When it comes to focal lengths, it seems that many photographers get very confused by “equivalent focal length” and “field of view” jargon that is often used to describe lens attributes on different camera sensors. To help fully understand these terms, I decided to write a quick article, explaining what they truly mean in very simple terms.
1) True Focal Length
What is the true focal length of a lens? This one is extremely important to understand. Focal length is an optical attribute of a lens, which has nothing to do with the camera or the type of sensor it uses. The true focal length of a lens is typically what manufacturer says it is on the lens. For example, the Nikon 50mm f/1.4G lens (below) has a true focal length of 50mm, irrespective of what camera you use it on.
2) Field of View
The “field of view”, which is sometimes called “angle of view” is simply what your lens together with the camera can see and capture from left to right, to top to bottom. If you are shooting with a DSLR camera, the field of view is typically what you see inside the viewfinder. Some DSLR cameras, have less than 100% viewfinder coverage, which means that what you see inside the viewfinder is actually less in size than what the final image will be. For example, if you shoot with the Nikon D90 DSLR that has 96% viewfinder coverage, what you see inside the viewfinder is going to be about 4% less than what the camera actually captures. Hence, the actual field of view is always what the camera captures, not necessarily what you see inside the viewfinder.
Here is an example of differences in field of view between 70 and 400mm:
The top-left 70mm image looks almost “wide”, while the 400mm image shows a much greater magnification with a much narrower field of view.
Lens manufacturers often publish the term “angle of view” or “maximum angle of view” in lens specifications, because they define the field of view in degrees. For example, the Nikon 24mm f/1.4G lens has a maximum angle of view of 84°, while Nikon 300mm f/2.8G telephoto lens has a maximum angle of view of only 8°10′ when used on film or full-frame cameras. Take a look at the following illustration:
300mm vs 24mm AoV
As you can see, 84 degrees is very wide when compared to 8 degrees. That’s why you can fit a lot of the scene when shooting with a 24mm lens, while a 300mm lens allows you to capture a narrower, but much more magnified portion of the scene.
3) Equivalent Focal Length
Let’s now move on to the term “equivalent focal length”, which like I stated in the beginning, is a term that many photographers misunderstand. The word “equivalent” is typically in relation to 35mm film. You see, back in the 35mm film days, the focal length of the lens was always whatever the lens said on the label. With the invention of digital SLRs, the camera sensor (the device that captures images) is often much smaller than the 35mm film, primarily because of high cost. This reduction in size of the sensor results in cutting of the image corners, the process that photographers call “cropping”. The interesting thing, is that the image is actually not cut by the sensor or the camera – parts of the image are simply ignored. Take a look at the following illustration (red arrows represent light entering the camera):
35mm Film/Sensor Camera (Left) vs Cropped Sensor Camera (Right)
As you can see from the above illustrations, the 35mm film/sensor cameras capture a large area of the lens, while the smaller sensors (also known as “cropped sensors”) capture mostly the center. Note how the light enters the camera chamber in exactly the same way in both illustrations, but the smaller sensor is only able to capture a certain portion of it, while the rest of the light falls outside of the sensor. The term “cropped sensor” can be confusing, since “cropping” an image is often associated with cutting it. Once again, in this case, there is no cutting – the light rays from the edges of the lens just overshoot and do not make it to the sensor.
Manufacturers knew about this “overshooting” process when they designed smaller sensors, so they started producing lenses specifically designed for cropped sensor cameras to make them cheaper. Nikon calls them “DX”, while Canon calls them “EF-S”. Basically, the lens itself passes through a smaller image circle and by the time it gets to the sensor, not much of the circle is actually wasted. Think of it as the right part of the above illustration, except the circle is much smaller. Obviously, lenses like these do not function as they should on full-frame/35mm cameras – only half of the scene will actually make it to the sensor. Nikon full-frame cameras are programmed to recognize DX lenses and will automatically decrease the image resolution, while the Canon EF-S lenses will not function on full-frame cameras at all.
How do two cameras with different sensor sizes have the same image resolution? For example, both full-frame Nikon D700 and cropped sensor Nikon D300s have 12.1 Megapixels while having different size sensors. This is because the Nikon D300s camera has much smaller pixels (and hence, higher pixel density) compared to Nikon D700 – that’s how 12.1 million pixels are able to fit on a smaller sensor. What this essentially means, is that the smaller sensors with smaller pixels enlarge the center area of the lens more in this case. If a lens is not of very high quality and is not able to resolve fine details, the images might appear less sharp on cropped sensors.
