FF (actually 36x24mm) 1x 35mm
APS-H (Canon) 1.26x 44mm
APS-C (Sony, Pentax, Nikon) 1.52x 53mm
APS-C (Canon) 1.62x 56.5mm
Four-Thirds (Olympus, Panasonic) 2x 70mm
P&S (various sizes – around 1/1.8"-1/2.5") 4.8x-6x 170mm-210mm

Note 1: Since some of these formats do not have a 3:2 AR, the comparison has been made using the FF diagonal length of 43.3mm.


Note 2: MF has other sizes besides the 3 shown.


With Pentax backwards compatibility, you can mount 6x7 & 645 format lenses on an APS-C camera using a mount adapter. For an picture of a 6x7 400/F4 lens mounted on a K-7 see:
https://www.pentaxforums.com/forums/pentax-slr-lens-discussion/73232-pentax-6...k-adapter.html(preview)

05-25-2013, 09:33 AM   #9
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Why the equivalence?

Sigma makes a "30mm f/1.4 DC HSM" where DC denotes a lens designed for APS-C sized sensor, HSM is the focus drive 'Hyper-Sonic Motor'.

From what I understand about lens focal length and sensor sizes, this statement, by Sigma, is very confusing:
"...this large-aperture standard lens with an angle of view equivalent to 45mm on a 35mm camera..." (emphasis is mine)
30mm F1.4 DC HSM | A | Sigma

If the lens is designed for an APS-C sensor and they say it is 30mm then should the angle of view not be the same as a 30mm full frame lens on a full frame sensor? Or are they marketing a full frame lens as an APS-C lens... If I'm not missing something obvious then I'll pose the question to Sigma.
05-25-2013, 09:38 AM   #10
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QuoteOriginally posted by adam. Quote
Sigma makes a "30mm f/1.4 DC HSM" where DC denotes a lens designed for APS-C sized sensor, HSM is the focus drive 'Hyper-Sonic Motor'.

From what I understand about lens focal length and sensor sizes, this statement, by Sigma, is very confusing:
"...this large-aperture standard lens with an angle of view equivalent to 45mm on a 35mm camera..." (emphasis is mine)
30mm F1.4 DC HSM | A | Sigma

If the lens is designed for an APS-C sensor and they say it is 30mm then should the angle of view not be the same as a 30mm full frame lens on a full frame sensor? Or are they marketing a full frame lens as an APS-C lens... If I'm not missing something obvious then I'll pose the question to Sigma.
What they're saying is that the field of view when using a 45mm on full-frame is about the same as the field of view when using a 30mm on aps-c. Since a full-frame sensor is bigger than an aps-c censor, at the same focal length it will simply "see" more of the frame. Focal length says nothing about field of view unless you know the size of the sensor/image plane With that said, a 30mm is an always will be a 30mm, regardless of what camera you put it on.

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05-25-2013, 10:28 AM   #11
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QuoteOriginally posted by Adam Quote
What they're saying is that the field of view when using a 45mm on full-frame is about the same as the field of view when using a 30mm on aps-c. Since a full-frame sensor is bigger than an aps-c censor, at the same focal length it will simply "see" more of the frame. Focal length says nothing about field of view unless you know the size of the sensor/image plane With that said, a 30mm is an always will be a 30mm, regardless of what camera you put it on.
Thanks, Adam. I see what you mean about focal length saying nothing about the angle of view unless we know the sensor size. Knowing that some lenses are designed for full frame sensors and some are designed for APS-C sensors means that we can have a focal length of 35mm, for example, for each type of sensor, each giving the SAME angle of view...
I don't shoot Nikon, but I found this interesting: Camera Lens Explained | DX & FX Format Lenses from Nikon from Nikon
It shows how some lenses have the same focal length but are designed for different sensor sizes. Unfortunately, the article is not technical enough to explain how they design DX (APS-C) lenses with the proper angle of view.
So I still wonder what Sigma is doing, marketing a lens for APS-C and stating an angle of view based on a full frame sensor with a different focal length. It seems like you can put this lens on a full frame sensor and get the 30mm angle of view.
05-25-2013, 10:35 AM   #12
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QuoteOriginally posted by adam. Quote
Knowing that some lenses are designed for full frame sensors and some are designed for APS-C sensors means that we can have a focal length of 35mm, for example, for each type of sensor, each giving the SAME angle of view...
This is where you're misunderstanding things. Focal length does not directly determine the field of view. If you have the same focal length but different sensor sizes, then you cannot avoid having different fields of view (though the DX lens may not fully cover the FX frame; this is what the "designed for" designation is all about).

