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Understanding Sensor Crop Factor and Equivalent Focal Length

Including WHY the cropped magnification is an illusion

There are four Crop Factor calculators on the third page, but first, a detailed explanation of what Crop Factor and Equivalent Focal Length actually are. These terms are not difficult, but without a few details, it seems to get confused. If you want to know how it works, this will be a in-depth actual explanation, but more details also follow.

Digital SensorsDimensions, mmAreaCrop
W×HDiagmm²Factor
1/2.6" Samsung5.5×4.16.8622.66.3x
1/2.55" iPhone XR5.66×4.247.07246.1x
1/2.3" compacts6.17×4.557.6728.15.6x
One Inch & CX13.2×8.815.861162.7x
Four Thirds17.3×1321.642252x
Canon APS-C22.2×14.826.73291.6x
Nikon DX & Sony23.5×15.628.23671.5x
Full Frame36×2443.2678641x

But first a brief summary which might be all you need.

Sensor Crop Factor is a description of the size of a digital camera sensor, as it compares to the well known 35 mm film size, which by convention is the standard comparison used. 35 mm film was the most popular film size, familiar to many.

There are many digital sensor sizes. Most are smaller sensors, which (in this comparison) are called a cropped sensor because a smaller sensor area literally crops the Field of View captured, creating a smaller view in a smaller image, as compared to the area the larger 35 mm film might include.

Numerical Crop Factor
the 35mm film frame diagonal (43.267 mm)

the digital sensor’s diagonal (mm)

The 35 mm film frame size is 36×24 mm. A digital sensor this same size is called a Full Frame digital sensor (i.e., not cropped as compared to 35 mm film), with crop factor 1x. So “Full Frame” and “1x crop” are synonyms for the size of 35 mm film. Full Frame is our 35 mm standard of comparison, of 1x itself.

The diagonal is the important comparison, because the view from a lens is a circular area, and the largest rectangular frame that can fit in the circle has a diagonal equal to the diameter of the circular lens view. Different aspect ratio frame shapes can fit in the circle, but their sizes all have the same diagonal, which is the largest dimension of the frame. Therefore, comparing the diagonals is important to account for Aspect Ratio differences. Two frame sizes with the same Aspect Ratio could compare widths or heights without error, but different aspect ratios can only meaningfully compare the diagonals.

A Crop Factor value of X is a size ratio that means the 35 mm film diagonal is X times larger than the diagonal of this sensor size. The smaller image necessarily requires X times greater enlargement to reach the same viewing size of full frame (for both to be the same specific print size for example).

If both sensor sizes are using lenses of the same focal length (and assuming all lenses are proper choices to at least cover their referenced sensor size), the larger frame shows a Field of View that is X times larger (a wide angle view) than the smaller cropped sensor which crops the lens Field of View smaller. If with same focal length, larger sensors see wider views, and smaller sensors see a smaller field of view.

But an illusion quirk makes the smaller cropped image appear as if it were zoomed larger then. This does get our attention, but the illusion only happens after the smaller image is enlarged more to be able to view it at same size (both viewed as a 8x10 inch print for example). Much more discussion of this illusion below.

Regarding Equivalent Focal Length, we can hear Incorrect stories on the internet, but the Correct facts should instead be obvious: The lens that we are actually using is totally unaffected by sensor size. Crop Factor (which is just sensor size) CANNOT physically change either the focal length or the effective f/stop of any lens. Those definitions DO NOT involve sensor size. The ONLY possible thing that can and does happen is that the Field of View captured by a smaller sensor is reduced (view is cropped to sensor size). The lens with so-called Equivalent Focal Length is instead used on a DIFFERENT camera with a Full Frame sensor (a 35 mm film frame size camera), for it to then show the same Field of View there as is seen by our lens on our camera sensor.

