www.scantips.com

Equivalent Focal Length for a Cropped Sensor

Crop Factor is mainly on the previous page. Crop Factor calculators are on the next page.

Equivalent Focal Length

We often hear beginner questions like this one:

What is the Equivalent Focal Length of a 50 mm lens when it is used on my crop 1.5x or 1.6x camera?

But it does NOT work that way. Any 50 mm f/1.8 lens is always a 50 mm f/1.8 lens, on any camera body and sensor. The Focal Length of the lens is as marked, 50 mm. The sensor size cannot change anything about the physical lens. Therefore, the focal length is of course still 50 mm, including even on the cropped sensor body. The widest aperture is still f/1.8. It is still the SAME EXACT LENS, with its own real focal length and aperture. If using the same lens, the smaller sensor simply captures a smaller Field of View (the view is cropped to sensor size), which is also a smaller image (same size as sensor). The actual difference of using a smaller sensor is just a smaller image, and if comparing with the same lens focal length, a smaller cropped Field of View.

Equivalent Focal Length is NOT about your camera, and does NOT affect your use of your camera. Equivalent Focal Length is a comparison with the Field of View seen by another camera, which conventionally is a full frame or a 35 mm film camera. Specifically, the Equivalent Focal Length is the Equivalent lens used on the 35 mm film camera to see an equivalent Field of View as your camera and your lens sees.

Why would we want to know Crop Factor and Equivalent Focal Length? 35 mm film was the most popular film used, and its "full frame" size is the comparison standard, because the many of us with years of 35 mm film experience well know what result to expect from various focal lengths on 35 mm film. This comparison then tells us what this smaller new sensor would see, with new-fangled crop factor 2.7x or 5.5x. This is very good information in certain situations. For example, if you are familiar with what a 24 mm lens does on 35 mm film (and many people certainly are), and if told a new compact camera’s tiny sensor and unimaginably short lens (maybe 4+ mm) has an Equivalent Focal Length of 24 mm on 35 mm film, then that tells you exactly what it will do, in your own terms. Or you know that a 1.6x crop DSLR needs 24/1.6 = 15 mm lens to match that same 24 mm field of view on Full Frame.

However new users who have never used a 35 mm film or Full Frame camera won’t have use for Equivalent Focal Length, which describes the lens needed for a full frame sensor to see the same Field of View that your camera sees. Understanding a reason to care probably is helped by some 35 mm experience. You will already know if it has meaning for you or not, and don’t otherwise worry about it.

Crop Factor CANNOT change your focal length. Equivalent focal length is NOT a new focal length of your lens. Your lens always remains what it actually is. If it is a 50 mm lens, then it is a 50 mm lens. If the focal length numbers are "equivalent" (meaning, if your camera uses your focal length N, and the 35 mm film camera uses focal length of N × your crop factor), then the thing that is Equivalent is the Field of View seen by both cameras. The so-called Equivalent Focal Length is mounted on the other referenced full frame sensor (like 35 mm film) so it would then have an equivalent Field of View, same as your cropped sensor sees using its own lens.

Larger Crop Factor simply Reduces your Field of View. A smaller sensor simply "crops" the lens view frame smaller than a larger sensor would have seen. This does NOT magnify the subject image, it instead merely crops its frame smaller. Then we normally must use a shorter lens to provide the wider view again, which is less magnification to fit the wider view onto the smaller sensor. However, then when we later necessarily must enlarge the smaller image more in order to see the same viewing size, the enlargement does appear larger and magnified (as if zoomed), but the contained detail is no greater. It is just a smaller image enlarged then. In contrast, if we had actually increased lens focal length to zoom in the camera, the subject is enlarged in the frame, with corresponding increased image detail. But just enlarging an existing small image later does Not increase its detail.

Equivalent focal length only applies to the field of view that a 35 mm film frame would see. Chances are, you might not care what the full frame format may show, unless you had significant 35 mm film experience to be familiar with it. But since many people do, the 35 mm full frame became the standard of comparison for Field of View.

Any lens can only do whatever its focal length does do. A lens cannot change by simply mounting it on a different sensor. The smaller sensor does capture a smaller cropped Field of View, but the lens does Not change in any way... not focal length, and not f/stop. A smaller sensor is simply smaller, so it can only capture a smaller Field of View.

