Crop Factor Calculators are below.
Digital camera sensors are of a certain size (the sensor area capturing the image), much like film frames were a certain size. Nikon calls their DSLR sensor sizes FX (full frame) and DX (APS frame). Canon calls them Full Frame and APS-C (EF-S). Full frame compares to the same size of a 35 mm film frame (36x24 mm), and APS is the smaller APS film frame size (about 24x16 mm).
The lens projects a circular image onto the sensor, the diameter designed to cover the corners of the sensor or film. Then the camera sensor captures a center rectangular portion. The picture above attempts to show these things:
Those red and blue marked crops are:
Blue Cropped sensor
But then enlarged to same size
We might think "Hey, that last one looks like a longer lens was used", as if we zoomed in on it. And enlargement does look telephoto, except it is of course the exact same smaller image, simply enlarged more to view it. The lens did not do this, and technically neither did the crop, but the smaller crop did require the greater viewing enlargement (back to same size), which is what enlarged it. The enlargement does appear as if we did zoom in. The 1.5x more enlargement may have some downside, that 1.5x enlargement reduces resolution to 2/3.
We often hear beginner questions like this one:
It's a confused question, which does not understand yet. A 50 mm lens is always 50 mm, on any camera body. The Focal Length of the lens is as marked, 50 mm. The sensor crop factor cannot change the physical lens focal length. Therefore, the focal length is of course still 50 mm, including even on the cropped sensor body.
Any lens always does whatever its focal length does do. A lens cannot change by simply mounting it on a different sensor. The Field of View does change (with sensor size), but the lens does Not change.
A smaller sensor is simply smaller, so it can only capture a smaller Field of View than does a larger sensor (the blue frame above).
Crop Factor is about this cropped Field of View of the smaller sensor. It is Not about the lens.
A Crop Factor of 1.5 means the larger sensor sees a Field of View 1.5x larger than the small sensor. The smaller sensor Field of View is 1/1.5 of the larger one (or 2/3 size if 1.5x, or 5/8 size if 1.6x). This is measured on the diagonal dimension (to account for Aspect Ratio).
That image from the smaller cropped view of the smaller sensor, when necessarily enlarged again, does appear to be the same view as if a longer lens had been used ON THE LARGER SENSOR. But of course, it appears on the smaller sensor as if THIS original lens were used (since it was used on the smaller sensor).
Equivalent Focal Length merely compares the Field of View that the OTHER full size sensor size would see with an "Equivalent" lens calculated to compare, compared to what this sensor actually does see with this original lens. The Equivalent Focal Length is mounted on the OTHER full size sensor, not on the cropped camera.
The standard convention used is that the Equivalent Focal Length compares:
the Field of View that this lens on the cropped sensor does see,
compared to the Field of View size that a larger "full frame" 35 mm film size sensor would see,
if the larger sensor were used with the computed Equivalent Focal Length lens.
That CANNOT change this original lens in any way.
35 mm "full frame" size is always the comparison standard, convenient simply because many users have many years of 35 mm film experience, and know well what result to expect from various focal lengths on 35 mm film. This comparison then tells them what this new smaller sensor should see, in terms they already well know. This is very good information in certain situations.
But if unfamiliar with using full frame 35 mm film size, then Equivalent Focal Length likely will not have meaning to you (because that is what it applies to). You will become familiar with what various lenses do on your cropped camera sensor. And if and when you switch to a full frame camera, then this may become important to you.
The literature can confuse us about this, to the point we have to already understand crop factor before we can understand their explanation about it. Some of the best sources word it as " For example, a 70-200mm lens becomes a virtual 105-300mm lens on a 1.5x APS-C sensor." However that "becomes" does Not happen, although if we are used to thinking in terms of full frame, we might think of it that way. The lens of course remains totally unaffected, it still does what it always did (that was how they meant "virtual", not physically existing). All that happens is the 70-200mm lens on a full frame and the 105-300mm lens on a 1.5x APS-C sensor simply see the same field of view (because the smaller sensor crops its view smaller, but normally, its shorter lens compensates to show the same wider view). It's like two film sizes, IF using the proper corresponding lenses, they can take the same picture (same field of view). However, the smaller film is still smaller, and requires greater enlargement to view at same size.
