Understanding the Crop Factor
One of the most commonly discussed topics on various photography gear forums, especially among bird and wildlife enthusiasts, is the camera’s crop factor. Unfortunately, this topic is sometimes misunderstood even among some of the seasoned photographers. Even worse, some camera manufacturers advertise short lenses on their small sensor cameras as “equivalent” to much longer and more expensive lenses. Such advertisement, while legally and technically acceptable, can be quite misleading. In this short article. I will explain the basic and simple concept of a “cropped” sensor to help shed more light on this topic.
Crop factor does not increase the focal length.
Contrary to the myth on the internet, a cropped-sensor camera does not increase the focal length of any lens. Any lens has a fixed focal length that does not depend on the camera the lens is mounted on. A 400mm lens is always a 400mm lens, whether it is mounted on an EOS-7D Mark II or an EOS-1DX Mark II or on a smaller sensor camera via an adaptor. Focal length is a property of the optics in the lens. The crop factor only refers to the sensor size. A 1.6X crop factor (also referred to as APS-C) means the image sensor is about 1.6X smaller than the standard 35mm film on each side, or approximately 22.5mm x 15mm. A Full-frame (FF) (1.0X crop) sensor means the sensor is approximately 36mm x 24mm. The common sensor sizes are shown in the figure below (source:Wiki). The Canon EOS-7D Mark II uses an APS-C sensor that is roughly 2.6 times smaller than a full-frame sensor in the EOS 1D/5D series (1.6 x 1.6 =2.56) as shown below.
common image sensor formats (source: Wikipedia)
Because the cropped image sensor is smaller, it sees a smaller portion of the image projected by the lens. Let’s assume you are shooting an owl from 18 yards away with a 500mm lens. The lens projects exactly the same image on the sensor plane of an APS-C camera and a FF camera. But because the APS-C camera has a smaller sensor, the image it captures is “cropped” relative to the image captured by the FF camera. The APS-C sensor has a narrower field of view (FOV).
Projected image with a 500mm lens in a full-frame (left) and an APS-C camera (right) camera. There is no difference in the projected images. The crop sensor sees a smaller portion of the projected image because it is smaller. That’s what the sensor is called “cropped”.
The image recorded by each sensor is shown below.
The image captured by a FF sensor compared to an APS-C sensor.
In order to get the same FOV with the FF camera, you can simply crop the FF image in Photoshop. But which image will have more pixels? You might think the image from the APS-C sensor. But that is incorrect! The correct answer depends on the pixel size. If the APS-C and the FF sensors have the same pixel size the cropped image from the FF sensor and the native image from the APS-C sensor will have exactly the same number of pixels. But if the APS-C sensor has smaller pixels, it will have more pixels than the cropped image of the FF camera. If the FF sensor has smaller pixels than the APS-C sensor, it will have more pixels on the bird after cropping. This is illustrated graphically below, pixels have been drawn very large for better visibility. Note that post cropping the FF image, both images will have exactly the same depth-of-field (DOF).
A:FF and APS-C sensor with same size pixels. (e.g. EOS 7D Mark II and the EOS-5DS R which have roughly the same size pixels). Both images will have same number of pixels on the owl.
B: FF sensor with larger pixels than the APS-C sensor. (e.g. EOS-1D X Mark II and the EOS-7D Mark II). Image from the FF sensor will fewer pixels on the owl.
C: FF sensor with smaller pixels . (e.g. EOS-5D S R and the EOS-50D). Image from the FF sensor will have more pixels on the owl.
So it’s all about the pixel size. For example when shooting with the original EOS-7D (APS-C 18 Mega-pixels) and the EOS-5DS R (FF 51 Mega-pixels) side-by-side, the FF image will have more pixels on the bird, even after cropping to get the same FOV as the APS-C sensor. Camera manufacturers don’t usually state the pixel size on the camera’s spec sheet, but it is easy to calculate how many pixels you will be left with when cropping the image to a given FOV. You can use this simple formula: # of pixels after cropping to a given FOV = ( total number of pixels on the sensor) / (FOV x FOV ). As an example, let’s calculate how many pixels will be left in an EOS-5D Mark IV file after cropping it to the same FOV of the EOS-7D Mark II.
