Photography / Tips and Solutions

Understanding Crop Factor

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There is a great deal of confusion surrounding crop factor, and it is particularly difficult to explain, but let’s give it a try, shall we?

Before we dive in, let me dispel two vicious rumors related to crop factor that are circulating through the photography (Internet) world today:

  1. Crop factor does NOT affect a lens’s focal length.
  2. Crop factor does NOT affect a lens’s aperture.

Before you scroll to the bottom of the screen to leave a comment to the contrary, let me explain why I am stating these facts…

Focal Length The focal length of a lens, expressed in millimeters, is the distance along the lens’s optically central axis (beginning at the rear nodal point) to the image plane in the camera (often illustrated by a "Φ" on the top plate of a camera body) when the lens is focused at infinity. The image plane in the camera is where you will find your digital sensor or film plate.

Therefore, a 50mm lens can measure 50mm from the point where light rays begin to exit the lens in the same direction as they entered the lens until they arrive on the image plane. Some “pancake” lenses and mirror lenses have optical tricks to shorten them, but in general, the focal length is that physical measurement.

A zoom lens can change the physical focal length of a lens. Sometimes this movement is contained inside the lens—the lens body does not physically change length—and other times the lens does change its size.

However, regardless of what kind of camera or sensor you place behind the lens, the focal length will not change just because you have a larger or smaller sensor or frame of film. I will explain later how sensor size (or film size) changes the equivalent focal length—not the true focal length of the lens.

Aperture  is the size of the opening in the lens. Some lenses have fixed apertures that cannot be changed, but most photographic lenses have variable apertures to control the amount of light entering the lens. This opening is regulated by a diaphragm comprising blades that can be adjusted to vary the size of the hole (aperture) through which the light passes.

In photography, aperture is expressed as a ratio of the focal length to the diameter of the aperture opening. The ratio is commonly referred to as an f/number, f/stop, focal ratio, f/ratio, or relative aperture.

This ratio is based on physical measurements and is completely independent of the size of the camera’s sensor or the size of the film you are shooting. Sensor size has an effect on depth of field, but not because it changes aperture. Aperture is independent of film frame or sensor size.

35mm Format

The first thing to know about crop factor is that, as with all “factors,” we need to have a base reference from which to work. In the photography world, this reference is a piece of 135 film. In the digital photography world, “full-frame” sensors are the same size as this film; a film frame with a width of 35mm. Cameras of this photography format are collectively known as “35mm cameras.”

A 35mm film strip measures 35mm across
 

One source of crop factor confusion is the use of “35mm” when discussing the reference. The value in this case is used not as a focal-length measurement, but as a measurement of the dimensions the frame of film. The film image area measures 24 x 36mm, but the strip is 35mm wide. So, when you think of “35mm” when it is used in reference to film or the size of a camera sensor, know that you are not referring to lens focal length. You can mount a lens of any focal length, even a 35mm lens, on a 35mm camera. The focal length is the focal length. Film and sensor dimensions are different.

For years, the 35mm camera has been, by far, the world’s most popular camera format. Because of this, for those of us who grew up in the world of 35mm cameras, when we think of the field of view given by a lens of a certain focal length, we can visualize what the photograph should look like. In the 35mm camera world, a lens with a focal length of around 50mm will provide a “normal” view with its human-eye-like field of view. Lenses with shorter focal lengths will provide a wider view and lenses with longer focal lengths will provide narrower or telephoto views.

Digital Sensors

Life was simple back when almost everyone was shooting 35mm cameras and 35mm film. Sure, there were those making magic with medium format and large format cameras, and there were point-and-shoot cameras that took specially made smaller films. My first camera, handed down from my grandmother, was a Kodak Instamatic 30, with its 13 x 17mm 110 film. Back then, no one really paid attention to “crop factor,” even though it existed. I’d bet most photographers didn’t know the dimensions of their 110 film, nor did they know the focal length of the tiny lenses! You just looked through the camera and took the picture it gave you.

Then, digital photography arrived. In its early days, most sensors were smaller than 35mm film, and a virtual can of worms was opened. Why? Because the sensors were smaller than 35mm film, the images seen through a lens of any particular focal length had a different field of view than that of the same lens on a 35mm film camera. Suddenly, a 50mm lens no longer had a “normal” field of view; it was a bit more of a telephoto.

The cropped sensor “sees” a narrower field of view
 

If you never shot 35mm film, this was no big deal because your mind’s eye did not have a 35mm film reference for different lenses. But photographers entering digital imaging decided that they needed to know the “35mm equivalent” field of view of various lenses when attached to a camera with a digital sensor smaller than 35mm film. The reality of it is, “crop factor” serves to translate a measurement into a language in which many of today’s photographers were never fluent to begin with. And, because of this, many of you out there have been very confused and frustrated by the mention of crop factor. Hopefully this article will end your confusion!