The standard convention is to compare smaller cropped sensor size to 35 mm film size, simply because many of us were very familiar with 35 mm film, with years or decades of experience to already well know by second nature what field of view to expect from various focal lengths on 35 mm film. That crop factor Equivalenet comparison tells us what view THIS new sensor will show now, in Equivalent terms already very familiar. But if you're not familiar with 35 mm film, then it won't have much meaning to you. You can ignore this Equivalent Field of View as not applicable, and your Field of View is what you see it is. That can work when using the lens, but when shopping for a lens, many of us were very familiar due to years of using 35 mm film, and now that there are SO MANY different sizes of digital sensors, this 35mm film comparison gives us an easy standard of comparison of expected field of view (in 35 mm film terms that many were long used to).
Or if you use two smaller sensors, say 1.5x and 2.7x crops, then the larger crop factor is 2.7/1.5 = 1.8x the smaller crop factor number (which is also the ratio of their diagonals). In this 1.8 example, the Field of View of the smaller sensor (larger crop factor) and its lens is the same as the larger sensor with 1.8 x focal length.
Otherwise, the Field of View of your one smaller sensor is whatever it is, and that's what you need to get familiar with. A full frame comparison is unimportant if you have no interest in full frame.
The term "Crop Factor" always means "Cropped Field of View Factor" (due to smaller sensor dimensions). Crop Factor compares to 35 mm film size, convenient because many people are very familiar with using 35 mm film.
The relative size of our digital camera sensor (THIS cropped sensor that we are using, here called THIS sensor) determines its Crop Factor, which is relative to 35 mm film size (which is called "full frame" size). Crop Factor is about Field of View size, and for that comparison, the 35 mm film size is selected to be a standard of comparison. We might hear things about the lens, but the lens is always totally unaffected. The lens cannot change, its design always remains exactly what it is, it does what it does. THIS smaller sensor simply crops the Field of View to show a smaller area of the lens image (the picture above). We see a smaller view from a smaller sensor, which is called a cropped field of view (cropped when compared to 35 mm film size).
In practice therefore, the smaller cropped sensor has to use a shorter lens (with a wider view) just to be able to see the full "normal" view size again. We might compare that view to what a camera with a larger sensor (35 mm film) sees with its longer "equivalent focal length" lens. But the smaller sensor of course uses the shorter lens to be able to see that same view. This view is what's equivalent, the two lenses are of course different, necessary because the sensor sizes are different. A camera with a crop factor of 2 sees a view of half that size, so it uses a focal length half as long, in order to still see the same view as the sensor of 35 mm film size.
If this division computes the Crop Factor to be 1.5x, it means that the 35 mm film frame diagonal dimension is 1.5x larger (the area is about 2.2x larger, varying slightly with aspect ratios). If 3:2 aspect, a 1.5x crop frame is 1/1.5 or 2/3 the dimensions of the 35 mm film. This size is compared numerically measured on the diagonals to account for different shape sensors. The diagonal of 35 mm film is 43.26661 mm.
We might not be told Crop Factor or even the sensor dimensions in our camera specifications. However we are often told its Equivalent focal length relationship of a comparison lens for 35 mm film, which can tell us Crop Factor and sensor size.
Equivalent Focal Length for 35 mm film =
Focal Length of lens on THIS camera x Crop Factor
The lens Focal Length stays what it is, it does Not get modified. A 50 mm lens on a full frame body is of course still the same 50 mm on any smaller cropped body. The Equivalent Focal Length applies ONLY to a different lens on a different sensor (specifically the size of 35 mm film) that gives the same field of view on that camera as THIS lens on THIS camera. The focal length of any lens on any camera is of course always whatever it is, unaffected, the lens cannot change itself by putting it on another sensor. Crop Factor does not change anything that your lens does, it still projects the same image. Crop Factor only describes the size of your sensor, relative to the size of 35 mm film. The difference is that a smaller sensor "crops" a smaller image with a smaller field of view, smaller than a larger sensor would otherwise see.
For a random example, the specification for some compact camera's zoom lens might say:
So this lens focal length is 4.5 to 81.0 mm.
