Examining the Myths and Confusion Around Crop Factor Equivilancy

There are countless videos and forum threads discussing and debating about the principles of crop factor, depth of field, and sensor size. However if you are the type to geek out over the math and physics of photography then this is the video for you. This is no simple examination, at 35 minutes long it requires some advanced knowledge on camera sensors.

Blake Evans goes deep into the differences between full frame and crop sensors and why there is so much confusion. With diagrams, examples and detailed explanations Evans gives you everything you need to get a true equivalent image from the variety of sensors.

Behind all the details and diagrams is Evans simple “recipe” for getting true equivalence across all sensors. This equivalence as he demonstrates is not just equal field of view or exposure but in fact equal everything: lens, aperture, distance, and depth of field. This is done by applying the crop factor to the focal length, aperture and ISO.

FOCAL LENGTH = Apply Crop Factor
APERTURE = Apply Crop Factor
ISO = Apply Crop Factor²

Although this formula seems simple and Evans provides more than enough to demonstrate the evidence behind his statements if you take a look at the comments on the video this is still a hotly debated subject. I highly recommend trying to make it through the full 35 minutes. It's clear from the video and comments that there is a lot of confusion surrounding this topic but for the vast majority of photographers this might just be useful with all the options offered today in sensors.

[via No Film School]

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33 Comments

Kyle Medina's picture

You trying to cause a shit storm?

this is still controversial? man... photographers are kinda bad at math

Mateusz Antonowicz's picture

Some are bad, and some are hiding from the truth, in a sense, that their smaller sensor camera is at disadvantage from start, and also that lenses for those smaller sensor cameras are being sold without stating full equivalence. Many manufacturers are actually lying to customers by converting focal length and leaving aperture as is. So some brand is selling 50mm f0.9 or something, and suddenly it's the best 50mm on market, because FF brands are not selling f0.9. I have hear many people who defend their gear like a rabid animal, and this topic really strucks a nerve for those people.

It's important to educate people, so they know what to expect when they buy given system. They might compare Nikon FF with Olympus M43, and they see lenses are superior on M43 [aperture]. And then, they buy the gear and are not getting the results they were hoping for.

Anonymous's picture

It's important for the manufacturers to educate people. Personally, I don't have time to educate others regarding gear...that's their job. If you spend all your time doing homework for others, you'd better get used to them sitting next to you for the test. :-/

Mateusz Antonowicz's picture

Actually manufacturers gain from people who aren't educated, so it's up to people to help each other and not get ripped off. I do agree though, that not every person that is educated has the duty to do it. I am learning new things as I go, yet I am not writing blogs or articles about this and that, simply because I have spent time and money to gain knowledge, and I'd rather spend more time gaining profits using that knowledge. Still, if someone asks, then I wont be a dick and say that I don't know, or wont tell. If it's relatively simple matter then I am happy to help others. And I also agree on the matter, that if you are too kind, people tend to try to use you. Simply put, people are stupid and ungracious, and those don't deserve my time, but people with genuine will to learn are different matter, it's really nice to see someone willing to learn, but thinks for himself, rather than being lazy and getting all job done without lifting a finger.

I am really frustrated though, that focal length and F stop aren't changed to something like field of view and transmission, or maybe DoF @ wide open from 10m or something. They could manufacture new number, like f stop, that dictates the depth of field when paired with certain sensor size, then we could use number + x, or - x to stop down the lens. It might make little to no sense, but it would actually show everything, before you even take a picture. You got horizontal/vertical field of view and a constant number which would dictate how much is in focus @ close focus, or 10m, or whatever. It would also be good to actually imprint T stop too on lenses, not just cinema ones. Nowadays it's kinda important thing to know.

Anonymous's picture

In my defense, I don't want to bore anyone so I don't give detailed or complete opinions. I agree with everything you've said in your first paragraph with a few provisions. If you're a manufacturer and your product has an advantage over the competition, which isn't immediately obvious (FF over APS-C sensor), it is up to you to educate consumers. That, of course, doesn't alleviate the consumers need to educate themselves and from as many sources as possible.

Mateusz Antonowicz's picture

Yeah, I am not condemning anyone for not sharing knowledge, don't get me wrong. It's OK to ignore, if you help you might seem like a kind person, not much more, so no worries, healthy dose of egoism is recommended for everyday life :)

Anonymous's picture

I help when I think it will. Have you ever gone into a Home Depot and ask someone about electrical stuff and get the reply, 'I actually work in the paint dept. but I'll help you'? They're NOT going to help you. I don't ever want to be that guy! ;-)

Mateusz Antonowicz's picture

So much true.

So I think I've got this?? A Canon with a crop sensor the factor is 1.6. Would these figures be correct? FF 80mm, f3.6, ISO 256 = CS 50mm, f2, ISO 100.

if your objective is using to achieve the same angle of view and the same exposure for both cameras, then yes your math is correct.