Let’s now get back to the term “equivalent focal length”. I’m sure you have seen manufacturers claim something like “The 28-300mm lens has an angle of view equivalent to a focal length of 42-450mm in 35mm format”, which is a correct way of saying it. Others may say something like “the lens focal length is equivalent to 42-450mm on DX sensor”, which is an incorrect way of saying it. As I have shown above, in relation to the camera sensor, the focal length of the lens never changes – only the field of view/angle of view does. Saying something like “my 28-300mm lens on my Nikon D90 is like a 42-450mm lens” is incorrect for this reason.
Where do these larger numbers such as 42-450mm come from? Let’s now look into the crop factor and how these “equivalent” numbers are actually computed.
4) The Crop Factor
By now you understand what “equivalent focal length” truly stands for and how the smaller sensors ignore the larger circle area. Let’s now talk about the crop factor – the term that manufacturers and photographers often use to describe camera sensors and to calculate the “equivalent focal length”. You might have heard people say something like “Nikon D90 camera has a 1.5x crop factor” or “Canon 60D has a 1.6x crop factor”. The term “crop factor” came up after smaller sensors were invented to make it easier for people to understand how much narrower the angle of view gets when a lens is used on a camera with a small sensor. Manufacturers had to somehow explain how an image on a smaller sensor camera looks enlarged or “zoomed in” compared to 35mm film.
If you take the sensor area of a full-frame sensor or 35mm film and compare it to a cropped sensor, you will be surprised to see that the former is at least twice larger than the latter. For example, the Nikon full-frame cameras approximately have a sensor size of 36mm x 24mm which gives us a surface area of 864. Cropped-sensor cameras like the Nikon D90, on the other hand, have an approximate sensor size of 24mm x 16mm, which is around 384 in surface area – a whopping 2.3 times smaller compared to Nikon D3s! But when it comes to focal lengths, you do not use the surface area of the lens. The crop ratio is computed by taking the diagonal of the full-frame sensor, divided by the diagonal of the cropped sensor.
Now you will have to remember some math. Remember how to compute the diagonal? Here is the formula in case you forgot it: √(X² + Y²). The full frame camera has a diagonal of 43.26 (square root of 1296+576), while the cropped sensor cameras have an approximate diagonal of 28.84 (square root of 576 + 256). If you take 43.26 and divide it by 28.84, you get 1.5 – the ratio of the full-frame sensor diagonal to the cropped sensor diagonal (these numbers are rounded – the actual ratio is a little bit higher, around 1.52).
What do you do with this ratio? You multiply it to get the “equivalent focal length”. For example, the Nikon 24mm f/1.4G lens has an angle of view equivalent to approximately 36mm when mounted on a cropped sensor camera like Nikon D90. What this means, is that if you took a 24mm lens and mounted it on a cropped sensor camera, then took a 36mm lens and mounted it on a full-frame camera, you would get about the same view. If you put it the other way, to have the same angle of view as the 24mm mounted on a full-frame camera, you would need a 16mm lens on a cropped sensor camera. For example, if you were standing from one spot and could fit a house in your frame using a 24mm lens on a full-frame/35mm camera, to be able to fit that same house on a cropped sensor camera, you would need to have a much wider lens with a focal length of 16mm.
Hope this clears up the true definition of the above terms for those who do not understand them well. If you have any questions or comments, please post them in the comments section below.
About Nasim Mansurov
Thank you for this excellent post! One thing I was wondering a while ago was how to compare binoculars with camera lenses. The binocs always advertise “6x magnification” or something like that. What I found was that a 50mm lens is supposed to be pretty much what the eye sees, so is effectively 1x. Every additional 50mm is an additional magnification. I wanted a pair that would do better than my Nikon 18-200 on my D300. I figured that a 200mm lens on a DX sensor gives an effective angle equivalent to 300mm focal length on 35mm, so should be the same as a 6x pair of binoculars.
I never actually had someone who understood both validate my thought – can you say whether that conversion makes sense?
After reading your post, I realize I should have just looked at the angles (since I think both lenses and binocs publish those).
-ben
Ben, you are most welcome!
Yes, you are right about 50mm – it is considered to be a standard/normal focal length. The “x” magnification is computed by taking the long focal length and dividing it by the short focal length. For example, the Nikon 28-300mm is a 10.7x zoom lens (300mm / 28mm = 10.7). The Nikon 18-200mm is an 11.1x zoom lens :)
Let me know if you have any questions.