It also says that a 35 mm film camera would see the same field of view if it used a 25-450 mm lens. If you have 35 mm film experience, this may be meaningful to you, to tell you what to expect that this camera is going to do.
THIS cameras 4.5 mm lens sees the equivalent view of a 25 mm lens on a 35mm film camera (the tiny compact sensor has to use the very short lens to fill its frame with the same field of view).
So simple division can compute crop factor to be (25 mm / 4.5 mm), or (450 mm / 81 mm), Both of which compute the same 5.556x crop factor. This is the actual size relationship of the two digital sensors (diagonals), which affects the field of view that can be captured from the lens. And since 35 mm film size is well known, then with the correct aspect ratio, crop factor can also compute sensor dimensions. However these published values (crop factor, sensor size, aspect ratio, even focal length) are often rounded, to be stated as slightly less precise values than they actually are.
Since any lens on any sensor size remains unchanged by the sensor, its reproduction ratio is also unchanged.
Any lens set to do 1:1 reproduction is 1:1 image size on any sensor size.
All that changes with the sensor size is overall Field of View size.
An American penny coin is 3/4 inch diameter, or 19.05 mm.
1:1 reproduction ratio means that coin image is also 19.05 mm on the sensor, at 1:1 reproduction.
This is true on a full frame sensor height of 24mm, or on a 1.5 crop sensor size of 16 mm height.
The lens does Not change. It is only the frame field of view that changes. The penny image is the same 19.05 mm size, but the smaller sensor cannot show all of this full image of the penny if at 1:1. Then a reproduction ratio of 19/16, or 1.19:1 should just show it all.
What 1:1 means is if photographing a ruler with a lens at 1:1, then a sensor width of 24 mm will show a field width of 24 mm, and a sensor width of 36 mm will show a field width of 36 mm. Objects will all be the same 1:1 size, but field of view size changes with sensor size. Different focal lengths will change the focus distance where the same 1:1 reproduction occurs, but 1:1 will still be 1:1.
Reproduction ratio is (actual real object size in mm) / (object image size in mm). Half size ratio is 2:1.
Magnification is (object image size in mm) / (actual real object size in mm). Half size magnification is 0.5x. Reciprocal 1/0.5 = 2.
So a 1.5x sensor using 1.5:1 lens ratio (0.67x magnification on a sensor 0.67x size) shows the same Field of View as a 1x sensor using 1:1 lens ratio (1x magnification on a sensor 1x size). This Field of View is then same size on both, but image object sizes are different (smaller on smaller sensor).
In contrast, same 1:1 lens on both sensors shows same 1:1 object image sizes, but different field of view sizes (smaller field on smaller sensor). That's the meaning of cropped sensor, it's smaller.
The effective focal length of the combination becomes 1.4 times the lens focal length. 100 mm becomes 141 mm.
The crop factor of the combination becomes previous crop factor x 1.4. Crop factor 1.5 becomes 2.1x.
A 1.4x converter reduces the field of view by 1/1.4, to be 0.7x previous width.
A 1.4x converter increases the lens aperture numbers (reduces light transmission) by one EV.
The effective focal length of the combination becomes 0.7x the lens focal length. 100 mm becomes 70.7 mm.
The crop factor of the combination becomes previous crop factor x 0.7. Crop factor 2 becomes 1.4x.
A 0.7x converter increases the field of view by 1/0.7, to be 1.41x previous width.
A 0.7x converter reduces the lens aperture numbers (increases light transmission) by one EV.
The formula is: f/stop number = focal length / aperture diameter.
If focal length becomes 1.4x longer, then f/stop numbers become 1.4x greater.
A f/stop Number 1.4x greater is one EV, 2x greater is 2 EV.
The focal length causes this, Not the crop factor.
The basic fact is that cropping an image on a smaller sensor can only show a smaller image of a smaller Field of View. The same lens can only project the same image onto any size sensor. Then the smaller crop sensor simply crops it smaller, for a smaller Field of View. Then when subsequently enlarged more to view at normal size again, it has an enlarged appearance, looking as if a longer lens was used. Or cropping smaller in a photo editor also acquires the same enlarged "telephoto" appearance, as if zooming in. See the diagram for the best explanation, that's exactly how it is in the camera. A smaller sensor shows a smaller Field of View.