Crop Factor

A round lens produces a circular image circle—not rectangular. The sensor, or film, at the back of the camera captures a rectangular portion of this image circle. When we use 35mm film as a standard, any camera with a sensor smaller than a frame of 35mm film will cover a smaller portion of the image circle produced by a given lens and will thereby change the field of view of that lens. This is the “crop” part of the crop factor.

However, because traditionally, the field of view produced by a given lens has been described not as a measurement of degrees, but by the focal length (kind of the “name”) of the lens, we need to translate the cropped field of view into an equivalent lens focal length.

For example, if you attach a 50mm lens to a camera with a smaller-than-35mm film sensor, you will have to multiply the focal length of that 50mm lens by a factor derived from the size differential of the sensor to calculate the 35mm equivalent focal length. This will then give you the means to figure out the lens’s field of view based on that new equivalent focal length. This is the “factor” part of crop factor.

This multiplication factor is the ratio of the size of the digital sensor to the dimensions of the 35mm film negative.

Formula: The diagonal of a rectangle can be determined by a2+ b2 = c2

Full Frame: 24mm2 + 36mm2 = c2

576 +1296 = 1872

Square root of 1872 = 43.3mm

Full-Frame or 35mm Diagonal / Crop Sensor Diagonal = Crop Factor

So, if you have a camera with an APS-C-sized sensor (circa 15.6 x 23.5mm or 14.8 x 22.2 on Canon), plug in the numbers and you will get a crop factor of 1.5x (or 1.6x for Canon).

Then, to find the equivalent focal length of the new field of view afforded by the smaller APS-C sensor, multiply the true focal length of the lens by 1.5x to get the 35mm equivalent focal length of the lens. A 50mm lens on a camera with a 1.5x crop factor APS-C sensor gives a field of view equivalent to that of a 75mm lens on a full-frame or 35mm film camera.

Remember, the actual focal length of the lens is unchanged, as is its aperture.

In our example, if you weren’t familiar with a 50mm lens’s field of view in the first place, this doesn’t really matter. But if you were familiar with the 50mm lens’s field of view, you will know that this same lens, when placed in front of the smaller sensor, has a narrower field of view than your normal vision has.

A comparison of relative sensor sizes.

 

If you have a zoom lens on a smaller-than-full-frame camera, you can figure out the effective focal-length equivalent by multiplying both focal length numbers by the crop factor. For example, a 70-200mm lens becomes a virtual 105-300mm lens on a 1.5x APS-C sensor.

Cameras with sensors or films larger than a 35mm frame will have sub-one crop factors. For instance, a medium-format Pentax 645Z’s sensor measures 33 x 44mm. This gives it a crop factor of 0.78x. A 50mm lens on this Pentax camera gives an equivalent field of view of a 39mm lens.

Full-frame versus The Rest

The crop factor discussion inevitably leads us to the full-frame versus smaller-sensor debate. For my take, click here.

So as not to drive down the well-trodden path here, in summary, full-frame cameras are ideal for landscape images because there is no crop factor and wide-angle lenses maintain their wide-angle field of view. Smaller-sensor cameras give lenses a virtual telephoto effect that is ideal for some sports, wildlife, and macro work. Both formats have advantages and disadvantages.

Another thing to mention: there are “regular” lenses and there are lenses specifically designed to operate on smaller-sensor cameras. These small-sensor lenses may not work well on their full-frame cousins. On a 35mm film or full-frame digital camera, you may experience heavy vignetting. If the small-sensor lens does work on a full-frame digital camera, the camera might simulate the smaller sensor the lens was designed for and automatically provide the crop factor field of view. A regular lens will work happily on a full-frame digital, 35mm film, or smaller-sensor camera. The crop factor will only apply to a lens if it is used on a small-sensor camera. Today, some manufacturers refer to their “regular” lenses as “full-frame lenses” to emphasize that they are not designed specifically for smaller-sensor cameras. But, before digital photography, all 35mm format lenses were “full-frame.”

The Final Word

Crop factor is really quite simple. The confusing thing is that, as I said earlier, it exists to translate an angular measurement (degrees of field of view) virtually into a linear measurement (millimeters of lens focal length) so that old-school 35mm photographers can figure out the real field of view of a lens based on an equivalent focal length resulting from using sensors smaller than 35mm film. Get it? Got it. Good!

I suppose that is useful in many ways, but I have seen many frustrated photographers over the years try to understand and explain this concept. Sprinkle in some bogus information on the Web about magically changing focal lengths and apertures, and everything has become a mess!

I hope this has cleared things up for those who are new to photography or who were confused a few minutes ago. If not, I stand by to take your questions! And, in case you were wondering, the Instamatic 110 film camera has a crop factor of 2x. 

For more information about the theory behind crop factor, be sure to watch this engrossing video.