The answer is : 30 Mega-pixels/(1.6 x 1.6 ) ~ 12 Mega pixels. This means each side of the EOS-7D Mark II image will be approximately 1.3 times longer than the 5D Mark IV image when viewed at 100% on the screen, in other words it is magnified by 1.3X. Note that this number is not equal to the 1.6X crop factor. Using the same math we get ~ 20 Mega-pixels for a cropped image from the EOS-5DS R. This means the EOS-7D Mark II has no magnification or “reach factor” over the high-resolution 5DS R.
The notion of the APS-C camera turning a 500mm lens to a 800mm lens is incorrect, and there is no such thing as crop factor magnification, the smaller sensor does not magnify anything. It is the smaller pixels that result in more pixels on a subject at a given distance, not the smaller sensor.
Another very important factor is that more pixels on the subject is not always equal to finer details or a higher quality image. Not all pixels are created equal. The smaller pixels have a lower dynamic range (DR), you can think about them as smaller buckets that collect less light than a larger pixel. Such densely packed sensors are also more prone to electronic and optical cross-talk or interference between the neighboring pixels in the array. All of this reduces the quality of the signal that is coming from the sensor and eventually the final image quality. Cameras such as the EOS-7D Mark II with small pixels often suffer from lack of micro-contrast and pixel-level sharpness as well as excessive grain at higher ISO’s. The noise reduction that is required to clean up the files often annihilates most of the additional detail that has been captured by the smaller pixels. Files from cameras with small pixels need to be sharpened more to compensate for the inherent softness. Trying to get closer to your subject or using a longer high-quality lens will result in a much higher image quality than trying to farm smaller pixels on the sensor.
Let’s now focus on another scenario. Let’s assume we are comparing the EOS-7D Mark II and the EOS-1DX Mark II. Both have 20 mega pixels, obviously the EOS-7D Mark II has much smaller pixels (each pixel’s area is roughly 2.6 times smaller). We attach the EF 400mm f/4 DO IS II to the EOS-7D Mark II, and the EF 600mm f/4 IS II to the EOS-1D X Mark II. Now both cameras capture roughly the same FOV with their sensors (no cropping is needed to match the final images). Are the images equal? Absolutely not.
The 600m lens has a much larger physical aperture, obviously it is a much larger lens. The aperture area is ~2.25 times larger in the 600mm f/4 lens compared to a 400mm f/4 lens. This means the larger sensor in the EOS-1D X Mark II collects 2.25x more light (photons) than the EOS-7D Mark II. The signal to noise ratio in an ideal sensor is proportional to square root of the number of photons collected. The higher the number of photons, the cleaner the image and less grainy it will be. The difference may not visible in good light and lower ISO settings but at high ISO or when raising the dark tones of the image the difference becomes significant. Plus the larger pixels of the EOS-1D X Mark II have a higher highlight saturation limit and better micro-contrast/sharpness. The image from the FF sensor will also have a shallower DOF, again because the aperture of a 600mm f/4 lens is much larger than a 400mm f/4 lens. A shallow DOF is desirable for avian and wildlife images in most cases, as it better isolates the subject from the background. This is why the FF cameras often deliver superior image quality compared to APS-C.
So in conclusion, the sensor’s crop factor does not change the focal length, it does not magnify an image nor does it give you more reach. It is ONLY the pixel size (or commonly referred to by “pixel pitch”) that determines how many pixels will be left on the bird when shooting from a given distance. A 400mm f/4 lens on a APS-C camera will never be the same as a 600mm f/4 lens on a FF camera, the lower the light, the bigger the difference.
I hope this article leaves no confusion on this topic, if you have any questions, please post them in the comments section.
Hello. Great helpful article. I have read many of your articles.
You have a typo in the title beside the first image of the sensor.
Thanks Zenon I will correct it.
You can delete my replies or edit them. I did know how to contact you.
Ari
This is a great great article.
While your are at it, you might add depth of field and perspective to it. That would make this pace excellent resource to link people who are lost with these matters.
Do not get me wrong it is good as it is, but if you give the end of the rope to somebody…
Jarmo
Hi Jarmo,
Thanks for good points. I will cover that too.
this was excellent article….. thanks arash
makes sense and the best explanation I’ve seen on the subject to date.
Thanks for taking the time to put this together Ari. Excellent read.
Hi Ari,
This is the first time that I read the correct explanation for the “crop factor magnification “.