Sir Nasim, you are so generous of knowledge. your article is so great, it will go a long way to many people all over the world needing to understand focal length, angle of view and camera sensor.
Many thanks to you. Wish you a happy life.
- jebey
philippines
Sir Nasim, I have 50mm 1.8g on D7000 (crop sensor) body, now I attach wide converter 0.7 on my lens so in my calculation it turns out I have a field of view of 52.5mm which means I get nearly a full frame sensor field of view on 50mm lens. If my calculation is correct do I still get same quality photo on full frame DSLR?
This is my calculation:
50mm (lens)
1.5 (Crop Sensor)
0.7 (wide converter)
50×1.5=75mm, 75×0.7=52.5mm
John
Bahrain
Any word on the “lens breathing” issue with some zoom lens (like the Nikkor 70-200 VRII) ?
Del-Uks, I knew somebody would have asked this question! :) The lens breathing characteristic has to do with focal length shifts due to the optical design of the lens to accomplish two things a) to have a shorter maximum near focus range and b) to not move external lens elements while focusing. It is just a different way the lens focuses, which is why the focal length is accurate at infinity.
Hi Nasim, excellent info. can you pls. clarify as to why 85mm is called a portrait lens(mounted on FX) ? What would i do wrong in terms of image quality if i do the same with a 50mm lens? I have seen a lot of beautiful images on your website with 50mm… but it seems several photographers are pretty strict about using 85mm for portraits? thanks.
Sekhar, the 85mm is called a portrait lens, because that’s what it is intended to be – for shooting portraits. It renders the background (bokeh) better than any other Nikon lens and the really large aperture of f/1.4 allows to isolate subjects, while keeping them sharp in the foreground. The Nikon 50mm is also superb, but it is certainly inferior in terms of wide open performance + rendering of bokeh.
I personally like both lenses and consider the 50mm f/1.4G to be a great value, given its price and performance.
Nasim, Yes, only after coming across your articles, i could make up my mind and purchased a 50mm f/1.4G for my d90. No doubt I see clear-cut difference from other lenses with smaller apertures. I guess, I will have to try the 85mm myself and see the difference, but it is too pricey !
Sekhar, don’t worry about the 85mm and enjoy your 50mm instead! :)
Nice article.
I always wondered if the focal length mentioned on an EF-S lens is the real focal lenght or already the equivalent focal length? I guess it’s the real focal length,but I’m still not fully sure.
Thank you Coby! The focal lengths on lenses are the real focal lengths, not equivalent ones. So if you are looking at the Canon 18-55mm lens, for example, the equivalent “field of view” is going to be that of a 29-88mm lens.
Hope this helps!
Hi Nasim,
Can you help me understand how the image is magnified in a DX versus a FX?
I understand that the DX only captures part of the image capable by the FX, but why the enlargement of the subjects?
If I have a photo on my desk, and I just cut around the outside perimeter of the photo to make it smaller in size, the subjects within my photo (ex: flowers) do not change in size, so how does this happen in the camera of a DX sensor? Something simple I am missing here I am sure bit I just cant see it yet.
Does the DX camera electroniaclly strech the image out to fill up a 35mm sensor size equivalent after the phot is taken? Is that how the magnification happens? If so, how do you not lose resolution by doing this (like photoshop cropping)?
Hope I was clear in what I am asking :)
Thanks, hope to hear back!
Francis, an image is not magnified in DX versus FX – it just gets cropped. Think of it this way – an image is cropped and then because there are more pixels on DX, you get a similar resolution as FX. Because of this, the pixel size on DX sensor is much smaller than on FX, which is why you also get less dynamic range.
There is no real enlargement happening here – all it is is physical (not software) cropping. That’s why the term “crop factor” is used. Have you had a chance to thoroughly read the article? Take a look at the last image – it will be easier to understand the concept.
In terms of your question about a photo on your desk, think of it this way. If you were to cut the outside perimeter of the photo, the image does not appear larger because you are keeping the same distance between yourself and the photo before and after you cut it. Now what happens if you move closer to the photo after you cut it? The image will appear larger right? Cameras don’t work the same way, because you don’t change the distance between yourself and the subject, but rather increase the number of pixels to effectively blow up the image in size :)
Hope this helps!
Thanks Nasim for taking the time to respond, it did help!