Kirk Darling's picture

"FF 80mm, f3.6, ISO 256 = CS 50mm, f2, ISO 100."

If all you are trying to do is equate the angle of view, the only thing you had to make equivalent was the lens focal length. You don't have to change the ISO or aperture.

If you were to measure the exposure with a handheld meter, that same combination of aperture, shutter speed, and ISO would work for any camera and any lens (ignoring T-stop differences and bellows factors, which aren't necessary to go into in this conversation).

Dallas Dahms's picture

This is 100% bollocks.

Equivalence is a crutch for the creatively challenged to play a game called "my camera is better than yours, ergo I must be a better photographer".

Use the damn camera for what it is intended for and stop comparing it to what other cameras do. Light is light and exposure is exposure. The only thing that changes between formats is depth of field. That's it. Chose one that works for you and shut up about it.

Yep. I'm still trying to figure out how in the film era they were able to make super tiny 35mm cameras but in the digital era that still hasn't happened with 35mm sensors. Not even close. My 35mm Olympus Stylus Epic was the size of a Sony RX100. Super sharp 35mm lens and weatherproof. I think it was only $100 or so.

Mateusz Antonowicz's picture

It's actually very informative when you operate on few cameras with different sensors. Trying to nail same exposure or the same frame, or the same DoF with crop and FF is not really that easy without knowing all this. It's also a major factor when buying a system, because sensor size will dictate what lenses you can use [the larger the sensor, the wider FOV and shallower DoF you can get]. Let's say you have 70-200/2.8 on FF, then you would need 35-100/1.4 on M43 to do the same thing, but there is no such equivalence lens on market. Same goes for most 'pro' glass, like 35 1.4 [would need 17.5/0.7, again, no such glass exists]. So all in all it's 100% useful info, if you want to make an educated purchase, or if you want to know what to expect of given lens on given system.

Dallas Dahms's picture

Why do you need to make anything "equivalent" for depth of field? If this is the logic, then surely you should compare the 35mm system to 6x7 and wonder why you are not getting such short d.o.f. with your 35mm lenses when compared to the 6x7 lenses?

Equivalence as a theory is counter-productive and has caused more damage to the thinking of photographers who don't understand these concepts than it has done any good.

For the record, Olympus has a 35-100mm f/2.0 lens that makes any Canon or Nikon "equivalent" lens look seriously inferior, especially when shot at a wide open aperture. I have owned 70-200mm 2.8's from Canon and Nikon and when I used the Olympus 35-100mm I was, as they say, gobsmacked.

Discount the smaller formats at your peril...

Mateusz Antonowicz's picture

Olympus is 2x crop so it's 70-200 f4 lens, nothing to write home about. With that thinking, you aren't grasping the concept I guess. Go step by step again, and you will see how and why your 35-100mm can be better, but it wont produce the same frame. Stop down 70-200 to f4 and I am sure it would beat that zoom [same DoF with f2 on M43 and f4 on FF].

I am not saying it's a bad lens, actually this one is great, still I must add that AF [sports] it's where it does not shine. Believe me, I have tried so many cameras and lenses, that I know where comparisons between systems are just moot.

I actually don't want to make anything of the same DoF, just stating that some people would see a pic made by 85 f1.2 on FF and they would have hard time reproducing that on M43, it's not a bad thing, it's about knowing limitations. And those limits only work really in extreme cases, both for FF and crops, with FF you can go way shallower, with smaller you can get way wider DoF without diffraction kicking in.

And finally, I am not discounting anything. I am stating why this matter is of any use to us photographers. I am really curious how you would make ultra wide pics with smaller sensor, but at the same time, I am wondering how you could produce a pic handheld for 2s on FF. Each system has strengths and weaknesses. So all in all, just want you to know that I am not bashing ANY system, I am just kinda mad about manufacturers calculating Focal Length and not eq aperture. This is lying to a customer, and those articles help people who struggle to understand those things. As a photographer, you pick a tool and you use it, and we all know well you got to choose a right tool for given job, that means there are moments larger sensors shine, and there are moments where smaller ones do.

PS: medium format lenses have calculated mm and f number, they are what they say they are, so there is no conflict here. Sure you can do eq and find a lens on FF that would produce the same frame and DoF, but MF does not lie about lens 'stats', so there is little point in dwelling on the matter.

Dallas Dahms's picture

The Olympus 35-70/2.0 is NOT an f/4 lens. It is an f/2.0 lens. Period. Nothing else to discuss in that regard. And it is not a 70-200mm lens either. It is a 35-100mm lens. It simply has the same angle of view as a 70-200mm on 135.