Very informative and detailed.
well done Ari.
Hi Ari,
This is an excellent article! I have often read that pixel size affects image quality but you explanation puts it into easy to understand terms.
Thanks for taking the time to write this.
Wayne
i read somewhere that the crop also changes depth-of-field such that there is MORE depth-of-field. i don’t quite understand that. can you elaborate on this phenomenon? thanks.
Hi,
Crop sensor itself does not change DOF of the lens, just like the focal length depth of field is the property of the optics not the sensor.To get the same FOV though, you need to either move farther back with the crop sensor camera or use a shorter lens when compared to a camera with a FF sensor, both of which mean you will have a deeper DOF.
Hi Ari,
I follow your articles. They are always well done and this is no exception.
I do believe for the majority of folks who try to understand the question they are really talking about FOV and how one lens is equivalent in FOV to another given the different sensor sizes.
I’m also starting to think that for a large number of shooting cases and output cases that the differences in image quality related to the article are not too meaningful. The systems like M 4/3 are getting pretty good. I know there are many situations, particularly small birds in dark settings where the differences are important, but for the majority of wildlife situations perhaps not as important.
Thanks Mike,
Thanks for your comments.
The M/4 system (or any mirrorless system) today is unfortunately not suitable for professional avian photography in my view, especially if a high image quality is required for such subjects as birds in flight. The AF is very primitive, the lenses are short (again remember crop does not change FL), the lag and the EVF simply cannot keep up with demanding BIF.
The lack of image quality is often evident in many cases to those who are critical about image quality and know where to look. For the hobbyist or those who enjoy or record snapshots, I think these systems are good choices as the cost of entry is much lower than a DSLR system today.
best
This article was very helpful to me! I tried to sign up for your email list, but it would not allow me. I had some questions about my kit and wanting to simplify. Thanks! April
Hi April, you are already subscribed to the mailing list.
The 7DII+400mm vs 1DXII+600mm is a good comparison to illustrate the choice. Same number of pixels on the bird, you just have to decide:
The full frame system has roughly 1 stop better low light performance, slightly better resolution, & contrast, and a shallower DoF.
The crop system is 5.5lbs lighter and ~$10,000 less expensive.
Pick your poison.
Hi Patrick,
I am afraid your comparison is too simplistic.
While a 600mm f/4 lens collects 2.25 times or slightly more than a stop of light than a 400mm f/4 lens, the limitation of the 7D2 is the sensors technology that is used in that camera itself. The dark shadows are limited by sensor’s read noise as opposed to shot noise.This limits the camera’s DR and low light capability far more than one stop in actual field use, In practice the 7D2 is pretty much useless above ~ISO 800 for avian photographers who are critical about image quality, while the 1DXII can be easily used at 3200. Couple that with a hit and miss AF of the 7D2 and you have a much less compelling combination.
The 7DII is not going to come close to a 1DX II in terms of overall image quality and AF performance. Some of the images a skilled photographer can capture with the latter combo are almost impossible to capture with the 7D2 combination. Hence the price difference. unfortunately there is no free lunch in this world.
Ari, I didn’t go into AF performance because this blog was nominally just about crop sensors vs full frame sensors, right?
Would you generalize your observed “7DII vs 1DXII” 2-stop advantage to the larger “crops vs full frame” discussion I thought you were trying to address?
In other words, do you want the world to know that, for the same number of pixels on the bird, full frame will have a 2-stop advantage over crop?
I am familiar with the academic details, but the reason myths about “extra reach” and so forth persist is because many people are simply not interested in academics- so a small, generalizable comparison can be handy. To writ, the x rule.
Hi Patrick,
Thanks for your post.
To answer your question about real world advantage of FF vs crop for equal FOV:
There are two types of noise that affect an image, one is the shot noise that is fundamental and scales with the amount of light collected as discussed in the article. However no image sensor is perfect, they all have read noise which itself has several components. The read noise does not depend on the amount of light collected or the sensor size. Usually within the same technology generation, the high density sensors with small pixel pitch have a higher read noise from electrical cross talk. The detail in the dark areas of the image is limited by the read noise.
