# Understanding Sensor Crop Factor and Equivalent Focal Length

## Including WHY the cropped magnification is just 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.

## The Zoom illusion from a Smaller Crop Factor

Yes, it is just an illusion that makes the smaller cropped image (smaller in sensor mm size) to appear as if it were actually zoomed larger. A camera with a smaller sensor will crop the image smaller, resulting in a smaller field of view. So normally such cameras with smaller sensors will routinely use a proportionally shorter focal length to maintain the same Field of View size as the normal view of other cameras. But the cropped sensor simply just makes a smaller image.

But if using the same focal length lens with two sizes of sensors (to compare cropped with uncropped sensors), the smaller one does appear to zoom larger, but that enlargement was Not done in the creation of the camera image. The same lens projects the same image onto any size sensor. Images on smaller sensors do crop the outer frame smaller, but the objects within the frame are the same size if from the same lens. They might seem larger in the smaller frame, but the scene objects are the same size from the same lens. But then, any smaller image must have greater enlargement to get back to the same viewing size, for example to an 8×10 inch print. Any apparent zoom size illusion is only due to the greater viewing enlargement afterwards. Viewing enlargement CANNOT add any additional image detail like actual lens zooming does. Lens zoom actually magnifies the projected image, same as binoculars would do. So the smaller cropped sensor merely provides a smaller image, which then is later necessarily enlarged more to view at the same desired viewing size.

There is no zoom magic in a cropped sensor. There is no larger image projection from the same lens. A smaller sensor does NOT capture a larger zoomed image. There is only the later greater viewing enlargement of a smaller image. FWIW, some digital compact cameras provide this same feature (called Digital Zoom), cropping smaller and then resampling an enlargement, which also reduces resolution in the same way.

So more enlargement is necessary later for viewing the smaller image at a comparable viewing size. This enlargement does get our attention, but it is nothing like the resolution of longer focal length zooms on a larger sensor that needs less viewing enlargement. To be extreme, viewing a cell phone camera with typical 7x crop factor has to be enlarged 7x more than a full frame sensor (then reducing to 1/7 resolution remaining), so there is in fact a real advantage of the larger image (especially for printing). Even if both cameras had the same megapixels, enlarging one 7x more reduces resolution to 1/7 in the viewed image. This may still be acceptable for your snapshots (which are often never printed), but it is certainly important in important images, like those we might hope to sell, or that might want a large print.

Some users with a 1.5x or 1.6x crop camera do imagine they are getting increased zoom results over a 1x crop camera using the same lens, but in fact, it is only a smaller cropped image that simply must be viewed after enlarging larger. Repeating, the illusion is only due to the larger viewing enlargement of a smaller image. The extra enlargement has Less resolution than an actual zoom with a longer lens focal length would provide. If you enlarge it 1.5x larger to view it, then the pixel resolution drops to 1/1.5 = 2/3 as before (which is NOT the case of an optical zoom in a lens).

Zoomed in a photo editor

This iguana image is also shown below, but it is merely zooming the same one existing image file in the photo editor later. It may look zoomed, but it is the same image file, merely cropped more and then enlarged more for viewing at the same size. But enlargement loses resolution in terms of pixels per inch (same pixels, but more inches, so any 2x enlargement is then 1/2 the dpi pixel density).

So do realize that you can get exactly this same zoomed illusion from any existing old image, by simply cropping your image smaller and then enlarging it more to view it at the same size as an uncropped copy again. The smaller image must then be shown enlarged more for viewing, which enlargement costs the loss of some of the resolution. But if instead a longer camera lens had zoomed it, then the sensor digitizes that larger lens view at full resolution. The only difference the smaller sensor contributes is just a smaller original image (which is the definition of "cropped"). The cropped image is in fact just a smaller image that must be enlarged more for viewing. More enlargement is necessary later, just to view the smaller image at the same viewing size. Much more discussion and examples of this illusion below.

Regarding Equivalent Focal Length, we can hear Incorrect notions on the internet, but the Correct facts should instead be obvious: The lens that we are actually using still always does exactly the same thing regardless of 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 convention is that the lens with so-called Equivalent Focal Length is instead used on a DIFFERENT camera which has a Full Frame sensor (same as 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 digital camera sensor. This can be useful to the many of us that are long familiar with using 35 mm film cameras, to know what to expect from lenses on a new digital camera. It likely won't have much meaning to a novice without 35 mm experience.