Example: You use a 50 mm lens on a Crop Factor 1.5x camera. It's focal length is of course 50 mm. The equivalent focal length in this case is 50 × 1.5, or 75 mm. The meaning of this is that a full frame camera sensor is 1.5x larger, and if standing in the same place, and both used the same lens focal length, then the larger sensor would see field of view 1.5x larger (because the smaller sensor "crops" the view). But if the larger sensor instead used the longer 75 mm "equivalent" lens, then the meaning is that it would see the same field of view that the 1.5x cropped sensor sees with its 50 mm lens. One purpose of this comparison is if you have years of experience using lenses on 35 mm film, this comparison tells you (in those terms) what Field of View to expect from the lens on your new cropped sensor digital camera.

Equivalent focal length is often the only sensor size specification given on small compact or phone cameras (sensor dimensions and crop factor are often not mentioned). For 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)

It says this Equivalent focal length on a 35 mm film camera would see the same Field of View if IT used a 25-450 mm lens, but it also says is the real focal length of THIS lens is 4.5 to 81.0 mm. From that, now we know THIS crop factor is 25 mm / 4.5 mm = 5.556 (because it is conventionally compared to 35 mm film frame size).

Diagram of Field of View
Fields of View of two sensor sizes:
If Smaller sensor is Crop Factor 1.5, then
Equivalent Field of View if Full frame has 1.5 FL.
If Same lens, Full frame is 1.5x Field of View.

Crop Factor is Not even about the lens. Crop Factor is about the cropped Field of View due to the smaller sensor size. Crop Factor is the ratio of the two sensor sizes, ratio equal to larger/smaller. It is specifically about the sensor size, as compared to 35 mm film size as being the standard comparison. This sensor size is measured on the diagonal dimension (to account for Aspect Ratio).

Equivalent Focal Length is often said as Effective Focal Length. But the meaning and use is:

Using a longer lens focal length magnifies size to crop the field of view smaller, and a smaller sensor simply captures a smaller image and smaller field of view. Crop Factor is the numerical degree in this concept of a smaller sensor cropping the image and field of view smaller.

A Crop Factor of 1.5 means that (if both are using the same lens with same focal length) the larger Full Frame sensor sees a Field of View 1.5x larger dimensions than the small sensor (orange sensor case in diagram). In this case, the smaller sensor Field of View is 1/1.5 size of the larger one (1/1.5 = 2/3 size if 1.5x, or 5/8 size if 1.6x).

So, if the 1.5x larger Full Frame sensor instead uses another lens focal length 1.5x longer, then it sees the same smaller (equivalent) Field of View as the smaller sensor using the shorter lens (the green sensor case in diagram). The usual concept about Equivalent Focal Length is that it is on the other camera with the larger sensor, normally compared to 35 mm film size (called Full Frame size). The Equivalent Focal Length applies to the 35 mm film camera frame.

Or, if both use the same focal length lens, standing in the same place, then the larger sensor simply sees a larger field of view. But if the smaller cropped sensor simply stands back 1.5x further than the larger sensor, it also again sees the same larger Field of View. It is still a smaller image, but the same field of view in this case.

This smaller image from the smaller cropped view of the smaller sensor, when necessarily enlarged again to be same size as the larger again, does appear to be as if zoomed, to be the same view as if a longer lens had been used ON THE LARGER SENSOR. Appears zoomed simply because we enlarged it more, same as if you zoomed it in your photo viewer. But on the smaller sensor, it appears 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 the field of view that this smaller sensor actually does see with this original lens (both will see same subject size and view, relative to the size of their frames). But the Equivalent Focal Length lens is mounted on the OTHER full size sensor, Not on the cropped camera. The cropped camera uses the lens that it has.

OK, yes, the ratio calculation can be reversed to show the equivalent view that THIS camera would see, as compared to this same lens on the full size sensor camera (and the third calculator below will do that).

Examples: If using the same lens, the reversed crop factor and equivalent views are:

A 1.5x crop sensor sees 1/1.5 = 0.667x or 2/3 size view that full size sensor sees, and would need a shorter focal length 2/3 as long (wide angle) to see the same larger view as the full size frame. Or the full frame sensor would need 1.5x focal length to see the same view as the small sensor.