Digital Crop Factor today is arbitrarily referenced to the 35 mm film diagonal, size of 35 mm diagonal / size of sensor diagonal. A sensor size with 1.5x Crop Factor means 35mm film "full frame" is 1.5x larger, and that this sensor Field of View is 1/1.5 = 2/3 the size of full frame Field of View.
|8 mm||5.5 mm||7.87x|
|Super 8||6.64 mm||6.52x|
|16 mm||12.7 mm||3.41x|
|Kodak Disc film||12.81 mm||3.38x|
|APS C||28.75 mm||1.51x|
|35 mm||43.27 mm||1x|
|127 40x40mm||56.57 mm||0.76x|
|127 60x40mm||72.11 mm||0.6x|
|120 6x4.5 cm||70 mm||0.62x|
|120 6x6 cm||79.2 mm||0.55x|
|120 6x7 cm||89.25 mm||0.48x|
|120 6x9 cm||101 mm||0.43x|
|4x5 inch||153.1 mm||0.28x|
|8x10 inch||325.7 mm||0.13x|
|Digital 4/3||21.64 mm||2x|
This Crop Factor situation has always existed, for film too. Film size affected choice of lens focal length that was suitable. Large film (like 4x5 or 8x10 inch sheet film) used a rather long focal length. Middle size film used an intermediate focal length, and 35 mm was smaller, but not as small as the tiny 110 or Kodak Disc film which needed a very short focal length. A "Normal" lens (meaning with a normal field of view on the specified sensor size, comparable to what the eye remembers seeing there) was considered to be a focal length approximately the same as the diagonal dimension of the sensor (a bit arbitrary, but that was a view typically around 40 to 44 degrees horizontal width was considered a "normal" lens). These different focal lengths were needed so that all formats would show about the same expected Normal field of view.
The point is, smaller sensors require a shorter lens to see the "normal" view size. But the lens mountings were not interchangeable among those film formats, so other than in the darkroom enlarger, their worlds did not interact much back then. The difference today is the digital DSLR sizes might be able to mount and use the same physical lens, and then we notice that the different size sensors cause a different field of view size. Smaller sensors crop the field of view seen. Which seems obvious, yet it causes confusion.
The term Equivalent Focal Length has the specific meaning that THIS camera with its lens and focal length and smaller sensor shows the same Equivalent Field of View as a larger full frame camera would show if using the Equivalent Focal Length. But that Equivalent focal length does NOT affect THIS cropped camera, it is on the full frame camera. The Equivalent focal length has no meaning to the cropped sensor camera, we can just forget about that. Why would we care what some different full frame camera might do? UNLESS of course, if you have experience using, or still do also use a full frame camera, then it does allow field of view comparisons to full frame usage (which you may already be very familiar with).
Newbies sometimes misunderstand at first, and imagine THEIR lens somehow magically became longer focal length on a cropped sensor. But there is no magic, that cannot happen, nothing can actually change. Any one lens always projects the same image regardless of sensor size. With the same lens standing at the same place, the smaller sensor simply frames that image smaller (crops it smaller), and then subsequent greater enlargement back to normal viewing size makes it look zoomed. But instead, if the focal lengths are adjusted to be the Equivalent relationship (full frame sensor instead uses a longer lens with focal length multiplied by the crop factor of the smaller sensor), it is possible to make the Field of View be Equivalent (no zoom effect then).
The following discusses examples of a 1.5x crop factor DSLR camera:
Since the field of view of THIS sensor is cropped smaller, it means that a full frame or 35 mm camera standing in SAME place must use a lens 1.5x longer to see THIS SAME smaller field of view. We call that Equivalent or Effective focal length, but it refers to the 35 mm camera, NOT to THIS camera. It means THIS camera sees a field of view equivalent to the 35 mm film camera, when the 35 mm camera uses the longer equivalent lens. The "comparison" makes it seem like a telephoto effect on this camera, only because its field of view is cropped smaller than the 35 mm camera numbers. The focal length of THIS camera is still whatever its lens actually is, nothing changes. And the focal length of the 35 mm camera is whatever it is, but the difference in sensor sizes make the fields of view be different.