Can I just add—try and think of the image being shrunk by the “lens”onto the 1.5/6 factored sensor to fit it “whole” then we get given the whole sensors worth as our image.
It’s pretty confusing, I [from my old film days] still have the 35mm eye but have to stop and recalibrate.
The best thing ever would be someone brings out a 17-80 1.4 zoom, all the angles are covered.
Hi!
After reading this, I’m not sure about purchasing 50mm 1.4G to my D300, should I go for the 35mm 1.8G instead? If the pics doesn’t get as good as if I had for example D3x/D3s I mean. Something about “cropped making the images less sharp” made me think… Is the sensor too small in my D300 to get the most out of 50mm 1.4G?
I’m a student and therefore it’s a big deal to me financially, I want to be positively sure before I get the glass.
Sorry about my bad english. ;)
Eli, if you have budget issues, then definitely go for the 35mm f/1.8G instead of 50mm f/1.4G.
Hi Nasim,
I have the same question as to what I want to buy for my D7000. My cousins bought 50mm f/1.8. You mentioned it in one of your articles that the 50mm f/1.8 does not really work well with some DX camera.
Do I really have to go for the large aperture (50mm f/1.4) or get the 35mm f/1.8? I want to have great pictures in low-light, disco light setting.
Thank you very much. And more power to you!
Hi Nasim,
Detailed good explanation in simple terms! kudos :) I am a beginner and going to make my first dslr purchase in a week. Decided the camera (D90)! Lens wise, I did read your other threads and found 50mm f1.8 and 35mm f1.8 to be very useful to buy (eventually will buy either one of them). I also read the kit lens pros and cons.
My question here is, d90 body costs SG $1180 (free – 18GB card) and D90 kit (with 18-105mm) costs SG $1480 (free – 8gb card, 1 Tripod, cleaning kit, nikon bag, nikon travel bag). Is USD $230 worth for the kit lens with freebies or should i have to just buy the body with one of my preferred prime lens. I mostly would like to take portraits, landscape in my point&shoot.
Thanks
Balaji M
Balaji, I would get the kit lens together with a prime lens.
Hi, I found your article very informative and clear; however, I do have one question. I just bought a D700, my first fx camera and have been using it with my old dx lenses. I am currently looking for an fx lens to shoot with but the whole crop factor thing has me confused. My question is this, the focal length of an fx lens on an fx sensor the same as a dx lens on a dx sensor? So if I like my 24-85mm dx on my D100, would I get the same with 24-85mm fx on the D700?
What an useful explanantion about focal lens, picture angle and crop factor. Have to say thanks..
Dear Nasim
I am a beginner and just bought D300s and found great of the explanation.
I have 2 questions regarding ” If a lens is not of very high quality and is not able to resolve fine details, the images might appear less sharp on cropped sensors ”
ie :
1. Might the image of ( D300s+ Nikon 24-70 ) be less sharp than (D-700 + Nikon 24-70) ?
2. is that ( D300s + FX lense ) more sharp than ( D300s + DX lenses ) ?
Appreciate if you could advise since I am considering to invest more to FX lenses ( 14-24 and/or 24-70 and/or 70-200 ).
I just bought Nikon DX 18-200 mm and Tokina 11-16 mm/f2.8 as starting point).
Tks n Rgds
Sunarto
Tks n Rgds
Sunarto
Hello,
First of all congratulations for the well-designed website and the information it contains. I find it very helpful.
I’m about to buy the nikon d5100. However my “problem” is to what type of prime lens should i get. Either the 50mm 1.4G or the 35mm 1.8G. In terms of budget there’s no issue. I’m between of these two lenses as I intend to take photos mostly at home, people portraits (close-ups and some distance), family photos as well as street photos.
I do not intend to change lenses frequently so I’d also consider sth to keep it for a long time before I upgrade to another category.
I’d appreciate it to have your advise on this and under these types of photo wwhich lens would add the maximum of value according to the use i plan to do.
Thanks & regards
Kostas
Hello Nasim,
I would like to congratulate you on a well informed article.
Very simple in explanation and easy to follow.
All the best with your website.