A 1.6x crop sensor sees is 1/1.6 = 0.625x or 5/8 size view that full size sensor sees, and would need a shorter focal length 5/8 as long (wide angle) to see the same larger view as the full size frame. Or the full frame sensor would need 1.6x focal length to see the same view as the small sensor.

A 2x crop sensor sees is 1/2 = 0.5x or 0.5x size view that full size sensor sees, and would need a shorter focal length 1/2 as long (wide angle) to see the same larger view as the full size frame. Or the full frame sensor would need 2x focal length to see the same view as the small sensor.

The normal way it is always seen published compares the field of view of the smaller sensor to a 35 mm film camera (called 1x full frame) with its longer Equivalent Focal Length to see the same field of view. The full frame camera sees a 1.5x or 1.6x wider view than the 1.5x or 1.6x cropped sensor. If you don't have much 35 mm film experience, that may not have much meaning for you. But many people have considerable 35 mm film experience using many familiar lenses, and this can tell them exactly what view to expect from the new smaller camera. I dwell on it because the typical beginner questions like in the little gray box above do need a better understanding about it.

So the standard convention used is that the Equivalent Focal Length means:

The Field of View that the cropped sensor sees with its lens,
is the same size of
the Field of View size that a larger "full frame" sensor would see
if the larger sensor uses the computed Equivalent Focal Length lens.

The full frame camera uses the "Equivalent Focal Length" lens (which is the smaller crop factor times its focal length). The larger sensor (which normally captures a wider view) uses the longer lens to limit its field of view to see the same smaller size field of view that the smaller sensor sees in its frame, which is the standard meaning of equivalence.

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 (typically they don't explain at all). Some of the best sources word it as "For example, a 70-200 mm lens becomes a virtual 105-300 mm lens on a 1.5x APS-C sensor." However that is simply is NOT true, the lens is NOT changed in any way by our camera sensor size. Our lens remains what it is, and no lens change happens... although if we are used to thinking in terms of full frame, we might still think of that view in that 105-300 mm way. What it means is that our smaller sensor crops the full view from the lens, so that our cropped field of view is what a larger full frame camera would see if IT USED the "equivalent" lens. If our experience previously learned to think in full frame terms, this is useful to us. But the "equivalent" lens is NOT on our camera. Our lens remains totally unaffected, it still does what it always did (that was how they meant "virtual", not physically existing, they just didn’t know to say it that way.) But the entire effect is only in our mind's eye, when we imagine what a full frame sensor would see with its equivalent lens. All that happens is the "equivalent" 105-300 mm lens on a full frame sensor and our 70-200 mm lens on a 1.5x APS-C sensor simply see the same field of view (and because the smaller sensor crops its view smaller, normally it would need to use a shorter lens to compensate to still show the same wider view). It's like two different 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.

Advantages of Full Frame or APS Cropped sensors

Nikon's name of 1.5x cropped APS-size sensor is called DX, and Canon calls them APS-C for 1.6x crop. I will try to call all of them "APS" here, meaning 1.5x or 1.6x cropped sensors (but for simplicity, will use 1.5x crop factor numbers below). The APS reference is a frame size comparable to the APS-Classic film size, roughly 24×16 mm or a bit less. So this is a comparison of 1x Full Frame size sensors to APS size cropped sensors (1.5x or 1.6x). Both sizes are found on DSLR models.

Pure and simple, in all cases of using the same lens at same distance, Full Frame shows a view 1.5x wider than APS, simply because APS is cropped to a smaller view (1/1.5 = 2/3), and Full Frame is not. The cropped sensor simply captures a smaller cropped image. This size and resulting enlargement has perceived effects.

This comparison of cropped sensor with full size sensor only has meaning to you if you are interested in a full frame camera, or if you have experience with 35 mm film cameras, or both. Otherwise, if full frame is of no concern, then it would seem that neither should crop factor be. However, a larger crop factor does mean the sensor is correspondingly smaller, requiring greater enlargement to viewing size, and also is subject to more digital noise than a larger sensor.