Or if both cameras use the same focal length lens, it means THIS camera would have to stand back 1.5x farther than the 35 mm camera, for both to see the same field of view (the larger "full frame" sees a wider uncropped view, and standing back lets the smaller sensor see the same wider view). So for THAT comparison, what THIS camera sees compares to AS IF the 35 mm camera were using a 1.5x longer focal length (if also standing back there with us). The view makes us think of an equivalent longer telephoto lens, but again, as used by the 35 mm camera. The lens on our THIS camera is always still what it always was.
It also means that any image on THIS smaller sensor will require 1.5x greater enlargement to produce the same size print or view as the full frame camera.
Sports and wildlife photographers may prefer the 1.5x crop camera (over full frame) because its crop makes their 300mm lens appear 1.5x longer (as compared to using that Equivalent focal length on a full frame sensor, like 35 mm film). And it does, they may not have to buy a new lens. With the same lens, the full frame camera would lose 55% of its pixels if cropping to the same smaller 1.5x "telescopic" view. The cropped sensor doesn't have to crop its image as much, so it has more pixels left. However, it does still have to use the pixels to enlarge the smaller image 1.5x more than full frame would.
300 mm lens on a full frame camera result is a 300 mm view, so to speak (in terms of 35 mm film frame size).
On a 1.5x crop camera, a 300 mm result "looks like" an equivalent 450 mm lens on a full frame.
However, it is of course still very much a 300 mm lens on a 1.5 crop camera.
18 mm lens on a full frame camera result is an 18 mm view (in terms of 35 mm film frame size).
On a 1.5x crop camera, an 18 mm result "looks like" an equivalent of 27mm lens on a full frame.
However, it is of course still very much a 18 mm lens on a 1.5 crop camera.
So cropped sensors may aid a telephoto effect (with the same lens),
but wide angle photographers (perhaps real estate agents) love the fully wide view of the full frame camera, because a cropped DX sensor would require a 12 mm lens in this example (to be Equivalent field of view to 18 mm on a full frame). Lens distortion becomes worse in very short lenses.
The smaller sensor certainly has effect causing its smaller field of view, but the literal Crop Factor and Equivalent focal length numbers do not affect THIS camera at all. THIS camera always does only exactly whatever its specific sensor and lens determines it does. Crop Factor is only a method of comparing field of view to that expected from a 35 mm film camera (which many of us spent decades learning).
Obviously, the top picture below is the view of the same scene, with the same lens, at same distance - if using the two sizes of sensors. The Subject size is obviously the same (again, same lens at same distance), but the frame size is not the same. The two drawn boxes show the size of the sensor that will capture the image, what the camera will see. This is simply how it works. When we enlarge the cropped image to be displayed at same size, it appears to be telescopic, as if with a longer lens, or as if standing closer. Any cropped image shows the same telescopic effect when enlarged to same size. Nikon uses the terms FX for full frame sensor and DX for a 1.5x crop smaller sensor. DX is a smaller sensor, and this "crop" changes the viewed area, which causes the differences between FX vs. DX.
The digital DX camera uses a smaller sensor to capture the center of the lens image, which is said to "crop" the image (edges are cut off, as shown above). A full frame lens is shown above, but DX lenses are designed smaller, to project a smaller circle, which only covers the corners of the smaller DX frame (which causes vignetting if on a FX body). Compact cameras use even a much smaller sensor, around 7x5 mm is a common size, but they include several sizes, all tiny (crop factors of 5 to 7 are common).
The difference in these sensor sizes causes different visual effects. For example, the FX sensor is 36 mm wide, and the Nikon DX sensor is 24 mm wide. The ratio of these two crop sizes is 36/24, which is 1.5 to 1, called Crop Factor (normally we compare sensor diagonals, but these two are the same 3:2 shape). The DX frame is cropped smaller (simply because its sensor is smaller). The FX view is obviously 1.5x wider than DX (more wide angle than DX).