There is a sometimes seen situation reversing it, that might confuse us until understood. Technically, any two sensor sizes could be compared this way, in either direction, so both have the same Field of View. But our camera is always using the actual focal length that is currently mounted on it.

So the Equivalent Focal Length is NOT the lens used by our camera (we already know its actual focal length), but again, the usual convention is that Equivalent Focal Length is instead only about the lens that a Full Frame sensor (which we might be very familiar with) would use to match the same Field of View size of the lens actually used on our smaller sensor that we now use. Crop Factor is all about our sensor size, and the sensor CANNOT physically modify the lens focal length (which we might hear it does, but it absolutely can’t). However, the 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 we 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 (but there can be exceptions). That will be 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, in 1892. He split 70 mm roll film lengthwise and spliced them together, creating the 4:3 format for his silent movie camera and later all silent movies. But then sound in 1927 had to use an 11:8 aspect ratio to make room for the soundtrack, and movie film speed increased to 24 frames per second to reproduce the sound better. Anyway, Edison's 35 mm film size was then used in some 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 (true IMO since the 1960s). Many photo 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 still know all about 35 mm film. Over many decades, its size was an unchanging constant.

Today, our various digital cameras use many different sensor sizes, nearly all of which are significantly smaller than 35 mm film format, cropping a smaller Field of View, unless compensated with a shorter focal length to retain the usual field of view angle. One significance of the 35 mm film history is that as the standard size comparison, we compare all of the digital sizes 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 (frame 25.1×16.7 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). Nikon uses the APS-C size as 24×16 mm for a 1.5x crop factor. 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 if 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).

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:

• The circular image projected by the lens (this case is a lens designed to cover a full frame sensor, with the wider coverage).
• The red box marks the scene captured in a full frame sensor (35 mm film size, 36×24 mm).
• The blue box marks the scene seen in a "cropped" sensor with same lens (shown as a 1.5x crop factor, approximately 24×16 mm. Meaning the full frame size is 1.5x larger, and the cropped frame is 1/1.5 = 67% of full size. The smaller sensor naturally captures a smaller central area. This example represents the same full frame lens used for both full and cropped sensors. The full frame lens can be used with a smaller sensor, but a lens designed for cropped use only is smaller, only large enough to cover the blue frame (seen in next image).
• So do not misunderstand, the image on a cropped sensor is simply a smaller image than the one on a larger sensor. Both images when shown later must be enlarged to viewing size on screen or paper.
• The lens is totally unaffected by which body and sensor it is on. The lens can only perform the same one way that it was built, and a lens simply uses its “real” numerical focal length. The lens image is projected onto the sensor, which captures and records it. The Field of View difference we see is only due to a smaller sensor, called “cropped”, because a smaller sensor “crops” a smaller Field of View to make a smaller image, like trimming the edges off of the image with scissors, so to speak.
• So another principle difference we notice is that (imagine this example simulates using the same focal length on two sensors of different sizes), the cropped image is simply smaller, and needs to be subsequently enlarged more to view both at same viewing size again. Then (assuming same focal length) the cropped image APPEARS to have a telephoto or zoomed effect. When we simply enlarge it more to view it, it certainly "looks" telephoto compared to the large sensor image. That is because we enlarged it more first. This actual cropping in this example was done in a photo editor, but any smaller cropped image which is then enlarged more "looks" telephoto (compared to the uncropped image).

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. Note that this is only a 1.5x crop factor.

Red-marked Full frame

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.

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

1. Simply zooming in on any existing image in your photo editor then shows a similar smaller crop and the greater enlargement back to the same viewing size (to same frame size). This zoomed viewing in the editor does the same thing as the cropping of a smaller sensor. It is simply a smaller cropped image, which is then also enlarged more, back to be the same viewing size again. But the photo editor may not be the best way to do it, due to substantial cropping greatly reducing the number of pixels remaining (a half size crop of both W×H leaves only 1/4 of the megapixels remaining). However, cropping in the smaller sensor retains the full megapixel count. The apparent magnification is only seen due to the greater viewing enlargement of the smaller image.