 

192 Comments

My question concerns the distortion. I've read that 50mm is a good lens to eliminate distortion. I have a dx3100. Will a 35mm on the dx eliminate distortion the same way 50mm does on a full frame? Or do i still need the 50mm on the dx . I like street photography and candid portrait shots of family, friends, and strangers. I sometime use them for oil paintings so I would like the photo to have less distortion. I travel and don't want to carry a lot so I'm looking to get a fixed lens for the DX for taking general landscape, people.  I'm considering buying a new mirrorless. But they're expensive and I'm not sure if I'd be happy with EVF view finder or not. I would love the x100f but I'm worried about the distortion. Also I really don't like to get too close to my 'subjects'.

Hi maureen,

Good question, but there are several different lens "distortions" that happen in the world of physics. Based on your amplifying information, I believe you are asking about distortion caused by shooting wide-angle lenses at close ranges that cause very unflattering portraits. This distortion is actually caused by the subject-to-lens distance...not the focal length of the lens. Therefore, any lens, aside from a fisheye, can be used so that faces are not distorted.

Assuming we are talking about that, you should be good to go with either the 50mm or 35mm lens on APS-C so long as you aren't getting extremely close to your subject. I shoot APS-C and do portraits with a 35mm lens all the time without issue. The X100F would work for you as well, again, as long as you aren't getting too close. For casual portraits and street photography, it's lens is great.

For an illustration of this kind of distortion, see this article: https://www.bhphotovideo.com/explora/photography/tips-and-solutions/perspective-distortion-photographic-composition

Please let me know if you have follow-up questions. And, sorry for the delay in replying...we were closed all of last week.

Todd, I just found this article, read almost all, and read the Q&A back about six months.  I THINK this wasn't answered.  If it was, my apologies.

I am considering Canon's EOS 77d camera, APS-C.  When I look through the view finder will I see the FULL FRAME image or will I see the CROPPED image that I will record?

Hey Steve,

Actually, that is a good question that I do not think we have specifically addressed.

On an APS-C DSLR, unless it is a really messed up APS-C camera, the view in the viewfinder will show you the approximate field of view of the sensor. Check the specs, some show 100% of the image, and some slightly less, but, you will NOT see a full-frame image that shows a smaller field of view inside grid lines or something. You see basically what you get, to use the old adage.

Not to confuse you, but to inform all...On a full frame camera, you see the full-frame field of view, and, if you attached an APS-C-specific lens, the camera might show you some electronic grid lines indicating the smaller APS-C field of view.

Thanks for stopping by! Let me know if you have more questions!

Hi Todd thanks for the article. I found it very helpful, and realized I had been believing the wrong thing for a couple years now.  I still have a few questions though that I was hoping you could answer.  Right now I'm shooting on an old Canon t2i (APS-C), and would like to upgrade to full-frame to better pursue landscape photography, but can't really afford the new body and new lenses all at once.  If I buy a lens to fit a full-frame camera, will I get the same image with the EF 50mm f/1.2L USM when compared to the EF 50mm f/1.4 USM I have now? Or does the lens designed for the crop factor account for the cropped region and provide a wider field of view? I know that 50mm on the crop sensor is similar to the 85mm on a full-frame, but do the lenses behave any differently because they were designed for different sensor sizes?

Hey Matt,

You are welcome! I am glad this article cleared some things up for you!

To answer your questions:

Yes, the 50mm f/1.2L will give the same field of view as the 50mm f/1.4 lens—a 50mm lens has the same angle of view when placed before the same sized sensor. The field of view changes for both lenses if the sensor size changes.

A lens designed for a smaller sensor will likely produce a smaller image circle, but the angle of view is determined by the focal length (more or less).

If you want proof, look at these two Nikon 35mm f/1.8 lenses. One is a DX lens (same as the Canon EF-S), the other is not.

https://www.bhphotovideo.com/c/product/1023361-USA/nikon_2215_af_s_nikkor_35mm_f_1_8g.html

https://www.bhphotovideo.com/c/product/606792-USA/Nikon_2183_AF_S_Nikkor_35mm_f_1_8G.html

Check the specs. Both produce an angle of view of 63 degrees. Put them both on a DX camera, and the field of view will be identical.

Do they behave differently on a full-frame camera? Yes, because the DX lens produces a smaller image circle, you would see the same field of view, but significant vignetting when placed before a full-frame sensor.

I hope that all makes sense!

Let me know if you have follow-ups and thanks for reading!

I'm moving from a Sigma 17-50mm on my Canon 80D (APS-C) to a GH5 (M4/3) with a Metabones XL speedbooster.  What full frame zoom lens should I get to be somewhat equivalent to the range I had with the 17-55mm?  Or am I out of luck?  Between the crop factor adjustment and the speedbooster, it's just too much math for my brain!  :-)

Thanks!

Hey Erik,

Sorry for the delay in replying...I was on vacation last week.

Are you looking to keep using the speed booster? Or do you want to slap on the Olympus 12-40mm f/2.8 or Panasonic 12-35mm f/2.8 lens and fuggetaboutit?