But the smaller DX view, when enlarged to show it same size, is magnified 1.5x more than the FX, which is the same effect seen when FX uses a lens that is 1.5x longer focal length (more telephoto than FX). So, the DX camera view "looks same as" if a 1.5x focal length were used on FX. The actual lens focal length is not changed, but the 1.5x number is called the DX "equivalent" or "effective" focal length (as compared to FX). The lens is NOT changed, but DX merely crops to see a different VIEW from it. DX would give same view as FX full frame would see if FX used the 1.5x longer lens at the same distance - or if with same lens, if DX stood back 1.5x times more distant than FX. Again, the lens itself is unchanged of course, it still does whatever it always does in both cases, but the view seen by a smaller DX sensor is simply a cropped and enlarged view, different than the wider view seen by a larger FX sensor.
The "effective" or "equivalent" focal length number (due to the crop factor) is simply the comparison to FX size, which is the same size as 35 mm film, which many of us were used to for many years. Back then, we knew what a 24 mm view did before, but it becomes something different on DX. And since the FX lenses are interchangeable (used on DX too), this comparison is important to some users. The only use or importance of this "Equivalent focal length on FX" is to compare the DX VIEW to FX VIEW.
We know the 1.5x number, but sometimes we miss the significance until we actually look though the viewfinder once ourselves. (or the Field of View Calculator should make it be clear). Using the same lens, and relative to each other, FX makes a wide angle view (wider view of more area, but with necessarily smaller contents within that view), whereas DX makes an apparent zoomed in telephoto view (technically, a cropped view), which shows less scene area of course, and the subject is magnified when it is viewed enlarged to be the same size again.
Below are D300 DX and D800 FX images, using the same 105 mm lens, on the same stationary tripod, at same distance. The only change was that the bodies were swapped out. The camera viewfinder shows these same views.
This is a 105 mm lens on FX (D800). Because the FX sensor is larger, then compared to DX, FX is simply a wide angle view, 1.5x wider than the smaller DX sensor. The larger sensor extends farther out from center, so now we see pixels way out there too. Therefore, because the overall view is bigger, the subject is necessarily shown at a reduced size (scene is bigger, wider, but shown here in the same space, the objects in it are necessarily smaller than DX).
The first obvious reaction looking in a FX view finder is that (compared to DX with same lens), it shows the subject smaller - but the scene is larger, a larger area, visually appearing as if from a greater distance. These two pictures were at the same distance of course, just the view is different (DX is cropped from the FX view - see next one.)
This is the same 105 mm lens on DX (D300), on the same tripod at same distance. DX is just a smaller cropped version of the lens view, but which after enlarging 1.5x more to appear same size here, then it looks like a zoomed in view, "as if" it used a lens of 1.5x more focal length on FX. In this case, DX sees roughly an eight inch view instead of twelve inch view on FX (12/8 = 1.5). It is the same lens however. The focal length is not changed. It is only the "cropped view" that is different. After we enlarge the smaller sensor image more, then the view is zoomed "as if" it had been a longer focal length on FX.
A 10 mm lens is always 105 mm on FX or DX. The "Equivalent" term just means this is the "Equivalent" VIEW (as if seen on FX) of 105 mm x 1.5x = 160 mm focal length (if on FX). The lens is always 105 mm, but after the smaller DX image is enlarged more on the monitor, the VIEW we see on the cropped DX sensor looks magnified, "as if" FX used a longer lens, or "as if" FX were standing closer. Any cropping followed by more enlargement would simulate that. The DX sensor is smaller, so then we enlarge it more, the larger view appears as if magnified by the "crop factor".
The DX image above is actually smaller than the FX image as seen here (cropped by the smaller sensor), but it is enlarged half again more above, just to show the images as the same size.
But (at same enlargement), the DX image is actually this relative size. The subject objects in the image are the same size here as in the FX image.
The same lens of course projects the same image on the two sensors. The same image is of course the same size, but the DX sensor is cropped smaller. DX is a smaller image, but you can see that the area in this DX crop size matches the central area of the FX image above (assuming same lens at same distance).
FX is 1.5x larger, so in comparison, DX is only 2/3 of FX size. We would normally show them at same enlarged size (as above), but they are not same size. The FX sensor is half again larger than DX. DX has to be enlarged half again more, which is not an equal comparison of what we have.