Nikon D800, ISO 400 f/8 1/1000
Nikon 24-120 mm lens at 120 mm
and then zoomed in a photo editor

Here's an animated example of the same enlargement illusion of a smaller “cropped” sensor. It sure does look like different pictures, as if each were zoomed with a different focal length. But all views of this iguana is the same one single image file, but simply zooming it in a photo editor, which crops the image in exactly the same way the crop factor of a smaller sensor crops it. So the final view is zoomed, as a "standing in the same place and using same focal length, but simply with different crop sizes" case. The zoomed Field of View gets smaller (both at subject and background view), but all details in that smaller frame just get larger, which reduces the resolution proportionally. Which is Not an issue for zooming in the camera lens, because the sensor then captures the larger view. Zooming in the editor is not a permanent change unless we save it, but it crops the view that we see smaller (cropped by the viewing frame). Then when the frame size we see is enlarged more to remain the same viewing size, then that enlarged visual result DOES appear the same as if we had zoomed in the camera with a longer focal length lens. But the cropped image is just a smaller image, which requires greater viewing enlargement. Greater enlargement of the smaller frame does appear as if magnified.

This cropped view is the same thing the smaller cropped sensor size does, but again, one big difference is that this zoom and crop later in the photo editor does cost MANY pixels, where the cropped camera sensor design is to keep all of the pixels. But any greater enlargement of a smaller image also costs loss resolution in some degree. Using a longer lens is the better magnification method, providing more options of use. The iguana image example cropped in a photo editor shows up to a bit more than 7x zoom (at the maximum). The sensor crop factor "magnification effect" works exactly the same way in the photo editor zoom. The smaller sensor simply crops it smaller, and then we must enlarge that image more to still view it at the same size. The iguana image was a 36 megapixel original with 7360 pixel width, so a 1/7 crop is only about 1000 pixels across, but when enlarged back to the same frame size, it appears 7x magnified. It’s a small image, too small to print 8x10 inches well now, but it’s shown here about 270 pixels width. Having lots of pixels helps to preserve digital reproduction resolution. The smaller camera sensor has a big advantage of not costing any loss of pixels.

2. Or as shown first above, just using a smaller cropped sensor (to capture a smaller cropped Field of View, same zoom effect), with the same lens focal length on both sensors, and then enlarging back to same viewing size is the same effect (same crop, same enlargement, same zoom effect). That is what crop factor is, it describes the size of a smaller sensor (relative to how much larger 35 mm film size is). The smaller cropped sensor creates a smaller image which necessarily requires greater enlargement of that smaller image back to be same viewing size, which enlargement then does appear as if we did zoom in. It is a smaller image, but simply enlarged more to view it. Real photo examples of this situation are compared on next page. This is exactly the same as the photo editor effect (smaller image enlarged more), except the advantage is that the sensor crop does Not remove any pixels. A small sensor today typically is designed to provide plenty of (smaller) pixels. Some do prefer its apparent zoom illusion because of the lower cost and size and weight of the necessary gear, but the smaller image must be enlarged more for viewing, which is no advantage. And the cropped sensor makes wide angle work require an unusually short focal length.
3. Or (in this 1.5x crop case) we could create the same field of view by using a 1.5x longer lens on the larger sensor, which is actual conventional cropping performed by greater lens zoom magnification. The full frame sensor using a focal length multiplied by the smaller sensor crop factor is its Equivalent Focal Length, meaning both sensors will see the same cropped Field of View then. For example, 1x full frame camera with 300 mm lens, or 1.5x crop camera with 200 mm lens sees the same Field of View (if standing in the same place). This longer lens actually does literally zoom in using more lens magnification (creating greater image detail, and this full frame’s larger pixels also offer better noise and ISO performance). The smaller sensor still creates its smaller image which must be enlarged more, and then these two images will look much alike, because the larger sensor’s Field of View is also cropped by actual zooming magnification, but it remains already a larger image. The pros naturally prefer this option, and it is optimum if you have the gear. Digital pixels do reproduce detail better than film grain did, but in a similar way that larger medium roll film and 4x5 inch sheet film were an advantage offering image quality over 35 mm film, the larger Full Frame digital sensor is also considered an advantage for image quality, but costing greater size, weight and price.

There are three aspects of “image resolution”:

• The original analog image detail created by the lens, as line pairs per mm. It won’t get any better than this.
• The resolution of the digital reproduction on the sensor (a rather tiny image), pixels per mm of sensor.
• and again later as enlarged for viewing (for example, printing resolution), pixels per inch or cm of paper or screen, that our eye will see.

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?

Too wordy, but if needed, here are more words 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.