When we crop it does not change the cropped view (to get same view with same lens). We could crop with the smaller camera sensor area, or we could do exactly the same thing later at home, by just cropping the Full Frame image to be smaller APS 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 would be about the pixel density — because if the final image were cropped, the final cropped dimensions would only have about 40% of the pixels left. Starting from the D700 12 megapixels, cropping Full Frame to APS 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 Full Frame, and wishing for the APS telephoto effect, either select the APS menu, or just plan to crop it later. However, there is a bigger difference. If instead using the real APS camera, it returns its normal 16 or 24 megapixels for that APS view, which is a plus.

The purpose of the equivalent 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 Full Frame sensor), now our lenses act that same familiar way in Full Frame digital — a 30 mm lens means the same thing on Full Frame (same view) that a 30 mm lens always meant for 35 mm film. So this is another relative advantage of Full Frame. Full Frame is like "Old Home Week" again — the way we learned to think of it in the past. "equivalent 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 Full Frame and APS lenses will "mount" on all DSLR bodies. Full Frame lenses are those that don't say APS. A Nikon Full Frame lens will "work" regularly and well on the APS body (but some APS bodies will need both Full Frame or APS lens to be AF-S to auto focus). And the APS lens will "mount" on the Full Frame body, but the big difference is that APS lens diameter coverage is smaller, and the circle diameter only covers its smaller sensor size. The Full Frame lens are designed larger to cover the large full frame sensor size. This makes Full Frame lenses be larger, heavier, and more expensive, to cover the larger frame. So (depending on zoom value) the APS lens on a Full Frame body probably suffers extreme dark unfilled corners, simply not designed for Full Frame bodies. However, most Full Frame DSLR do have the option to create a smaller APS size cropped image, and then APS lenses can work that way, but this APS crop loses more than half of their pixels, like 10 megapixels instead of 24 megapixels.

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:

A general purpose walk-around lens like 24-120 mm is great and versatile on full frame, but be aware that the big downside of using one lens like a 24-120 mm for APS cropped mode is that 24 mm offers no wide angle then. Crop 1.5 requires 16 mm to do what 24 mm does on full frame, so plan on needing the 16-85 mm lens for cropped APS mode.

The Nikon Full Frame (FX) models give you both choices so you can shoot DX or FX mode, for both Raw and JPG. That makes DX show cropped size 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 we can always crop FX to the DX view and size anytime later.


Diagram of Field of View
Fields of View of two sensor sizes:
If Smaller sensor is Crop Factor 1.5, then
Equivalent Field of View if Full frame has 1.5 FL.
If Same lens, Full frame is 1.5x Field of View.

The basic fact is that cropping an image with a smaller sensor can only show a smaller Field of View, but it cannot affect what the lens does. Then a smaller 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, the size of 35 mm diagonal / size of sensor diagonal. A sensor size with 1.5x Crop Factor means 35 mm 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. Carrying the 35 mm film size comparison over into film sizes produces this chart:

 Film SizeFrame
Diagonal
Area
mm²
Crop
Factor
8 mm5.5 mm14.57.87x
Super 86.6 mm21.26.52x
16 mm12.7 mm65.63.41x
Kodak Disc film12.8 mm803.38x
Minox13.6 mm883.18x
11021.4 mm2212.02x
APS C28.7 mm3911.51x
12639.6 mm7841.09x
35 mm43.3 mm8641x
82848.8 mm11200.89x
127 40x40mm56.6 mm16000.76x
127 60x40mm72.1 mm24000.6x
120 6x4.5 cm70 mm23520.62x
120 6x6 cm79.2 mm31360.55x
120 6x7 cm89.2 mm38920.48x
120 6x9 cm101 mm47040.43x
4x5 inch160 mm256250.28x
8x10 inch326 mm515620.13x
 Digital SensorsFrame
Diagonal
Area
mm²
Crop
Factor
1/4"4.50 mm9.729.61x
1/3" iPhone 66 mm17.37.21x
1/2.6" Samsung6.9 mm22.66.31x
1/2.55" iPhone XR7.1 mm246.12x
1/2.3" compacts7.7 mm28.15.64x
One Inch, CX15.9 mm1162.73x
Four Thirds21.6 mm2252x
Canon APS-C26.7 mm3291.6x
DX Nikon28.2 mm3671.5x
Full Frame43.3 mm8641x