Another factor is resolution/sharpness, the high density sensors have much higher requirement in terms of the MLA (micro-lens array), CFA (color filter array) and the LPF (Lowe pass filter) that is on the sensor. All of these components will have a higher detrimental effect as the pixels get smaller and smaller.The burden on the optics is higher too in order to resolve for the smaller pixels. This usually shows up as the lack of pixel-level contrast /softness when you view the images at 100%. Thus to get the same quality you will need to sharpen the image more which itself will aggravate noise.
So in practice the difference is more than the theoretical two stops that’s just based on the amount of light collected. It is difficult to provide a general number because it is sensor/manufacturer specific.
In terms of the perceived image quality which is what a photographer cares about, it depends on too many factors and eventually becomes a completely subjective issue.
For the type of photography that I do and the quality that I expect from my RAW files, I usually reject files taken with crop cameras such as the 7D2 or the Nikon D500 above ISO 800 whereas with FF I have no problem going to ISO 3200 and sometimes even 6400. But someone else might find files from the crop camera acceptable even at much higher ISO’s.
Who knew greater-than/less-than brackets wouldn’t render- I meant to say, “the crop-factor x focal-length rule”
Ari hi and thank you for all the effort that you put into your articles.
What’s your opinion regarding diffraction when comparing full frame with crop?
Does diffraction play a significant role to the image quality or it is more of a labatory term?
Regards
George
Hi George
Diffraction can be a limiting factor but it does not depend on the sensor size, it depends on the pixel size. A sensor with smaller pixels is more prone to diffraction. best
hi Ari,
i agree with you and i think that crop factor cameras are good if you dont have supertele lens .
i use mainly a 500F4isII with tc1.4 and 2x with FF
another discussion that you avoided,amybe off topic is the difference between FF cameras..and i think that pixels count a lot.
for my experience in good light conditions(till 1600/2000iso) 5DSr is much much better than 1DXII.in south europe and in some areas of africa to approach birds isnt easy and many times we have to crop on Ps.but also when i dont need crop the 5DSr files are tremendusly sharper than 1DXII…this is my experience,i’m i wrong?
Hi Stefano,
I agree having a higher resolution is desirable as long as the packing of extra pixels doesn’t increase the noise floor of the image sensor itself. I think you are talking about details, in my experience the 1DXII files are sharper than any other camera but it has “only” 20 mega pixels so it doesn’t capture as much detail as the 5DSR. For my applications 20 mega-pixels is enough though since I try no to crop my images too much
I have recently bought a Canon 400 F4 Do 11 and I am using the 7DMark11 and would like to upgrade . I use it mainly for birds but also for mammals what Canon camera would you suggest upgrading to? I have a 1.4x and 2x both 111 version.
I understand that you are considering Nikon but your past experience is Canon
Thanks
Hi Doug, you will love the 5D4, If you want to shoot a lot of action and in-flight shots I recommend a 1DX MKII or even a used 1DX. best
Helpful as always
Thank you!
Hi Ari,
my congratulations for this clear and enlightning topic.
I have two questions:
1) admitting to use the same zoom Canon 100-400 II as is on a 7D mark II, or multiplied by 1.4X III on a 5D Mark IV, I should have a lower magnification (1.3 x (400/560) = 0.92) in the case of the 7D II than in 5D mark IV. Is it correct? This would be another big incentive towards the switch to a FF (now I have an old 7D), admitted that shooting at f/8 with 1.4X would be acceptable for other aspects.
2) I wonder how relevant is the difference in AF performance shooting the same bird in flight with a FOV of an APS-C respect to a FF. In my experience, it could be even easy to follow a small (not too small, anyway) bird in the wiewfinder, than a frame filling subject. On the contrary, metering correctly would be more difficult. What is your experience?
Many thanks in advance, and please apologize me for my English.
Fabrizio
Hi Fabrizio
1) I think you want to compare the following 7D2 vs 5D4 + 1.4X TC. The reach is defined by the number of pixels on the subject follows from : (inverse ratio of pixel pitch) ^2 x (ratio of focal length ) ^2. this means 54/7D2 = (4.1um5.36um)^2 x (1.4)^2 = 1.14 so the 5D4 will have 14% more pixels on the subject.
2) I use manual mode all the time, I never use the camera’s meter as it doesn’t work well for BIF. As for AF the APS-C has better coverage of the AF sensors but the AF system in the Canon 7D2 is not great when it comes to tracking challenging subjects so it negates all the theoretical benefits. The 5D4 AF is slight years ahead in that regard.