There are lots of threads discussing and clarifying this, though I'd say that the first post of this thread is a good starting point. After you've read it, take a look at this discussion:
https://www.pentaxforums.com/forums/pentax-dslr-discussion/30900-crop-factor.html

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05-25-2013, 10:50 AM   #13
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QuoteOriginally posted by dosdan Quote
Using FF and 35mm FL as the reference, here are the crop factors & "equivalent FF FLs" (for the same FOV):

MF (film) Pentax 67N ("6x7"format 6x7cm - actually 55x70mm 0.49x 17mm
MF (film) Pentax 645N ("645" format 6x4.5cm - actually 56x41.5mm) 0.62x 21.5mm
MF (digital) Pentax 645D (44x33mm) 0.79x 27.5mm
FF (actually 36x24mm) 1x 35mm
APS-H (Canon) 1.26x 44mm
APS-C (Sony, Pentax, Nikon) 1.52x 53mm
APS-C (Canon) 1.62x 56.5mm
Four-Thirds (Olympus, Panasonic) 2x 70mm
P&S (various sizes around 1/1.8"-1/2.5") 4.8x-6x 170mm-210mm

Note 1: Since some of these formats do not have a 3:2 AR, the comparison has been made using the FF diagonal length of 43.3mm.


Note 2: MF has other sizes besides the 3 shown.


With Pentax backwards compatibility, you can mount 6x7 & 645 format lenses on an APS-C camera using a mount adapter. For an picture of a 6x7 400/F4 lens mounted on a K-7 see:
https://www.pentaxforums.com/forums/pentax-slr-lens-discussion/73232-pentax-6...k-adapter.html(preview)
Actually the photo of my K-7 is with the SMC Pentax-6x7 165mm F2.8 just like this photo on my K-01 . The shot of the funny car was taken with my 400mm F4 6x7 lens on my 6x7 Pentax.
05-25-2013, 01:04 PM   #14
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QuoteOriginally posted by adam. Quote
So I still wonder what Sigma is doing, marketing a lens for APS-C and stating an angle of view based on a full frame sensor with a different focal length. It seems like you can put this lens on a full frame sensor and get the 30mm angle of view.
Yes, it's misleading, in this case.

A lens is designed for one sensor or another, and the image subtended by the lens must cover that sensor size. It doesn't make much sense talking about how images might appear on a sensor the lens cannot cover!

However, in the digital camera world, we have various smaller sensors available from the same manufacturers (Canon, Pentax, Nikon, etc.) who also make (or made) 135mm cameras (so-called "full frame"). For example the FA 43mm Limited, which was designed initially for 35mm film. Since it can be used on an APS-C sensor, it is useful to know its effective field of view. More recently, we have been able to adapt it to still other sensor sizes (MFT for example). So our photographic world is now much more complicated. The focal length itself only tells us the FOV when we know the sensor size.

I once wrote an article on Equivalence of Camera Systems, which might be a useful counterpart to this one.
05-25-2013, 06:26 PM   #15
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Thanks!

Thanks to Adam and rparmar. I understand my error now.

I'm going to use the word 'resolution' and when I do, consider the light that the lens is refracting - do not think about sensor resolution!
The simplest way I can think of to summarize (dangerous, I know):
When designed for different sensor sizes, the same focal length will have a different field of view because
a) the light arriving at the sensor plane is covering a different sized area (full frame cm^2 > APS-C cm^2) and
b) the resolution of the image arriving at the sensor plane is the same for each lens.
ergo, the field of view for an APS-C designed lens is smaller than the field of view for a full frame designed lens at the same focal length.
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