The Equivalent Focal Length is NOT the lens used on the smaller sensor, but the convention is that it instead is about the lens that a Full Frame sensor would use to match the same Field of View size of the lens used on the smaller sensor of concern. Crop Factor is all about the sensor size, and the sensor CANNOT physically modify the lens focal length (which we might hear it does, but it absolutely can’t). But sensor size surely does influence the lens focal length you may choose to use, because small sensors crop the Field of View smaller, and so routinely must compensate by choosing a shorter focal length lens, in order to see a wider view (wide angle). A so-called “normal lens” (showing a “normal” or ordinarily expected camera view) is considered to be a lens with focal length more or less approximately same as the sensors diagonal dimension. That is a short focal length for a tiny sensor.

Influence of 35 mm film size

35 mm was the first movie film, created by Thomas Edison for his first movie camera, 1892. He split 70 mm roll film lengthwise and spliced them together, creating the 4:3 format. His film size was then used in still cameras too. Leica was not the first one to use it, but the influential early impact was the first Leica in 1925. Leica doubled Edison’s frame size (winding horizontally instead of vertically), and 4:3 doubled became 4:6, which is 3:2 aspect ratio. The Leica made 35 mm popular enough that Agfa and Kodak soon released 35 mm preloaded cassettes. And then 35 mm film was popularized by many of the early cameras (Argus 1936, Exakta 1936, Nikon F 1959, Kodak Retina 1960, etc), to become the most popular film size world-wide (IMO, true since the 1960s). Many users became familiar with the expected Field of View seen by various focal lengths on 35 mm film (and learned to think of Field of View in those terms). Many of us know all about 35 mm film. In the day, its size was an unchanging constant.

Today, our various digital cameras use many different sensor sizes, most of which are significantly smaller than 35 mm film format (cropping a smaller Field of View, unless compensated with a shorter focal length to achieve wider field angle). One significance of the 35 mm film history is that as the standard size comparison, we compare all of them to 35 mm film size. The term Crop Factor is a ratio defined to mean:

Numerical Crop Factor
the 35mm film frame diagonal (43.267 mm)

the digital sensor’s diagonal (mm)

For example, a Canon APS-C sensor diagonal is 26.7 mm. The Crop Factor is 43.267/26.7 = 1.6x. 1.6x means the 35 mm film is 1.6x larger than the compared digital camera (each measured on the diagonal). The ratio specifies digital sensor size (inversely), which also specifies relative Field of View size (inversely), and also specifies how much additional enlargement is needed so that the smaller image frame will view at the same size as a larger full frame image (for both to be an 8x10 inch print for example). A digital sensor the same size as the 35 mm film frame (36 × 24 mm) therefore compares as a 1x Crop Factor, and is called Full Frame size.

By convention, the term Equivalent Focal Length definition is the focal length that a 35 mm film camera would use to see the Equivalent size Field of View as the compared digital camera sees with its own lens. A digital sensor CANNOT change the focal length of its lens (as some confusion we might hear implies), but its lens focal length multiplied by its crop factor is the Equivalent Focal Length that is used on a 35 mm film camera for both to then see the same Field of View.

Why 35 mm film? It was the most popular film size, so this can be useful to the many photographers with years of 35 mm film experience. If that’s you, you already think in those terms, and can appreciate the comparison. Otherwise, possibly not, if you’ve never used 35 mm film. The 35 mm comparison may not be useful to everyone, but it is easily ignored. This info should not hurt anyone, except that the internet does confuse us about it. If any confusion, and if you're not interested in what a 35 mm film camera might see, then simply forgetting about Equivalent Focal Length is an easy answer. This number absolutely does NOT affect what your camera might do, which does whatever it was designed to do.

My notion of the "Equivalent" idea is this (for example): The new small digital camera you are thinking to buy has a tiny sensor and a very short focal length lens, say 4 mm, which to you is a very new and different set of strange numbers. But it is claimed to have a 27 mm Equivalent Focal Length (which means the view seen on 35 mm film). You have much 35 mm film experience, and you know well what field of view to expect from the 28 mm lens you had then. Therefore, now you automatically know what view to expect from this new little camera.

