Understanding Crop Factor

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There is a great deal of confusion surrounding crop factor, and it is particularly difficult to explain, but let’s give it a try, shall we?

Before we dive in, let me dispel two vicious rumors related to crop factor that are circulating through the photography (Internet) world today:

  1. Crop factor does NOT affect a lens’s focal length.
  2. Crop factor does NOT affect a lens’s aperture.

Before you scroll to the bottom of the screen to leave a comment to the contrary, let me explain why I am stating these facts…

Focal Length The focal length of a lens, expressed in millimeters, is the distance along the lens’s optically central axis (beginning at the rear nodal point) to the image plane in the camera (often illustrated by a "Φ" on the top plate of a camera body) when the lens is focused at infinity. The image plane in the camera is where you will find your digital sensor or film plate.

Therefore, a 50mm lens can measure 50mm from the point where light rays begin to exit the lens in the same direction as they entered the lens until they arrive on the image plane. Some “pancake” lenses and mirror lenses have optical tricks to shorten them, but in general, the focal length is that physical measurement.

A zoom lens can change the physical focal length of a lens. Sometimes this movement is contained inside the lens—the lens body does not physically change length—and other times the lens does change its size.

However, regardless of what kind of camera or sensor you place behind the lens, the focal length will not change just because you have a larger or smaller sensor or frame of film. I will explain later how sensor size (or film size) changes the equivalent focal length—not the true focal length of the lens.

Aperture  is the size of the opening in the lens. Some lenses have fixed apertures that cannot be changed, but most photographic lenses have variable apertures to control the amount of light entering the lens. This opening is regulated by a diaphragm comprising blades that can be adjusted to vary the size of the hole (aperture) through which the light passes.

In photography, aperture is expressed as a ratio of the focal length to the diameter of the aperture opening. The ratio is commonly referred to as an f/number, f/stop, focal ratio, f/ratio, or relative aperture.

This ratio is based on physical measurements and is completely independent of the size of the camera’s sensor or the size of the film you are shooting. Sensor size has an effect on depth of field, but not because it changes aperture. Aperture is independent of film frame or sensor size.

35mm Format

The first thing to know about crop factor is that, as with all “factors,” we need to have a base reference from which to work. In the photography world, this reference is a piece of 135 film. In the digital photography world, “full-frame” sensors are the same size as this film; a film frame with a width of 35mm. Cameras of this photography format are collectively known as “35mm cameras.”

A 35mm film strip measures 35mm across
 

One source of crop factor confusion is the use of “35mm” when discussing the reference. The value in this case is used not as a focal-length measurement, but as a measurement of the dimensions the frame of film. The film image area measures 24 x 36mm, but the strip is 35mm wide. So, when you think of “35mm” when it is used in reference to film or the size of a camera sensor, know that you are not referring to lens focal length. You can mount a lens of any focal length, even a 35mm lens, on a 35mm camera. The focal length is the focal length. Film and sensor dimensions are different.

For years, the 35mm camera has been, by far, the world’s most popular camera format. Because of this, for those of us who grew up in the world of 35mm cameras, when we think of the field of view given by a lens of a certain focal length, we can visualize what the photograph should look like. In the 35mm camera world, a lens with a focal length of around 50mm will provide a “normal” view with its human-eye-like field of view. Lenses with shorter focal lengths will provide a wider view and lenses with longer focal lengths will provide narrower or telephoto views.

Digital Sensors

Life was simple back when almost everyone was shooting 35mm cameras and 35mm film. Sure, there were those making magic with medium format and large format cameras, and there were point-and-shoot cameras that took specially made smaller films. My first camera, handed down from my grandmother, was a Kodak Instamatic 30, with its 13 x 17mm 110 film. Back then, no one really paid attention to “crop factor,” even though it existed. I’d bet most photographers didn’t know the dimensions of their 110 film, nor did they know the focal length of the tiny lenses! You just looked through the camera and took the picture it gave you.

Then, digital photography arrived. In its early days, most sensors were smaller than 35mm film, and a virtual can of worms was opened. Why? Because the sensors were smaller than 35mm film, the images seen through a lens of any particular focal length had a different field of view than that of the same lens on a 35mm film camera. Suddenly, a 50mm lens no longer had a “normal” field of view; it was a bit more of a telephoto.