This is the Same FX image, but now it is marked to indicate a DX crop that matches the DX image area. And it is shown enlarged 1.5x more here, so that the cropped DX frame comes out the same size as the FX size above. DX is simply a cropped smaller view of the full size FX frame, enlarged more, because the DX sensor is cropped smaller.
Note that the cropped DX frame is smaller (2/3 which is 1/1.5), and the FX frame is 1.5x larger than DX. I am emphasizing the fact the smaller DX frame has to be enlarged 1.5x more to view or print it at the same size as the FX image. It is simply this crop (and resulting smaller angle of view) and the following greater enlargement, that zooms DX to give the apparent telephoto effect. No other magic illusions are involved. Any crop, done anywhere, anytime, will appear to show the same telephoto effect when subsequently enlarged more back to same viewing size. The smaller image has to be enlarged more to view it at the same size. This is the entire cropped factor telephoto effect, due to the smaller sensor.
And you can also see this same "FX vs DX" view by cropping any image in your editor, by just marking a crop box that is 2/3 the dimensions of the original 3:2 image you use (1/1.5 is 0.667, or 2/3). Or use any crop factor, but this 2/3 dimension will show exactly the view a 1.5x DX camera would see, as compared to the FX view, assuming if both are at the same distance with the same lens. Or just zoom in on any image in your editor (a smaller view, enlarged to same size, appears as a telephoto effect). This crop (shown just above) is the only difference of DX and FX. DX is simply a smaller sensor, which cannot capture a view as wide. When you can believe that, then you've got it.
So DX is just a smaller sensor, which crops out a smaller central area, which necessarily has to be enlarged more, to view at the same effective size. This does change the view it sees - DX sees the same view FX would see if FX used a telephoto lens 1.5x longer (at same distance). Or, if with same lens at same distance, then DX sees a smaller view width, which is necessarily enlarged more (to be the same size print).
FWIW, a typical compact camera with a tiny 7x5 mm sensor and shooting with maybe a 9 mm lens does even more of this, with a crop factor maybe 5 to 1 compared to 35 mm film FX size. Compacts use special very short focal length lenses to compensate for the tiny sensor. The lenses are not interchangeable with DSLR, so this difference is less discussed. The camera specs will mention the equivalent 35 mm film size equivalent focal lengths however (focal length multiplied by crop factor), since many of us were familiar with 35 mm, then we also know what this lens will do.
This is nothing new. In the film days, medium size roll film, and view camera sheet film, were very different sizes than 35 mm film, which again required lenses with different focal lengths to be used (to get the same normal viewing angle). Since these lenses were not interchanged among cameras of different film sizes, it is just something we knew, but did not worry about much.
Speaking of field of view... A "normal lens" is one with a focal length more or less approximately same as the sensor diagonal, significant because this lens is often considered to give what we remember as an eye's "normal" view of a scene. So different size cameras, each with their "normal lens", will take a picture covering about the same "normal" view of the scene.
|iPhone 5||4.8x3.6 mm||6.0 mm||7.2||4.2 mm|
|APS C, or DX||24x16 mm||28.8 mm||1.5, 1.6||30-35 mm|
|35 mm, or FX||36×24 mm||43.3 mm||1||45-50 mm|
|120/220, 6×6||56×56 mm||79.2 mm||0.55||75-80 mm|
|120/220, 6×9||84×56 mm||101.0 mm||0.43||105 mm|
|4×5 sheet film||118×93 mm||150.2 mm||0.28||150 mm|
|8×10 sheet film||194×245 mm||312.5 mm||0.13||300+ mm|
Pure and simple, in all cases of same lens at same distance, FX shows a view 1.5x wider than DX, simply because DX is cropped to a smaller view, and FX of course is not. This has perceived effects.
A 24 mm lens on FX is serious wide angle, twice wider than a normal lens. In comparison on DX, the same 24 mm lens effectively looks like a 36 mm lens would look on FX, but 24 mm is only mild wide angle on DX. We can put a 16 mm lens on DX which would look like 24 mm on FX, which extreme then involves more lens distortions.