This Crop Factor situation has always existed, for film too. Except it wasn't called Crop Factor back then, it was called film format. Film format size affected choice of lens focal length that was suitable, in the same way as Crop Factor, for the same reason. For a "normal lens" (giving a normal field of view), large film (like 4x5 or 8x10 inch sheet film) necessarily used a rather long “normal” focal length, like 150 to 300 mm. Medium size film used an intermediate focal length (about 75 mm), and 35 mm film was smaller (lens about 50 mm), but not as small as the tiny 110 or Kodak Disc film which required 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 more or less approximately the same as the diagonal dimension of the sensor (a bit arbitrary, but a field of view typically around 40 to 45 degrees horizontal width was considered a "normal" lens. Cell phone cameras often are wider.) These different focal lengths were needed so that all size of formats would show a picture with about the same expected Normal field of view.

The point is, smaller sensors necessarily require a very short lens to see the "normal" view size. But the lens mountings were not normally interchangeable among those film formats (often not removable at all), so other than in the darkroom enlarger, using the same lens on different film formats was not often possible. The difference today is the digital DSLR sizes might be able to mount and use the same physical lens, and then it gets attention when 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 common standard of comparison for Crop Factor is the familiar 35 mm film, and Crop Factor is the diagonal of 35 mm film divided by the diagonal of the various other sensors, which is a comparison of the sensor size and its field of view. The surface area of a cropped sensor size compares to the 35 mm film full frame area as 1/crop factor² (then × 100 to be a percentage, e.g., 1.6x crop area = 1/1.6² × 100 = 39% of 35 mm film area).

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 instead 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 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 that they are told that THEIR lens somehow magically becomes an "equivalent" longer focal length if on a cropped sensor. And some poor descriptions do confuse it that way, but there is no magic, and that cannot happen, nothing can change in the lens. Your camera lens (without optical adapters like teleconverters or extension tubes) always uses its real focal length, and any lens always projects its own image regardless of sensor size. The only thing that changes is that with the same lens standing at the same place, the smaller sensor simply crops that image smaller, and then subsequent greater enlargement back to normal viewing size makes it look as if zoomed in the full frame camera (same field of view). But instead, if the focal lengths used are adjusted to be the Equivalent relationship (instead on a full frame sensor that uses the longer lens with equivalent focal length multiplied by the crop factor of the smaller sensor), it is possible to make the Field of View be Equivalent. The "equivalent" focal length is used on the other full frame sensor. The cropped camera always uses the lenses actual real focal length.

The following discusses Examples of photo from a 1.5x crop factor DSLR camera compared to a Full Frame 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 DSLR 1.5x crop camera (over full frame) because its smaller cropped area makes their lens appear 1.5x longer (only 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. But actually using the cropped sensor can provide a full count of pixels. However, it does still have to enlarge the smaller image 1.5x more than full frame would.

Obviously, the top picture below is the view of the same scene, with the same lens, at same distance, but 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 "equivalent" 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, 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 "Equivalent" or "effective” 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, and then 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. The ruler roughly shows fields of view of about 12 and 8 inches, which is roughly the 1.5x crop factor. Crop factor computes the diagonals, but these are the same aspect ratio (same shape, so crop ratio applies to W and H too).


This is a 105 mm lens on Full Frame (D800 FX). 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 overall scene is larger, a larger area, visually appearing as if from a greater distance. These two pictures were at the same distance, 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 always projects the same image on the two sensors. The same image is the same size, but the smaller DX sensor crops it smaller.

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, 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 Sam 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. 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.

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 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 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, its size is what it is, but the literal Crop Factor and Equivalent focal length describe that size, but the 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).


So a smaller sensor is just a smaller sensor, which simply crops out a smaller central area from the lens, which necessarily has to be enlarged more, to view at the same effective size. A "normal" lens" (considered to offer a customary camera "normal" field of view) is a lens with focal length more or less about the same as the sensors diagonal dimension. So a smaller "cropped" sensor must therefore instead use a shorter lens to see a customary similar "normal" field of view. At the same distance, DX sees the same view FX would see if FX used a telephoto lens 1.5x longer (larger sensor with "equivalent" focal length × the crop factor). Or, if with same lens at same distance, then the smaller cropped sensor sees a smaller cropped view width.

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 64.8x3.6 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 mm145-58 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


There are four Crop Factor calculators on the next page.

Copyright © 2012-2022 by Wayne Fulton - All rights are reserved.

Previous Menu Next