The cropped sensor “sees” a narrower field of view
 

If you never shot 35mm film, this was no big deal because your mind’s eye did not have a 35mm film reference for different lenses. But photographers entering digital imaging decided that they needed to know the “35mm equivalent” field of view of various lenses when attached to a camera with a digital sensor smaller than 35mm film. The reality of it is, “crop factor” serves to translate a measurement into a language in which many of today’s photographers were never fluent to begin with. And, because of this, many of you out there have been very confused and frustrated by the mention of crop factor. Hopefully this article will end your confusion!

Crop Factor

A round lens produces a circular image circle—not rectangular. The sensor, or film, at the back of the camera captures a rectangular portion of this image circle. When we use 35mm film as a standard, any camera with a sensor smaller than a frame of 35mm film will cover a smaller portion of the image circle produced by a given lens and will thereby change the field of view of that lens. This is the “crop” part of the crop factor.

However, because traditionally, the field of view produced by a given lens has been described not as a measurement of degrees, but by the focal length (kind of the “name”) of the lens, we need to translate the cropped field of view into an equivalent lens focal length.

For example, if you attach a 50mm lens to a camera with a smaller-than-35mm film sensor, you will have to multiply the focal length of that 50mm lens by a factor derived from the size differential of the sensor to calculate the 35mm equivalent focal length. This will then give you the means to figure out the lens’s field of view based on that new equivalent focal length. This is the “factor” part of crop factor.

This multiplication factor is the ratio of the size of the digital sensor to the dimensions of the 35mm film negative.

Formula: The diagonal of a rectangle can be determined by a2+ b2 = c2

Full Frame: 24mm2 + 36mm2 = c2

576 +1296 = 1872

Square root of 1872 = 43.3mm

Full-Frame or 35mm Diagonal / Crop Sensor Diagonal = Crop Factor

So, if you have a camera with an APS-C-sized sensor (circa 15.6 x 23.5mm or 14.8 x 22.2 on Canon), plug in the numbers and you will get a crop factor of 1.5x (or 1.6x for Canon).

Then, to find the equivalent focal length of the new field of view afforded by the smaller APS-C sensor, multiply the true focal length of the lens by 1.5x to get the 35mm equivalent focal length of the lens. A 50mm lens on a camera with a 1.5x crop factor APS-C sensor gives a field of view equivalent to that of a 75mm lens on a full-frame or 35mm film camera.

Remember, the actual focal length of the lens is unchanged, as is its aperture.

In our example, if you weren’t familiar with a 50mm lens’s field of view in the first place, this doesn’t really matter. But if you were familiar with the 50mm lens’s field of view, you will know that this same lens, when placed in front of the smaller sensor, has a narrower field of view than your normal vision has.

A comparison of relative sensor sizes.

 

If you have a zoom lens on a smaller-than-full-frame camera, you can figure out the effective focal-length equivalent by multiplying both focal length numbers by the crop factor. For example, a 70-200mm lens becomes a virtual 105-300mm lens on a 1.5x APS-C sensor.

Cameras with sensors or films larger than a 35mm frame will have sub-one crop factors. For instance, a medium-format Pentax 645Z’s sensor measures 33 x 44mm. This gives it a crop factor of 0.78x. A 50mm lens on this Pentax camera gives an equivalent field of view of a 39mm lens.

Full-frame versus The Rest

The crop factor discussion inevitably leads us to the full-frame versus smaller-sensor debate. For my take, click here.

So as not to drive down the well-trodden path here, in summary, full-frame cameras are ideal for landscape images because there is no crop factor and wide-angle lenses maintain their wide-angle field of view. Smaller-sensor cameras give lenses a virtual telephoto effect that is ideal for some sports, wildlife, and macro work. Both formats have advantages and disadvantages.

Another thing to mention: there are “regular” lenses and there are lenses specifically designed to operate on smaller-sensor cameras. These small-sensor lenses may not work well on their full-frame cousins. On a 35mm film or full-frame digital camera, you may experience heavy vignetting. If the small-sensor lens does work on a full-frame digital camera, the camera might simulate the smaller sensor the lens was designed for and automatically provide the crop factor field of view. A regular lens will work happily on a full-frame digital, 35mm film, or smaller-sensor camera. The crop factor will only apply to a lens if it is used on a small-sensor camera. Today, some manufacturers refer to their “regular” lenses as “full-frame lenses” to emphasize that they are not designed specifically for smaller-sensor cameras. But, before digital photography, all 35mm format lenses were “full-frame.”