If you are using the 0.64x adapter crop factor, you would need the equivalent of an 11-35mm lens to get to 17-55mm. There is a Canon 16-35mm f/2.8L lens (two versions), the Canon 16-35mm f/4L, Canon 11-24mm f/4L, and more including lenses from Tokina, Tamron, and Sigma.

Standing by for follow-ups!

Hi Todd, 

Great article thank you!  I have a question though.  I am working with a sony fs5 that has a super 35mm sensor, to expose in SLog2 I have to over expose the image by two stops.  The problem I have is that I am exposing my Canon 24-70mm f2.8 lense at f2.8 then calculating the over exposure by two stops using the shutter speed.  Due to the crop factor between the lens and the sensor should I be exposing based on the f2.8 of the lens or the aperture with the crop factor added, which I think is about 1.5 in this case?  Basically does the crop factor between camera sensor and lens mean that there is essentially less light entering the camera and how can I expose correctly taking this into account?

I'd really love any help as I can't find much on this!

Thanks 

Luke

Hey Luke,

Sorry for the delay...I was on vacation last week.

I am not a video expert, but I do know that the light-gathering power of an f/2.8 aperture lens is the same regardless of the sensor size of the camera—if it was different, all exposure calculations would be forever changed and photography would become a mathematical mess.

Thanks for stopping by and sorry for the delay in getting back to you!

Hi Todd,

Thank you for the article. Along with reading a few others, I have somehow unsuccessfully attempted to determine the magnification ratio of my, Sony Cyber-shot DSC-h300, digital camera. 

I know that the crop factor is 5.62.

35x optical zoom with 25mm-875mm equivalent focal length to the 35mm.

Marco focus range down to 1cm.

The only other value I am not sure required is the sensor size - 1/2.3" (~ 6.16 x 4.62 mm)

---

So, does the magnification ratio change as the focal length changes?

will this device ever achieve 1:1 magnification ratio?

Thanks for any help or details you could provide.

Robert

Hey robert,

I found a calculator online that has a sensor size close to your DSC-H300, and, at the wide angle focal length and 1cm, you are probably working close to 1:1, but this is an estimate.

It is interesting that Sony does not publish the magnification for this camera. I am guessing it isn't a macro machine if they aren't touting its capabilities, but I did come across a forum thread where folks were talking about getting more macro with close-up lenses.

To answer your questions: Yes, magnification will change with focal length. And, I do believe you are near 1:1.

I will ask around to see if I can get you a more precise response. Sorry to not have the formula handy!

Hey thanks for the ultra fast response Todd! 

I'm trying to learn as I go here, and i hope the questions aren't too amateur, but in regards to being near 1:1. Would you say that this only applies when i am in the minimum, 1cm, focal range? Then there is a linear or non linear multiplier to apply as I get farther from the subject? For example, what magnification could be achieved at 10cm or 1 meter. 

Hey robert,

No worries! Glad to be of some assistance

Yes, you would theoretically achieve the maximum magnification at the close focus point—regardless of the focal length. As far as a non linear multiplier, I would assume there is one, but I am not familiar with the math. In fact, if you had seen my college transcripts, you wouldn't be asking me anything about mathematics aside from spherical geometry (used in navigation)! :) Yet, I am sure there are formulas for this...there has to be as optics and math are completely intertwined.

Why are you inquiring, may I ask? Sounds like you are about to do some technical shooting!

Hi Todd, I was recently gifted a vintage Canon FTb. To which I realized that while I lose the luxury of modern camera electronics, I gain the affordability of lenses and equipment all over the internet. I want to use the camera for macro 1:1, or even magnification with a bellows.

My good friend shoots with the aforementioned Sony. She raves about the macro ability and has even won some small town contest with it. This got me to thinking about the true macro ability of a $200 point-and-shoot digital camera.

So honestly, I guess my questions were to try to establish a relative baseline of expectations. Delving into magnification, and all the intertwined relationships, led me to the comparison. Will I take some technical shots, absolutely! Will they amount to anything is yet to be seen 😊

Ahhh. Got it! As you obviously know, there are a lot of ways to do macro photography. You can break out the big guns, extension tubes, bellows, focussing racks, etc. Or, you can get a relatively inexpensive point-and-shoot and break out "serious" macro gear from your pocket!

Check out this article I did on the Olympus TG-5. I am not sure what the magnification is, but you can get super super close and the image quality is great!

Good luck!

This article is helpful. One thing I'm confused about still. Its the implications regarding DOF. Lets take my Nikon D5 and D500 cameras each with a 500mm lens attached. Settings are the same - lets say F11. The crop factor of the D500 will decrease the field of view, I understand - but does the depth of field change? One of the more popular DOF Calculator Apps says it does. This does not make sense to me. Thanks for your counsel. 

Hey Jerry,

Great question and one that opens a small can of worms for some...

Yes, your depth of field does change. Most folks think it is because the focal length of the lens virtually changes (crop factor), but that is not correct. The change in DOF is due mostly to the difference in the reproduction ratio caused by the smaller sensor.