The conventional nomenclature compares Equivalent Field of Views to 35 mm film. However, Calculator 3 (see link at top of this page) will compare Field of View of other crop factors (up to four sensors, plus one always 1x is included).

Sensor Crop Factor (with Aspect Ratio) does describe the actual size dimensions of a digital sensor, and also comparative terms of what 35 mm film does with Equivalent Focal Length. Such comparisons are nothing new, film sizes always varied too, with the same situation of different fields of view and similar equivalent focal length situations. See Crop Factors of Film Sizes.

Here We Go, the actual Details of Cropped Sensors

Digital camera sensor sizes are many, but each is of a certain size (its area capturing the image), just like film frames were a certain size. Nikon calls their DSLR sensor sizes FX (full frame) and DX (APS frame, crop factor 1.5). Canon calls them Full Frame and APS-C (EF-S, crop factor 1.6). Full frame is the same size of a 35 mm film frame (36x24 mm), and APS is the smaller APS film frame size (near about 24x16 mm). Compact cameras and phone cameras use much smaller sensor sizes, tiny, typically around 5 to 7 mm sensor width, no larger than the diameter of a pencil, with crop factors maybe around 7x to 5x. Crop Factor (as commonly used) compares the digital sensor size to the size of a 35 mm film frame (which many of us were well accustomed to using).

Cropped and Uncropped area of lens image

A lens projects its circular image onto the sensor, the circular size designed to cover the diagonal corners of the sensor or film. Then the camera sensor captures a rectangular portion of that circle. The picture above attempts to show these things:

Limited lens coverage

Getting this special case out of the way first, this black image shows the general result of a Full frame body incorrectly using a lens designed to only cover a smaller 1.5x cropped sensor size, which is a different lens, but this representation assumes it is the same numerical focal length. Zooming a lens wide possibly might make the circle size a bit larger, but this is the general idea. The full frame lens can be used on the cropped body without issue (if it will mount), then only the central area is used. But the lens designed for a cropped body will also crop on the full frame body. My full frame Nikon has a option for this use to crop that image smaller (to fit the blue frame), but that retains only 45% of the megapixels (if 1.5x).

Anyway, here we go, general usage showing those red and blue marked crop areas above that will appear this way:

Full frame image
Red-marked Full frame

Cropped image
Blue-marked 1.5x Cropped Sensor (with the same lens).
It would NOT be described as Magnified size. All details are still the same size, it is simply a cropped and smaller image, with less Field of View. This is what smaller cropped sensors do.

If your browser screen is less than 400 pixels wide, it will shrink these images to fit on it, which then will Not show a true size comparison.

Enlarged cropped image
This is still the same last image file simply repeated again, but here just enlarged more to view at the same size again. Then as compared to the larger first red-bordered image, it does look zoomed. But which is seen only after being enlarged more, back to the same viewing size again.

We likely do think "Hey, that enlarged one looks like we zoomed in with a longer lens". And this enlargement does look telephoto; this 1.5x crop looks the same as if the full frame camera used a 1.5x longer lens. The fact is that a smaller sensor does in fact see the same field of view that a larger sensor would see if it were zoomed with a longer focal length, specifically an Equivalent Focal Length which was multiplied by the smaller sensor crop factor. And that’s true, and it does sound like zooming, except for the obvious fact that the same lens can only produce the same image, focusing the same image on either sensor. That is Not zooming, but there is still a difference; The cropped sensor is smaller and simply crops the outer frame of the field of view smaller. Cropping is the only change that the smaller cropped sensor can possibly do. So the same lens image is just cropped into a smaller frame, and then we must enlarge it more to view it at the same viewing size again. We do tend to like this enlargement, but more enlargement has the cost of lowering the resolution. If it were somehow not cropped, the same lens would necessarily show exactly the same image from either sensor.