Different lens focal lengths, or standing in different places, do show different effects such as depth of field or perspective, but speaking only of field of view, the effects of cropping are the same, regardless if cropping with sensor size, or a zoomed lens, or later in the photo editor. Cropping is cropping. The view of the smaller sensor may require a different lens or subject distance, but its actual effect is just cropping the view. You can do the same later in the photo editor, however then you lose pixels that the sensor or zoom lens could retain.
A 200 mm lens on FX acts like 200 mm, in comparison to 35 mm film. In comparison on DX, the cropped view from the same lens looks like 300 mm (would look on FX or 35 mm). In that way, DX shows 1.5x effectively longer telephoto view (as seen on FX). The lens and its image does not change, but DX sees a cropped view on the smaller sensor (which when enlarged later, appears telephoto). This is perceived as an advantage at longer range, and for this reason, DX is popular for sports or wildlife. But FX shows wide angle much easier.
Of course, it does not matter when we crop it (to get same view). We could crop with the smaller camera sensor area, or we could do exactly the same thing later at home, by just cropping the FX image to be smaller DX size, and then enlarging more. You can see this same telephoto effect in your photo editor by simply zooming in. Other than the initial file size and the cropped telescopic view, the only difference and concern might be about the pixel density - the final cropped dimensions would only have about 40% of the pixels left. Starting from the D700 12 megapixels, cropping FX to DX leaves 5 megapixels. The D600 24 leaves 10 megapixels, and the D800 36 leaves 15 megapixels. But this is the same result, regardless if cropped in the camera, or done later. So if you are shooting the distant wildlife with FX, and wishing for the DX telephoto effect, either select the DX menu, or just plan to crop it later. However, there is a bigger difference. If instead using the real DX camera, it returns its normal 16 or 24 megapixels for that DX view, which is a plus.
The purpose of the effective focal length comparison (compares lens view to that using 35 mm film frame size) is simply that for anyone who was long accustomed to 35 mm film (same size frame as the FX sensor), now our lenses act that same familiar way in FX digital - a 30 mm lens means the same thing on FX (same view) - that a 30 mm lens always meant for 35 mm film. So this is another relative advantage of FX - FX is like "Old Home Week" again - the way we learned to think of it in the past. "Effective focal length" (actual focal length x sensor crop factor) is used to compare a lens view to 35 mm film format, which helps old timers "know" or predict what other sensors will show. Which may be pointless to newcomers who never used 35 mm film, but nevertheless, it is important to those many who grew up thinking that way.
Compatibility: Both FX and DX lenses will "mount" on all DSLR bodies. FX lenses are those that don't say DX. A Nikon FX lens will "work" regularly and well on the DX body (but some DX bodies will need both FX or DX lens to be AF-S to auto focus). And the DX lens will "mount" on the FX body, but the big difference is that DX lens diameter coverage is smaller, and the circle diameter only covers the Blue frame above. The FX lens are designed larger to cover the red frame above, as shown. This makes FX lenses be larger, heavier, and more expensive, to cover the larger frame. So (depending on zoom value) the DX lens on a FX body probably suffers extreme dark unfilled corners, simply not designed for FX bodies. However, most FX DSLR do have the option to create a smaller DX size cropped image, and then DX lenses can work that way, but this DX crop loses more than half of their pixels, like 10 megapixels instead of 24 megapixels.
K.I.S.S. tells me not to complicate things, but who listens? Just a quick note: Changing where we stand with the camera to get the same view may give the same angular view, but it does still change a few things:
The Nikon FX models give you both choices - you can shoot DX or FX mode, for both Raw and JPG. That makes DX show different in the viewfinder (not like actual DX cameras), in that the DX frame is seen as the smaller cropped area bordered with a red box inside the full FX frame (not enlarged in viewfinder - the DX viewfinder view is very much like my last picture example above - a smaller box marked inside a larger frame). The viewfinder is optical, but Live View is digital, so DX mode in Live View can show the enlarged DX frame. The final DX image result will be necessarily enlarged. Or of course, we can always crop FX to the DX view and size anytime later.
However FWIW, be aware that the big downside of using one walk-around lens like a 24-120 mm on a FX body in DX mode is that 24 mm offers no wide angle when switched to DX mode. DX requires 16 mm to do what 24 mm does on FX, so plan on needing the 16-85 mm lens for DX mode.