You can now nod and agree and press the "I believe" button...or, if you like painful mathematics, head to this article that I wrote and find the section on crop sensors: https://www.bhphotovideo.com/explora/photography/tips-and-solutions/depth-field-part-3

Let me know if you have follow-ups! 

Thanks for reading, Jerry!

Thanks Todd. I had forgotten of my question to you but the question still lingered in my mind. Thanks for the response and I'll work thru the math. Certain aspects of the math intuitively made sense anyway because the field of view would be narrower with the crop factor and thus the DOF at the wider ends of the field of view would be different. I think. Its puzzled me for quite a while that folks invariably insist(believe) their focal length increased just because they go to a crop factor. The optics did not change. I look forward to reading the "myths - pt III" and seek to get my head around the reproduction ratio.

Ha! Good luck, Jerry! Remember, the "I believe" button is available to push at any time. :)

You bring up something interesting that I had not considered, but my guess is that the effect is mathematically small—the difference in DOF from the center of the frame to the edge. To the best of my knowledge, all DOF mathematics and distances are calculated from the center of the lens on the longitudinal axis of the lens. With a telephoto lens, this isn't a big deal, but on a wide angle lens (and definitely a fisheye), the difference in the distance from what is in the center of the lens to what is on the edge can be great. Having said that, depth of field with wide angle lenses is very short, relatively speaking, so it isn't much of a factor in practical photography.

Regardless, that "fact" wouldn't really be a part of the difference in DOF with a crop sensor versus a full-frame sensor.

Let me know if you have questions, if you find errors, or if Part III makes your hair hurt!

Great article, took me back to my high school physics!

One very minor point I would disagree with, is whether people need to think / worry about crop factor. One important thing to remember is that a lot of people when thinking about getting a new lens will go on the web, Youtube etc. This was the very reason that I started looking into crop factors and came across this page, because a YouTuber (Peter McKinnon) made a video about the benefits of a Macro lens for more general use than traditional macro work. The lens he was using was a 100mm Macro lens BUT he shoots on a full frame camera. So if I wanted to get a lens to give me a similar effect that he was getting then I would need to buy something like a 60mm macro (i.e. 60*1.6 = 96mm) on my Canon 80D.

So if you are looking at reviews or videos when thinking of inspiration for new purchases then definitely take crop-factor into consideration.

Hey Dave,

You make a good point there, but, you have just opened a can of worms that I am happy to dive my fingers into! :)

So, when you are talking about macro lenses, the focal length does matter, but not in the manner in which you described it. With macro lenses, the important number is the magnification ratio. A 1:1 macro lens will reproduce an object at life size regardless of the focal length. So, you can get virtually the same macro image with a 60mm 1:1 Macro lens, a 100mm 1:1 Macro lens, and a 200mm 1:1 Macro lens.

Why would you get a longer focal length macro lens then? Well, because the thing that changes is your minimum working distance—the distance from the camera to the object you are photographing. The longer the focal length, the further away the camera and lens will be from the object when you achieve the 1:1 reproduction. This is beneficial for certain types of macro subjects and lighting issues.

I do realize you mentioned he was using the lens for non-macro work, but it is important to know that macro lens field of views are less considered than magnification factors and working distances. How do those worms work for you? :)

I think I understand the crop factor in term of the photo, my question is around the description of lens.  Given that the Canon EF lens can be used on both the 5D (full frame sensor), and the 7D (APS-C sensor) is the focal length of the lens always given in terms of the full frame sensor?  Put another way if I am using a Canon EF 70-200mm lens on a 7D am I getting 70-200mm field of view or am I getting a 112-320mm field of view? And conversely if using it on a 5D am I getting 70-200mm or 44-125 field of view.  

Assuming the answer is lens size is given in terms of a full frame sensor (for all lens makers)?  

Hey Michael,

First of all, I apologize for missing your post. I am not sure how this one slipped through!

To answer your question, if you put a Canon EF 70-200mm lens on a 7D, you will get the same field of view as if you had placed a 112-320mm lens on a Canon 5D. On the 5D, you get the field of view of the true 70-200mm lens.

The focal length of a lens is the same regardless of what kind of camera it is attached to...or if it is attached to a camera at all!

Again, I apologize for the delay!
 

Hi- I have An expansion on the same question above. Been trying to find an answer to this with no luck or differing opinions. I’m new to all this so bear with me. I’m shooting on a Nikon d3400 DX (cropped). If I buy A lens that’s a Nikon 35mm fixed DX which is specifically meant for a cropped sensor, what field of view am I getting? Is it the 35MM or is it like 52mm? If the lens description specifically states a focal length for cropped, is that the field of view I’m getting? I ask because I’m looking to get more of a wider view than the human eye at 50mm.  Thank you! 