This is a valid simulation of two cameras with two sensor sizes, both standing in same place and using the same lens. The lens did not do this effect, it’s all about the additional viewing enlargement, but the smaller cropped sensor did require that greater viewing enlargement (back to the same viewing size to compare them). We can enlarge either image for any reason, but an image from a smaller sensor necessarily must be enlarged more to see it same size as a larger image (if both are to be printed as an 8x10 inch print for example).

Three methods showing this zooming illusion of magnification

There are three aspects of “image resolution”:

Enlargement is not entirely free. We know there can be some downside. More megapixels do preserve better digital reproduction detail, but pixels do not increase the original lens analog detail available to reproduce. Meaning, a lens does all it can, and then the question is “Can the megapixels reproduce that same detail?” Greater enlargement reduces effective lens resolution proportionally, meaning the actual visible original image detail created be the lens ... because more inches of viewed image (spread over more mm) means proportionally fewer line pairs per mm of image resolution. X times enlargement results in resolution of 1/X of before. We know too much enlargement becomes proportionately soft and visibly blurred. Nevertheless, having lots of pixels does help printing resolution (better digital reproduction of that available analog image resolution). Today’s cameras have lots of pixels (unless we are printing too big). And greater enlargement also reduces Depth of Field, making blur more visible. By convention, calculated Depth of Field numbers refer to what should be visible when viewing an 8x10 inch print size (and the necessary enlargement of a smaller sensor is factored into the CoC factor that uses).

The smaller sensors are very popular, and offer great value with less cost, size and weight, and have become pretty good (even if the camera controls are limited to automation). We do like to think the cropped sensor using the same 200 mm lens gives us longer reach for sports or wildlife photos, and it may perform adequately, but the full frame sensor with longer lens technically can do it better. A larger full frame image has advantages (smaller images, less enlargement needed, a larger Field of View, and often larger pixels with less noise at higher ISO). See advantages/disadvantages on next page.

WHY the Perceived Zoom Illusion in cropped sensors?

Trying to be very clear with greater detail about WHY crop factor causes the perceived illusion of magnification: This should be obvious if you just stop to think a second. A smaller sensor (has a larger crop factor) is called a cropped sensor because it literally captures a smaller cropped image (on a physically smaller sensor, like using a smaller film size). A smaller sensor can only capture a smaller Field of View (a “cropped” Field of View as compared to a full frame sensor, which is uncropped, relatively speaking). And because the image is smaller, it captures a narrower Field of View, so in practice, cropped sensors normally must use shorter lenses to compensate by seeing a wider and more normal Field of View (called Equivalent Field of View when lens focal lengths are chosen to make each sensor size show the same Field of View). A shorter lens provides a wider view than a longer lens, but which is also less magnified, which then allows fitting the same wider view onto the smaller sensor too. But in this example, both sensor sizes will use the same lens focal length.

Suppose that we are photographing a distant bird with two cameras (say the two are 1x and 2x crop for simple numbers), and both are using a 200 mm lens. The same lens focal length projects the same size image of the bird onto the two sensors. So the image of just the bird part is the same size in both cameras (because both are a 200 mm lens, both are the same magnification). You can see that in the red and blue marked images above, the detail is the same size, being the same image with same lens, just cropped to different sensor sizes. Focal length image magnification is not affected by the sensors, a 200 mm lens does whatever a 200 mm lens does, but the sensor sizes do crop the image frame dimensions differently.

So if with the same lens focal length, that only difference is that the camera with larger 1x sensor sees the larger full frame size (a larger Field of View) around the bird, and the smaller 2x "cropped" sensor size crops that frame smaller (a smaller image), which sees a smaller frame (smaller Field of View) around the bird. The same size bird image does more completely fill the smaller sensor frame. But again, it is the same size bird, and the full frame sensor is simply larger around it, and sees a Field of View frame with dimensions twice larger than the smaller 2x cropped sensor sees (assuming same aspect ratio, but they are different fields of view if with the SAME lens), but both see the same size bird inside both frame sizes. This is clearly obvious. The next page contains actual photos on different sensor sizes which shows exactly the same effect of a smaller cropped image simply enlarged more, back to same viewing size.

