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Camera Sensor Crop Factor
and Lens Equivalent Focal Length

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 APSC. 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:

The lens projects the same image regardless of what sensor is present. If you can remember back to film days, it's exactly like the image projected by a movie projector or a slide projector. Regardless of what size projection screen we might place at the same 10 feet, the projector projects the same image on it. A smaller screen would be like a cropped sensor, seeing only a smaller field of view in that larger projected image. We could call that a "cropped screen". It's exactly the same concept as the cropped sensor. The sensor is a projection screen for the projected lens image. The cropped sensor is simply smaller, so its field of view is smaller.

In the same way, later cropping the image smaller in an editor would crop the field of view smaller too. Or substituting a longer telephoto lens would crop the field of view smaller too. Messy example, because these are not exactly equal, except the smaller Fields of View could be made equal. Cropping with a smaller sensor retains all of its pixels (however it does require greater subsequent enlargement to match size of a larger sensor). Cropping later in an editor loses a significant number of its pixels, and requires greater subsequent enlargement. The telephoto lens provides enlargement of the subject, and retains all of its pixels, which seems the optimum way to reduce field of view. But all reduce field of view, and the point is that crop is all about the field of view.

Crop Factor

Crop factor is about the corresponding Field of View captured by a smaller sensor size, as compared to larger 35 mm film results. Quite simply, a smaller sensor crops a smaller image than a larger sensor could have captured larger and more completely.

We can say that 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 (simply 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.

Crop Numbers

Crop Factor =  
Diagonal dimension of 35 mm film
Diagonal dimension of THIS camera sensor

Calculate Crop Factor

Sensor Width mm

Sensor Height mm


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 2.25x larger). THIS 1.5x crop frame is 1/1.5 or 2/3 the dimensions of the 35 mm film. This is numerically compared 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:

Crop Factor =  

Equivalent focal length with 35 mm film
Focal length of lens on THIS camera

Equivalent Focal Length for 35 mm film = Focal Length of lens on THIS camera x Crop Factor

Calculate Crop Factor from
Equivalent Focal Length

THIS Focal Length mm

35mm Equiv FLen mm

Aspect

The Equivalent Focal Length applies ONLY to a different lens on 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, the way the lens was made. The sensor size can have no effect on the lens. Crop Factor does not change anything that your lens does. Crop Factor does describe the size of your sensor, relative to the size of 35 mm film.

Repeated, because beginners are often confused by this. Crop Factor DOES NOT MEAN that your lens somehow magically acquires a multiplied focal length. There are adapters that you can add to your lens to change its "Effective" focal length, but "Equivalent" means something else. Equivalent focal length is about a different lens on a full frame 35 mm camera. If your camera has crop factor 1.5, and you are told that your 200 mm lens has Equivalent Focal Length of 300 mm, the Equivalence is that a 300 mm lens on a 35mm camera will see the same field of view that your 200 mm lens on the cropped sensor would see (assuming both are standing in the same place). The smaller sensor simply crops the image (and thus, the field of view). If you're familiar with using 35 mm cameras, and know what 300 mm does there, this can have useful meaning to you, to also know what to expect from THIS lens on this cropped sensor. If not, then maybe not. But we have so many different smaller cropped sensors now, and this comparison to old standard 35 mm size is helpful to sort out the many fields of view.

Compute Crop Factor from Equivalent Focal Length specifications

For a random example, the specification for some compact camera's zoom lens might say:

Focal Length: 4.5 - 81.0 mm (35 mm film equivalent: 25 - 450 mm)

That example lens says its zoom focal length is 4.5 to 81.0 mm. It also says that a 35 mm film camera would see the same field view if it used a 25-450 mm lens. That says 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 a very short lens to fill it 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.

Our standard convention is to compare cropped sensor size to 35 mm film size, simply because many of us were very familiar with 35 mm film for years or decades, and already well know what field of view to expect from various focal lengths on 35 mm film. That crop factor comparison tells us what equivalent view THIS sensor will show now. If you're not familiar with 35 mm film, then it may not have much meaning to you. But many of us are, and now that there are SO MANY different size digital sensors, this 35mm film comparison gives us an easy standard of comparison of expected field of view (in terms of the 35 mm film many were long used to).

We might call the longer focal length lens on the larger sensor to be the "equivalent" focal length, but of course, nothing can physically change in our lens. All that happens is that the smaller sensor naturally crops the field of view more. All it means is that the cropped narrow view of the cropped sensor appears "as if" it were instead a longer lens on a larger sensor that we might be familiar with. It is the field of view that is equivalent on the different sensor sizes (if using a longer lens on the larger sensor to make this appear so).

Overkill, but said another way: If you move closer to half the distance, your camera sees a smaller view, and must use a lens with half the focal length to see the previous equivalent view. Or, if you instead stay where you are, but switch to use a sensor half as large, this also sees a smaller view which then requires using a lens with half the focal length to see the previous equivalent view again. Crop factor (2x in this case) is entirely about sensor size, and it refers to an equivalent field of view of an uncropped full sensor size (full size meaning 35 mm film size by convention).

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 same lens 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 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 full frame.

18 mm lens on full frame camera result is an 18 mm view.
On a 1.5x crop camera, an 18 mm result "looks like" an equivalent of 27mm lens on full frame.

So cropped sensors may aid a telephoto effect (with the same lens), but wide angle photographers love the fully wide view of the full frame camera, because a cropped sensor would require a 12 mm lens in this example.

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 above 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 simply 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 simply a smaller sensor, and this "crop" changes the viewed area, which causes the differences between FX vs. DX.

The digital DX camera simply 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). Nikon shows a clear description of FX vs DX. Compact cameras use even a much smaller sensor, around 7x5 mm is a common size, but they include several sizes, all tiny (crop factor of 5 or 6 is 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 simply 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 (cropped by the smaller sensor), but it is enlarged half again more there, just to show the images as the same size.

But relatively (at same enlargement), the DX image is actually this size. The subject objects here are the same size 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.

Below 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, simply because the DX sensor is cropped smaller.


Note that the cropped DX frame is smaller, and the FX frame is 1.5x larger. 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. The smaller image simply 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 on any image in your editor, by simply 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 simply 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 simply 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.

FormatSensor
dimensions
Image
diagonal
Crop
Factor
Normal lens
focal length
iPhone 54.8x3.6 mm6.0 mm7.24.2 mm
APS C, or DX24x16 mm28.8 mm1.5, 1.630-35 mm
35 mm, or FX36×24 mm43.3 mm145-50 mm
120/220, 6×656×56 mm79.2 mm0.5575-80 mm
120/220, 6×984×56 mm101.0 mm0.43105 mm
4×5 sheet film118×93 mm150.2 mm0.28150 mm
8×10 sheet film194×245 mm312.5 mm0.13300+ mm

Advantages of FX or DX

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.

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 simply 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 simply 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.

The same FX lens will perform the same on either a FX or DX camera body. The body does NOT affect the lens design at all, but the smaller sensor certainly affects the smaller cropped field of view captured.

The smaller coverage of a DX lens on a FX body will not be able to fill full frame, so the corners will be black. Some FX cameras can then crop that view smaller to simulate DX coverage, at the cost of losing 55% of the pixels.

Actual Disadvantages:

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 (D700, D600 and D800) 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.


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