Thank you & regards,
peter
Thank you for your feedback Peter!
hey
im an amateur photographer . i wanted to ask you something, i decided to get a nikkor 50mm 1.8 G, and i bought it the other day. i use nikon D7000 which has a cropped censor, and that 50mm lens should give me 75mm on cropped censor but it is still giving me 50mm on my nikon d7000, why so? is there any defect? hope you will soon answer my question
thnku
As I notice you did either not read or not understand this great article. 50mm is always 50mm, it gives the “equivalent perspective” of an 75mm on full-frame, but it is still 50mm. The working distance, if for example you were to take portraits, has to be further away because there is less sensor to make a wider picture, and that is why some people claim the “mm” difference. Just concentrate on the angle of view and remember to understand what “equivalent” means.
hey
im an amateur photographer . i wanted to ask you something, i decided to get a nikkor 50mm 1.8 G, and i bought it the other day. i use nikon D7000 which has a cropped censor, and that 50mm lens should give me 75mm on cropped censor but it is still giving me 50mm on my nikon d7000, why so? is there any defect? hope you will soon answer my question
thnku
Hello-
Just came across you site while searching to understand about the lens.I recently bought a Nikon D3100 and planning to but extra lens to capture some family pictures at parties. Should I go with 35mm or 50mm or 85 mm lens? Which lens would have the ideal focal length to cover indoor events without losing the picture quality?
Thank you for your effort in writing this article.
Hi, Nasim,
First of all, congrats on the excellent explanation.
I just want to clarify one doubt. Suppose I’m 10m far from my subject and I take a picture with a 50mm lens mounted on 35mm sensor camera.
To acquire the same image with an APS-C sensor (let’s say 1.5 crop factor), I’d have to use the same 50mm lens, and take the picture 15m away from the subject.
That is taking a picture with a 75mm on 35mm is not the same as a picture with a 50mm on 1.5 crop factor APS-C camera on the same distance.
Am I correct?
Thanks in advance.
Hi Nasim,
Above article is seriously a great help of understanding between the “real” and “equivalent” focal lengths depending on the format of the sensor in camera. And I believe I’ve got it cleared of course due to your explanation. I appreciate that…
But what I’ve understood, the fact is that photographers have made the “focal length” of lenses more friendly to relate with full-frame cameras to call it the “real focal length” and when you put these lenses on cropped-sensor camera the term “equivalent focal length” is derived. But “focal length” is actually an element of a lens, irrespective of the camera it is used on. (just like you stated in your article above)…
Just to let you know that I am also waiting for an opinion of yours on another article… please reply if you got time….
http://photographylife.com/reviews/nikon-d5100#comment-19936
Thank you for your content on line… seriously since the day, I have found your website, I didn’t need to keep hunting around….
Hi,
Tanks for this great article and the even greater site. there’s still a thing though which i don’t understand.
Since I’m planning on buying the d7000 i wonder about the 100% viewfinder and the crop factor. Ok, the crop factor determines the actual angle of view on the final picture. But what do I see in the view finder with an 50mm lens, for example??? The angle of view of the final picture will show an equivalent of 75mm. Will the viewfinder show the same 75mm or will it show 50mm???
thanks in advance
Hi Nasim
Very good article ,easily inderstand,the best web page I ever read.please continue to serve people to become good photographers.congratulatipn
Wasantha
Hi Nasim
This is a very good article and I have learn many things from your site. I have one question only is a 12-24 mm wide zoom lens will perform better also on a dx lens like d90? Im going to use it for landscapes.
Thank you and more power…
Hi,
Is your diagram showing the 35mm and cropped sensor incorrect? More specifically, with the lens focused at infinity, shouldn’t parallel light rays entering the camera intersect or converge at the image plane, i.e. the sensor? The diagram shows them converging in the middle of the camera.
Thanks,
Tony
This is one of the best, easy to read explanations of the crop factor.
I use this general rule for handholding without lens stablization.
50mm lens = 1/50 or faster shutter 200mm lens = 1/200 or faster shutter.
With the crop factor figured in, the rule would still be the same because the lens is not becoming longer, just cropping, correct?
MAny thanks for the article but there’s still a question i havent been able to solve yet:
Taking a photo with a 300mm lens on a 35mm is said to be equivalent, in FOV terms, to a photo taken with a 200 mm lens on a APS-C camera (crop factor 1.5).
What i would like to understand is if that equivalence exists in terms of IQ aswell.
Saying otherwise, giving the same shot conditions (aperture, exposure, lights conditions, object distance etc) and quality of lenses used, the level of details captured with a 300mm on a 35mm shoud be”exactly” the same of those captured with a 200mm on a APS-C (if cameras have same resolution too, saying 24MP) ???
or the equivalence is only in terms of FOV (field of view captured by sensors) and not also in terms of IQ (image quality)???
many thanks!
gianni