And micro four thirds is NOT a 2x "crop". The system doesn't crop anything off its own lenses. Micro four thirds system is "full frame" within itself. Period. If you put a lens from a larger format system onto an m43 body only then does it become a "crop" of that lens.

Regarding depth of field on f/1.2 lenses on 135: that is so shallow as to be useless in reality. In fact, one of the biggest problems I had with the 135 system is that most of the fast lenses that cost an arm and a leg couldn't be shot with at their widest aperture because they got so soft. Hardly something I would want to emulate.

Mateusz Antonowicz's picture

So what you are saying that if I were to mount 35mm f2 lens on FF I would have the same characteristics as your 25-70 f2.0 @30mm? That is simply not true, and you can test it. There is no such thing as 35mm lens but with angle of view as 70mm lens. You can't cheat physics. Imagine that there is no sensor behind that lens, and you shine the light. The image on the wall would equate to 70mm field of view, and f4 as far as DoF goes. It would transmit light as f2 lens, true, but none of the characteristics as f2, because it would have 70mm field of view. So in that regard you f2 is ONLY brightness. It's easy to test if you use 35mm f2 lens for FF and mount it on M43. What angle of view would you have? What f stop? Total light the lens gathers will not be equal to FF, that's why you would use speed booster to concentrate light on smaller sensor. And what would you get? wider FoV AND increased brightness, because the light that was outside of sensor, now falls on it. So you are wrong with what you say, again you can not cheat physics. There is no way to to it. 35mm will always have the same FoV, as showed with 'no sensor' scenario. And if you shine and see something other than 35mm FoV, then it is NOT a 35mm lens, no matter what you put behind it.

And as to your shallow DoF. If you used cheap lenses, then yeah they are soft, but try 105mm 1.4 for Nikon, 85mm 1.4, 35mm 1.2L etc. They are tack sharp @ wide open. And your personal feelings and lack of skill to operate shallow DoF doesn't create an argument, it only shows that you either never actually shot on FF, or just you lack creative vision or skills to properly use shallow DoF.

Finally, yeah...

https://www.dpreview.com/forums/thread/3073156

Soft and unusable, better use 5.6 lenses.

Dallas Dahms's picture

Again, you're trying desperately to equate one system with another and in the process you are shooting your own argument in the foot. There is NO equivalence other than angles of view. It's not a discussion. It's not an argument. Each system operates independently. Pick one that does what you want it to do. Stop trying to compare them. You will only run yourself into deeper circles of confusion. (see what I did there?)

Mateusz Antonowicz's picture

There is equivalence in angle of view, exposure and depth of field. And there is no fallacy in anything I said, feel free to test it yourself, I have. Lens is an optical instrument, it has certain properties, independent of what sensor does. Again, you cannot cheat physics. If you think your 35mm is equal to 70mm without changing any other parameters, then you are deluding yourself. You cannot just change focal length without changing the basic parameters of lens. And there is no such thing as an 'independent system', you can use adapters and fit any lens to any system, the results are clear as day, you just seem to be in a self contained bubble, covering your eyes and ears shouting 'this is not an argument, there is discussion'. Well there is, and truth is, you are wrong as to your statements. You cannot have cake and eat it too.

Also, please don't embarrass yourself with circle of confusion, if you knew what that is, we wouldn't have this conversation at all. You just showed that you have no idea about the inner workings of cameras. So stay with your 70-200 f4 eq lens and enjoy. If you still think it's something else, then sorry bub, you are just wrong.

http://ptitboul.free.fr/lenses-and-formats.html

Perhaps this site is wrong as well? That and countless other sites that try to educate people to make educated purchases. Clearly you are immune to knowledge, since everyone knows this by now, yet you still struggle and come up with silly ideas such as 35mm lens with 70mm field of view. Just listen to yourself.

Dallas Dahms's picture

Do you realise that you are actually arguing with yourself?

Mateusz Antonowicz's picture

Nope, I am just trying to dispel you from false information, shed a light on this matter. I have given you examples as well as explanation, I really don't see how is that 'arguing with myself'. If you wish to be left uneducated, then so be it, I am not going to force anything on you. Some people still believe Earth is 10000 years old, or its flat, it's hard to argue with them, as they don't accept proof, I don't mean to insult you, but you seem ignorant in the face of evidence. Not much I can do here, if you ever want to learn more, I'd be happy to have a chat with you.

Dallas Dahms's picture

You are patronising to the nth. A conversation with you is not something I wish to have. I still don't know what I might have said that has irked you.