Wow. Don’t know why that posted three times. But I think I have My answer below. I was looking at the exact same 35mM f/1.8 as stated below. So looks like this really isn’t too much of a wide angle for my DX

Hey Mikhaila,

Smart question! Yes, that DX 35mm lens will have the same field of view as a 50mm lens on a full-frame camera. This makes it a "normal" focal length lens and NOT a wide-angle lens.

A couple of things: 1) That is a terrific lens and incredible value. 2) I think that everyone should have a "50mm" lens for their photography. https://www.bhphotovideo.com/explora/photography/buying-guide/one-lens-every-photographer-should-have-and-use-50mm

So, I would grab that lens, and then get a wider-angle lens as well! :) How wide are you looking to go?

I still don't understand one thing. If it's a crop factor it means that the image will be cut on the edge correct? So let's say I use 2 20mp nikon cameras, one dx and one FX, both fitted with a 300mm lens to take some pictures at birds. Will the center of the image where I place the bird be the same or will the dx magnification be as if I was using a 450mm? I mean just the center of the image I understand that the field of view is different but I am interested in the magnification of the image. I hope you can understand what I am asking. 

Hello Noberto,

Great question. Let's see if I can clear this up for you.

Two Cameras—one DX, one FX. Both 20MP. Two 300mm lenses. One bird. Two prints of the same size, or same size computer screen.

The bird in the photo from the DX camera will appear to be closer to the camera—the bird will be larger in the viewfinder and in the image/print. This is because the DX camera's image will be a virtual crop of the FX camera's image.

So, theoretically, you could crop the FX image to an identical field of view of the DX image. The difference is that the DX image has 20MP of data, and the cropped FX image would have 13.33 MP of information in the same shot.

Does that clear things up? If not, let me know!

Well yes I undestand that since the 2 cameras are 20mp in the croped area of the FX image I have more pixels in the DX. BUT BUT BUT... the problem stands if we take the megapixels out of the picture and consider the plain image, as the one we can see throught the viewfinder. Now the full frame just has a larger field of view ... correct? So the center HAS to be the same. Even if I can be fooled by the fact that with the larger field of view the center (in this case the bird) looks smaller, it has to be the same size as the bird in the DX camera, otherwise I would be changing the magnification of the lens. Now let's not forget that the focal lenght of the lens can't change in any possible way unless we had a different focal plane. So the magnification of the center of the image has to be the same. I understand compleately that the problem exists ONLY because we count the mega pixels in the picture, but taking that out of the equation, am I right or not?

Norberto M. wrote:

Well yes I undestand that since the 2 cameras are 20mp in the croped area of the FX image I have more pixels in the DX.

I ment the oposite. 

Hey Norberto,

Yes, you are correct. To the camera, the image projected by the lens is identical in size regardless of the size of the sensor—the DX camera just shows you a cropped view of the same image. You are not increasing optical magnification with a DX camera. Lens magnification and field of view are independent of the size of the sensor or film.

Good question!

Hi Todd,

I am mostly generally ok with understanding crop factor interms of sensor size and it's impact upon field of view etc etc. I came by this article whilst searching for a definitive answer on the subject of why crop factor affects shutter speed e.g. in the case of the 500 rule and 1/focal length. 

You yourself, in this article's comments have answered the question posed so often with a simple yes you must take it into consideration. What I'd like to understand is exactly why it needs to be considered. I have attempted to think this through logically but cannot rationalise several 'seemingly' conflicting things. Let me explain:

When I consider the impact of crop factor on the shutter speed required to reduce camera blur my confusion is partly resolved. This is because, as I see it, camera blur is a function of the movement of the subject across the sensor during the exposure. Since the focal length of the lens has not been changed from full frame to crop, the same amount of lateral camera movement must result in the same movement across the sensor. Now, I must consider the pixel density of the sensors in question. If both sensors have the same pixel count, the density is of course greater on the crop sensor and this does mean that for the same lateral movement the subject will move across 1.6 (Canon in my case) more pixels compared to the full frame body. It therefore makes sense to me that 1.6x faster shutter on the crop would balance this effect. But I need to clarify that this is not about the lens magnifying the image on the sensor by 1.6x. Now come the problem(s). If I was shooting with the crop sensor at 1.6x the distance to the subject compared to the full frame, thus producing the same subject size at 100% crop, would this not have exactly the same effect as having 1.6x the shutter speed in terms of the physical movement of the subject in relation to the pixels on the sensor. Conversly, If I were to shoot at the same distance then crop the full frame and enlarge 1.6 to get the same subject size what would happen then?

The thing I'm really struggling with though is understanding the need to factor crop into the 500 rule for avoiding star trails. I can just about understand the need to adjust the shutter speed as the focal length increases, if I assume this is because the longer focal length lens will always result in a larger image on the sensor at infinity focus. Here's the thing though. With star trails my camera is fixed on a tripod and the trails are a function of the stars movement in the sky. The stars speed through the sky is fixed in terms of degrees or radians per unit time about the pole star (I recognise that statement is not entirely 100% accurate but the argument is not affected). Here's the cause of confusion for me. Whilst the stars speed of rotation is constant, the distance travelled in a given field of view is not. So if I were to point my lens centered on the pole star on a crop body I see less stars than on a full frame with the same lens, furthermore, the additional stars in the full frame field of view are are necessarily covering more distance on the sensor. The inevitable conclusion of this is a contradiction that the full frame sensor needs a shorter shutter speed to avoid trails in the extended field of view that was not captured by the crop sensor.