So when we use the same lens focal length on both sensors, the magnification of the bird is the same size in both, but the frames and fields of view are different size. If we enlarge the smaller 2x crop more to be the same viewing size as the 1x (to be same frame size, for example, both to the same 8x10 inch print size), now the bird becomes 2x larger too, which is now enlarged to be 2x larger than the 1x sensor’s bird. This is simply due to the extra enlargement when we look at the enlarged viewing size. It certainly does appear zoomed in, but only because the smaller sensors image must be enlarged more (to be same frame viewing size again).

You will see exactly the same effect if you simply look at ANY existing image in your photo editor, and then zoom in to see it 2x larger size, which is then cropped to half of Field of View size. See the image just above doing this photo editor zoom, but you should try doing that too (to realize that you know it is true). You see it is the exact same concept as the cropped sensor, for the exact same reasons. It sure will look like a longer telephoto lens was used, but the additional enlargement is what did that. That is the same picture, just cropped and enlarged, so this test is a "with same lens" example (not Equivalent Field of View), but the bird in it will be seen a larger size (because it is enlarged more to view the same size frame). The smaller 2x crop sensor also crops it’s frame to half size, but the necessary extra enlargement enlarges it 2x more, exact same thing. The magnification of a lens cannot be affected by sensor size — a lens can only do what a lens does — but sensor size does affect the cropped Field of View size. The only zoom effect is due to the greater enlargement of the smaller crop.

So yes, if both sensors are using the same lens, the necessary extra enlargement of the smaller sensor creates the illusion of zooming in (which is same effect as you see when zooming in your photo editor). It is still the same smaller original image, but that half size image and subsequent necessary 2x viewing enlargement has the effect that the smaller sensor does get magnified more, but it is only because you enlarged it more for viewing. You could always enlarge the other one too.

You can always enlarge and crop any image in your photo editor. Cropping in the photo editor additionally costs the loss of many pixels (half size crop leaves only 1/4 of the pixels), but the cropped sensor is designed to still provide a full count of pixels. But either way, this illusion of apparent 2x zoom does come at the cost of requiring 2x greater viewing size enlargement of a half size image.

Sports and wildlife photographers might think of the cropped sensor illusion as somehow magically magnifying their view of the bird (with the lens that they have), but which only happens after they enlarge the smaller image more, back to regular viewing size, for example, after printing both sizes at the same 8x10 inch print size. It can be a helpful effect, but there is no magic, and it is detrimental for wide angle efforts. But in fact, 2x greater enlargement reduces image resolution by half. Sometimes we have sufficient resolution to spare, but at extremes, often we don’t. But if both sensor sizes are using the same focal length, then the bird image will originally be the same size (before the smaller image is enlarged more to view it at same size again). If there are enough pixels, it is a choice if to enlarge it more or not (which is the same choice available to either sensor). It can be a handy effect, but you should realize how it works. To avoid these issues, the pro photographers are likely using a longer lens on a full frame camera, but yes, that will be pricey. The real choice is about price, and maybe size and weight of the gear.

Zooming is Cropping. Zooming is also enlargement of that crop, keeping the same viewing size. But cropping is not exactly zooming, because that enlargement is not free. Enlargement costs resolution. Enlargement of X times results in resolution of 1/X of before. And reduces Depth of Field too. You can see here that the distance extremes become more blurred as we zoom in and enlarge more (even if it is still in the same image). Depth of field is affected by viewing magnification, by how well we can see the enlarged blur.