Best
Ari,
Without consideration for BIF how would you compare the images of the 7D2 with a 400 f4 as opposed to a 1DXII with the same 400 f4 but with the added addition of a 1.4 teleconverter? Both would have the same number of pixels on the subject. The APS-C sensor would be gathering light using the full light gathering ability of the f4. The FF would be shooting at f5.6. It would, therefore, be at a disadvantage, however, I suspect the positive effect of the increased size of the pixels should outway the advantage that the increased f-stop gives to the smaller sensor.
The above situation presents itself when one lens, such as the Canon Duo (or any telephoto), is shared with 2 bodies, one with a small sensor and one with a large sensor, as may be the case when traveling by air. As such it may make sense to also leave one body at home if the results are very similar. I just ordered the 1DX2 as opposed to the 5D IV. This will be my primary body before I venture into the high-end Nikon systems. I do have the D500 and it outperforms the 7DII. This is not quite about the 7DII or even the eventual 7DIII. It is more about the D500 and the D5 with, let us say, the Nikon 500 f4 VR. As of this moment, you have had considerable experience with Canon systems and not as much with Nikon but the physics should be the same.
Once again I value and respect your insight.
Hi Anthony,
in your example both sensors receive the same amount of light and all things being equal on paper they would perform similarly, however this is clearly not the case when using a 7D2. The 7D2 image sensor uses outdated technology, it is known for poor dynamic range, elevated high-ISO noise and loss of sharpness. The sensor itself adds read noise often seen as banding which limits the dynamic range, and the camera struggles to deliver the same image quality as the 1DX II. I would personally never use a 7D2 under any condition and for any purpose as it falls below my standards but that’s me. if I had to use a 7D2 I would probably give up photography and do something else 🙂
In the case of of Nikon cameras the DX sensors such as the one used in the D500 are superior to that of the 7D2 so the difference is smaller but still visible at high ISO.
You nailed it!
Everything you said about the 7D2 is true and that is why even a slower full framed camera is a better choice for birds. Even for birds in flight. The 5D Mark 4 is an example when you consider that 7 frames/sec seems slow compared to the 7D2’s 10 frames/sec but what good is speed when seven to eight, if not all ten of those frames, are not what you expected and therefore not what you want. Nikon never was very good at producing a cropped sensor until they created the D500. At least with that camera, you get what you expect, even if you would want more. In the final analysis, it appears that top of the line FF cameras along with good glass has the edge. What many of us are waiting for are cameras, such as the current flagships, with higher resolution sensors without sacrificing speed and/or buffer capacity.
Thanks for your input.
In the Nikon world, it appears that the small pixel size of the D850 performs almost as well as the large pixels of the D5. This is not the same regarding the 5DRS as opposed to the 1DX2. The increased resolution of the former system does not compromise the image with the same amount of noise as the Canon system does. Canon seems to have made some progress with the 5D4 in this regard but never put enough computing horsepower in that camera to make better comparisons between the actual sensors.
The high ISO performance of the D850 is great but nit as good as the D5.
[…] sensor) body, before getting into image quality I highly recommend you read my explanation of the crop factor here to understand this topic. The pixel pitch of the D500 sensor is identical to the D850 so the […]
Hi Ari,
Thanks for the article. I had been using Nikon AF 30-700 with D7000 and currently use Nikon 200-500 for bird photography with D7000. I am now considering Nikon Z5 (FF) and Z50 (Cropped frame). As I understand, with Z5, my object will proportionately occupy less part of the frame than what it will occupy with Z50. It means I will have to apply higher crop while processing the image to get the details of the object (e.g., a small bird). If I were to use Nikon 200-500 with Z5 and Z50 to capture a small bird and then crop the images to get the same sized bird in both the images, will I get a better image with Z5 or worse?
Thanks, in anticipation.
Shirish
Hi Shirish, thanks for your comments I don’t have any experience with the cameras you mention but since they are both about 20 mega pixels you will need to crop the FF image to get the same detail as the cropped sensor if shooting from the same distance. if you can get closer the FF will definitely have a better image quality but if not, the image quality could be comparable as the Nikon sensors are generally good in terms of read noise. The other factor is AF, the camera with the better AF/ faster frame rate will likely give better results overall.