I really hope you can pull all of this apart and explain to me and maybe others why I've got this all wrong.

Thanks in anticipation...

Hey Shaun,

Superb question. Well-written, too!

The manner in which you arrived at your query would lead me to believe that the 500/600 rule applies to both full frame and crop sensor cameras. I do a lot of astrophotography and have used the 600 rule successfully with APS-C cameras, but I haven't really done a super scientific test. And, as you mentioned, the rate of the star's varies based on your position on the planet and their position in the sky...so it won't ever be an exact science for the casual shooter. The math is accessible, but who wants to crunch those numbers in the dark?

I can see how people would just use the 35mm-equivalent field of view in their calculations, or they could just change the formula to make the math work for them. But, as you stated, the motion across the sensor is identical with the same lens on a full-frame vs. crop sensor camera. If you changed focal length, the new field of view/image circle would produce different pixel distances across the frame per a given shutter speed.

B&H night photo guru, Gabriel Biderman, wrote this article a while back and uses different "rules" for the different sensors: https://www.bhphotovideo.com/explora/photography/tips-and-solutions/epic-battle-between-choosing-star-trails-over-star-points

I hope that didn't read like I danced around the answer. My advice to you: Use your own gear and do some tests. Peep some pixels! The popular app, Photo Pills, does crunch some numbers for you and shows both the 600 and 500 rule based on minimal declination of the stars in the frame. And, realize that even though it could be an exact science, these "rules" are more guidelines.

Standing by for follow-ups!

Thanks for taking the time Todd,

On first read of your answer I did feel a bit cheated, but your advice is sound. Who needs to understand the complicated maths (I'm a Brit), when it's the results that count? Much better to use the guidelines as an entry to understanding your own gear and develop a flexible and experimental approach in the field rather than break out the rule book for every new shooting challenge. I shall try and temper my need to know and shoot more instead !!!

Cheers

Hey Shaun,

Sorry you felt temporarily cheated!

As tempting as it is to start crunching numbers, my math skills tell me that I am not the guy to do it. Rest easy, however! Others have! Use PhotoPills or check out some other more techy blogs if you crave some equations! :)

But, yes...the proof, as they say, is in the print (or on the screen).

Here is a paraphrased anecdote for you: When the Apollo Lunar Module (LM) was being designed, one of the astronauts engaged in the engineering process was Pete Conrad—a former Naval Aviator. The designers showed him a pressure gauge for some sort of oxygen tank. They said, "When the tank drops below a certain pressure you will see it on the gauge and this light will come on and you will be in trouble."

He asked, "What do I do when the pressure drops and the light comes on?"

"There is nothing you can do about it," the engineers said.

"Well, I'll tell you what. Why don't you get rid of both the gauge and the light, because if I am going to die, I want to die calm."

I used that same argument (and failed) when I was told I needed to memorize the temperature at which the tail rotor gearbox hot light came on in the H-3 Sea King (140F + or - 2 deg). There was no gauge to show the temperature, so why did it matter what the temperature was?!

Knowledge can be dangerous. :)  Go out and shoot using the 500 or 600 rule and see what you get! Also, check out this LonleySpeck link: https://www.lonelyspeck.com/milky-way-exposure-calculator/

Cheers!

Thank you for a great article, I'm only mildly confused on one last thing. Does crop factor in regards to field of view only apply when using lenses that weren't made with that sensor in mind?

For example, 50mm ef mount lens made for full frame sensors on a micro 4/3 sensor will have a field of view of 120~

But, will a 50mm m43 lens on an m43 sensor also have the crop factor applied, or will it have the fov of a 50?

In even simpler terms! Veydra 13mm m43 mini prime on a black magic pocket cinema camera, results in a 13mm fov or a 30mm~ fov?

Hey Vin,

Great question.

Any 50mm lens built for, or adapted, to a Micro Four Thirds sensor will have a field of view equivalent to that of a 100mm lens on a full-frame camera.

And, the Veydra 13mm on a Micro Four Thirds camera will have a field of view equivalent to that of a 26mm lens on a full-frame camera.

This is why the "Nifty 50" options for Micro Four Thirds are 25mm lenses. From the outside, it looks confusing, but if the fields of view changed arbitrarily, we would have quite a mess of mathematics on our hands!...especially for those adapting different lenses to smaller sensors.

Thanks for your question!

Hi Todd,

Thanks for the thorough explanation.