Equivalent Focal Length

The discussion has been about the same focal length on different size sensors. A different case is about Equivalent focal length, which is about two combinations of sensor sizes and lenses, with two different focal lengths each chosen so that both sensor sizes see the same Field of View, meaning the same outer framed size of the Field of View is seen. Compared to a 2x crop factor, the 1x full frame sensor has to use a lens 2x longer (say 400 mm) than the 2x crop sensor uses (200 mm) to see the Equivalent Field of View. In this case, the bird will be half size on the 2x cropped camera, due to the 200 mm lens. However, the smaller 2x cropped sensor and image are half size too, and so must be enlarged 2x more to be the same viewing size (both the same 8x10 inch print size for example). But both the half size bird and the half size frame are enlarged 2x more, and now the two images will appear much the same, both bird size and the Field of View size, when the smaller one is enlarged twice as much (but reducing resolution by half). This is the concept of Equivalent focal length to produce equivalent fields of view (more detail on next page).

I prefer the word Equivalent focal length rather than Effective focal length (we see both, but Equivalent is the more popular wording). Effective suggests that the lens does change magically somehow to see something different, but that doesn’t happen (unless you zoom the actual lens). But actually, Equivalent is about the focal length that gives the Equivalent Field of View if it were used on a full frame sensor. Our camera is using its own lens. The concept is about a comparison of the Field of View of a full frame sensor, compared to the Field of View of our cropped sensor camera that uses the real focal length of its own lens. Then the two cameras then take the pictures with the same fields of view, meaning the same frame size. We cannot quite say they take the same pictures, because they are using different focal lengths, and distance will affect the size of various objects in the picture.

Regardless of what you may hear on the internet, SENSOR SIZE CANNOT AFFECT the lens focal length in any way, which is obviously true, but the term "Equivalent focal length" does confuse newcomers, who often conclude it should change focal length of their lens. Which is Not their fault, many online descriptions confuse it badly. They say a smaller sensor looked like a longer Equivalent focal length was used, but very few ever say that is speaking of when that longer equivalent focal length is used on a full frame camera. It is simply comparing the full frame equivalent Field of View. Equivalent focal length technically means the specific focal length used on 35 mm film size that will then show the same or equivalent Field of View on both sensor sizes. A sensor CANNOT CHANGE the focal length of your own lens, your lens always uses its real focal length. The Equivalent Focal Length is on the full frame camera, not on yours.

Example: A manufacturer’s compact camera lens specification of Equivalent focal length as said correctly:

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

That is from a Canon compact camera specification of its 4.5-81 mm zoom lens. It says that its zoom lens focal length is simply 4.5 to 81 mm, the “real” focal lengths always used. It specifically says that the 35 mm film camera uses the 25-450 mm lens for an equivalent Field of View. That equivalent info is provided for the many users with years of 35 mm film experience, so they will know (in their own terms) what to expect that this tiny sensor will do. If that is not you, then Equivalent focal length may not be of much interest to you.

The only thing that any smaller sensor can possibly do is to simply capture a smaller image, which crops the Field of View smaller. This does then normally require compensating by using a shorter (wider) lens focal length able to reproduce the same field area lost by the smaller cropped sensor. The shorter focal length produces less magnification, but which if short enough, can then fit onto a corresponding smaller sensor, producing the same Field of View again. This then requires more viewing enlargement to see it. "Equivalent focal length" only refers to the longer lens used on the larger sensor (conventional practice assumes it is 35 mm film size as a standard) in order to see the same Field of View as the smaller sensor sees with its shorter lens. Equivalent focal length describes the lens used on the 35 mm film frame size in order to see the same Field of View that our smaller cropped sensor sees. So that is about the OTHER camera, but it can be useful if you are still thinking in terms of your 35 mm film experience.

Sensor size is all that crop factor is... it's only about a smaller sensor that crops the Field of View that it can see... a smaller image which then we have to enlarge it more, to get back to the same viewing size. Crop factor is just about a smaller cropped image, which we then have to then enlarge more, to get it back to a comparable viewing size again. Crop factor is Not about a longer focal length. The so-called longer Equivalent Focal Length is used on a 35 mm film frame for comparison with the smaller cropped sensor, to see the equivalent same Field of View.


More on Equivalent Focal Length continued on next page

Calculators for Crop Factor and Equivalent Focal Length are on a third page

Menu of the other Photo and Flash pages here


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