Mateusz Antonowicz's picture

I am just bringing down the tone to match your level. And what might have you said? Well, let's see... Outward lying about the state of things, or just ignorant to the truth. I wanted to correct you, seeing as you are wrong, but you don't seem to accept this fact about our world. This makes me think you are really close minded person, who chooses belief over facts. Your 'faith' doesn't change the truth, but if you feel better lying to yourself, then so be it. Just don't expect people to take you seriously if you do. You realise that everything you say/type is stored somewhere and possibly will be used against you in future? That's why I wouldn't spread misconceptions or plain lies,because you only ruin your reputation by doing so. I mean it's your life, and your work, but if I saw person saying that Earth is flat, I wouldn't bother to hire him for anything. Think about it, I wish you no harm. But I see you are biased against me, so I won't bother you. Have a nice life.

Dallas Dahms's picture

Are you drunk? What exactly am I wrong about? Point it out to me and then maybe you'd have an argument on your hands but all I read from you is blah-blah-blah-you're wrong. About what exactly?

Mateusz Antonowicz's picture

You're wrong about the whole topic. You think that you can multiply focal length without any other conversions, you said it yourself, that your lens is 35-100 f2, I have provided you with info, that it isn't, so you went around and said, that it is 35mm with 70mm field of view, and that this is the only thing that is being equated [fov], this is simply not true at all. What you have is a lens that has characteristics [framing, depth of field, light transmission etc] as 70-200mm f4 lens. I don't say that it's a bad thing, I am only correcting your mistake in assessing the gear. That's why it is important to know this stuff. Manufacturers are doing what you do, multiply focal without any other conversions, and you can end up with some 45mm 0.9 lens, but is anything like such lens? Of course not. And the whole point is knowing what to expect from your gear, so that you wont be surprised or dissapointed. I am in no way saying that this format is better than that format, all I am saying is that math needs to be done in order to really know what you are using. Think of it this way, you have a picture shot on a FF camera with certain lens and certain settings. Now you wish to replicate this frame, DoF, angle of view etc., using M43, how would you go about that? It seems to me that your answer would be 'trial and error', but it's much simpler than that. And if you know how lens characteristics translate to other formats, then you can make a better, educated purchase on future lens. You will do conversion, and decide then, because as I said before, manufacturers are lying in our face with lenses stats. So this, you are wrong about all of this, and your earlier comments prove it. Again, I don't want to point fingers and blame anyone, you asked, I replied. I hope you will accept this fact about lenses and formats, and what is going on when you change a sensor. For very in-depth explanation as to why it happens and why those lenses seem faster, you can visit this link:

https://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why...

It has images, compared side by side, with commentary etc. That person is very well versed in this topic, I can assure you that this is all valid info, and not some weird theories.

Kirk Darling's picture

The entire concept of "crop" is irrelevant for a photographer who uses only one format. It's barely relevant for anyone else. "Back in the day" when we shot with medium and large format cameras that used different format backs for the same camera, nobody sat and calculated "crop factors" when they swapped backs.

What's missing from general understanding these days is the concept of "normal lens" for a given format. The "normal lens" is the shortest approximate focal length for a given format that draws the image in a generally "normal" perspective. That happens to be roughly equivalent to the diagonal of the format.

For any given format, we only needed to know the "normal" lens for that format, then selected a different lens based on how we wanted to change the image from its appearance with the normal lens. Want a wider angle? Use a shorter lens than "normal." Want a narrower angle? Use a longer lens than normal.

If we used more than one format, we knew the "normal" lens for any format we used. Any kind of calculation when changing formats was merely a quick and rough calculation (we aren't doing a moon landing) based on the difference from normal of the lens we were using on one format to the same difference from normal we want on the second format.

So I was shooting with a 100mm lens on a 35mm camera. That was about 2x normal. Now I'm going to use my 6x7 camera, which has a normal focal length lens of around 90mm. So I pull out my 180mm lens for that camera to match (roughly--this isn't rocket science) the field of view I was shooting on the 35mm camera.

We don't have to get into calculating multiple decimal places here, we just need to spend time using the danged equipment and get to know what it does.

Mateusz Antonowicz's picture

But 'back then' there was no bullshit with labelling lenses incorrectly. This is a major thing actually, yes one thing is knowing what to expect of lens, but other thing is how manufacturer converts focal length leaving everything else intact. This is not fair in the least, and people should know this stuff, so they wont be scammed by 'false advertisements'. While most people see math math math and people who say that their gear is superior because this and that, others can actually learn few things and know the limitations of lens/system etc. It wasn't at all useful in the past, just because no one had the idea to label MF lens as FF lens etc., and exactly this is happening now in crop or smaller.

Michael DeStefano's picture

I think that is the point though nowadays a lot of photographers are shooting multiple cameras and sensors. Plenty of people are shooting both canon and a sony body. as mirror less and 4/3rd cameras get better plenty of people are using both as they transition. If people are comparing the quality of those cameras it helps to have equivalence.

However I do agree to the point that in real world usage this matters very little. I myself shoot with a 5dm4 and 7dm2 at the same time and never care that they have different sensor sizes.