The thing that I don't get now actually has nothing to do with the technical side of this. I just don't understand why almost every photo online with the listed metadata next to it (like Flickr does) doesn't list the 'equivalent focal length' instead of the normal focal length, or at least mentions the crop factor.

You're supposed to look up the camera in order to find out if it's a full frame or not and then calculate the equivalent focal length. Or am I just wrong in thinking they display the regular focal length?

Thanks again.

Hey Vince,

You are welcome.

Unfortunately, I think you need to do the math in your head as Flickr just mentions the camera and lens type—not the 35mm-equivalent.

Yep...just checked my own Flickr and it only shows the focal length of the lens, not the equivalent focal length on a cropped sensor camera.

Fun fun!

Thanks for reading!

Do you consider crop factor when finding the minimum hand held shutter speed? Using a 50mm 1.8 on a crop sensor. Would it be 1/60 with no crop factor figured, or 1/125?

Hey Steve,

Great question!

When figuring out theoretical hand-held minimum shutter speed, I would definitely use the 35mm-equivalent focal length...so, 75mm in your case if you are shooting 1.5x APS-C.

Usually the rule is: 1/focal length. So, on a full frame, you need to take care shooting slower than 1/50th of a second. On APS-C with the same lens, 1/75th.

Shoot steady!

Hi todd

i thought I had this, but after rereading again, I may have confused myself

i have a Nikon  APS-C crop body and shopping for lenses   I bought a FX 70-200 lens, which I understand from your explanation will give me an 35mm equivalent of 105-300 at the 1.5 CF.  So far, so good.   

What is getting me now is the difference between buy a FX lens and a DX specific lens.  Originally, I had thought that the CF applied only to the FX lens when used on a APS-C body, and that design of the DX lens meant that the "focal length" as stated did not need the CF "adjustment".   Thus, for example, an FX 24-80 lens on my camera would yield the 35mm equivalent of 36-120mm, but if it was a DX 24-80,  it would give the 35mm equivalent as "stated", just 24-80, no CF adjustment needed as it was a DX lens on a APS-C body

ok - that is what I thought, but now thinking the CF applies to both lens.  The only difference between the two lenses being that the image circle in the DX lens is smaller and thus will not work well on an FX body

so, is my understanding right now, or was it correct the first time?    I think it is right now - the CF applies to FX AND DX lenses.   Why is this important.    I am trying to by 1-2 shorter lenses and want to make sure I have he right "overlap" with a shorter zoom I am considering 

thsnks in advance

Hi Todd. 

Any thouhts as to whether I had it right the first time or now (now being that CF applies to any lens used on a APS-C body, regardless of if it is a FX or DX lens?

Hey david,

See below. Thanks and, again, sorry I missed your question! I got inundated with questions and comments last weekend leading up to the eclipse and yours, unfortunately, fell through the cracks as I was answering them while on vacation and away from our "system."

Hey david,

Sorry I missed your post! I apologize!

Good question...and you aren't the only one confused by this.

First off, there are only DX lenses and lenses that are not DX. There is no such thing as an FX lens.

Secondly, the lens's focal length is a physical measurement and not related to the size of sensor that the lens is placed in front of. That is why lenses on point and shoot cameras have incredibly short focal lengths, but give "normal" perspectives when placed in front of tiny sensors—for instance, the lens on an iPhone has a focal length of around 4mm. Pretty wide on a "normal camera!"

So a non-DX 24-80mm lens on a DX camera gives a 35mm-equivalent field of view as a 36-120mm lens on a full-frame or 135-format film camera. A DX 24-80mm lens on a DX camera gives the exact same 35mm-equivalent field of view as the previous lens. The difference is that if you put that DX lens on an FX camera, you would get some vignetting as the image circle projected is smaller than the non-DX lens.

So, yes, crop factor applies to both lenses in your example. In fact, it applies to any lens you put in front of that sensor.

Again, sorry for the delay in replying!

Thanks.   That is what i got the second time I read it.    Once I started thinking about it, it meant I needed to have one end of my "walking around zoom" very short and the other end medium focal lengt, so my "16-80" lens gives me the equivalent of a 24-120 on my 1.5CF body- will be good and an not give me too much  overlap with the longer lens that I have.    Thanks so much

Hey david,

No worries! That 16-80mm lens is very very good. https://www.bhphotovideo.com/explora/photography/hands-review/nikon-af-s-dx-nikkor-16-80mm-f28-4e-ed-vr-lens

It is a perfect everyday workhorse lens.

Thanks for reading!

Hey Todd, 

Finally the answer i was looking for! As a newbie in photography, i was very confused in whether the crop factor was applied to any lens out there. I bought a DX 35mm f/1.8 for my crop sensor camera, so that means that it's equivallent focal length is 50mm for a full frame dslr, right?

Thanks again!

Hey Matthew,

Kind of right...let me try to rephrase it to be clear:

On your DX camera, your 35mm f/1.8 lens will give you the same field of view that a 50mm lens would give you on a full frame camera.

Crystal clear?

Thanks for reading!

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