The Final Word

Crop factor is really quite simple. The confusing thing is that, as I said earlier, it exists to translate an angular measurement (degrees of field of view) virtually into a linear measurement (millimeters of lens focal length) so that old-school 35mm photographers can figure out the real field of view of a lens based on an equivalent focal length resulting from using sensors smaller than 35mm film. Get it? Got it. Good!

I suppose that is useful in many ways, but I have seen many frustrated photographers over the years try to understand and explain this concept. Sprinkle in some bogus information on the Web about magically changing focal lengths and apertures, and everything has become a mess!

I hope this has cleared things up for those who are new to photography or who were confused a few minutes ago. If not, I stand by to take your questions! And, in case you were wondering, the Instamatic 110 film camera has a crop factor of 2x. 

For more information about the theory behind crop factor, be sure to watch this engrossing video.

 

Discussion 18

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Here is what I am still struggline with. Let me see if I can explain. The full frame sensor, by definition, includes the area of the smaller sensor with the crop factor within the full frame. So, if I take an image with a full-frame camera, and at the same distance take an image with a crop factor camera with the same lens at the same aperture, and then I crop the full-frame image to the same dimensions of the crop factor camera, what is the result? At the same aperture, is there a difference in DOF? In sharpness? In some other way? To put it another way, is there really a "telephoto" effect with a crop factor camera that makes for a better (in some way) image than cropping down a full-frame image to get the dimensions, and thus, the same picture?

If the two sensors are identical in every other respect than dimensions - especially with respect to pixel density - there should be no difference.

Having said that, the pixel density is typically different. For example a crop sensor Canon 7D Mk II has a higher pixel density than a Canon 5D Mk III and you'll get better resolution with the 7D Mk II if you have to crop significantly.

Thanks for chiming in, Paul. You are correct!

There would be no difference, except for a possibly higher resolution for the cropped sensor. Depends on the sensor.

Thanks for helping Rick, Tom! And, thanks for reading!

Hey Rick,

Paul and Tom are correct. The cropped portion of the images will be identical in DOF and sharpness if the sensors have the same pixel density (and design). You could split a lot of hairs here, but, in general, same lens, same distance, same aperture, same crop = same image.

Sensor size does effect DOF (see this link), but in the example you gave where you crop a full-frame image to crop sensor size, everything will remain the same.

Thanks for reading and thanks for your question!

-Todd

The lens projects the same image onto the camera's sensor plane. All of the differences between camera bodies using the same lens are based on how much of that projected image is digitized by the sensor, and at what resolution.

To answer your first question, the results will be nearly indentical if the sensors have the same pixel density. People have already done the exact experiment you describe, using an APS-C-sized crop from the center of the new Canon 5DS, whose 50MP sensor has the same pixel density as the current APS-C cameras (7DmkII, 70D). The 5DS actually has modes built into the firmware to capture only the APS-C or APS-H size areas of the sensor (1.6x and 1.3x respectively).

When people talk about crop-sensor cameras like the 7D mkII having more telephoto "reach", they mean as compared to a full-frame camera like the 5DmkII that has about the same pixel *****, but spread out over a larger sensor area. The smaller, denser sensor gets you more reach at the expense of noise performance and some sharpness because it's digitizing the center of the projected image at a higher resolution.
 

Note to the editors: your blog software's profanity filter should probably not be censoring that particular word which starts with C, ends with T and is synonymous with number, quantity, etc.

Hey Adam...don't get me started! On another article, a reader tried to write "ear pl_g," but had to change that to "ear protection" because of the filter. Sorry for the frustration!

Hey Adam,

Thanks for the comments! You, too, are correct.

Thanks for reading!

comment

Response.

How about the perspective for portraits?  An 85-105mm on a full frame was considered a portrait lens for head and shoulders shots. If a 50-70mm on a cropped sensor shows the same area as the longer lens on a full frame would the perspective be the same?  You would have to move in closer with the cropped sensor in order to photograph the full head and shoulders portrait so you would be closer to the face.

Hey jerry,

Great question. This is where you get into the land of something we call, "Opinions." 

The facts are that a 50mm lens gives you the same field of view of a 75mm lens (APS-C) or 80mm lens (Canon APS-C). So, when it comes to things like working distance and how the subject fills the frame, the "normal" 50mm lens acts like a classic 80-ish mm portrait lens.

However, the perspective of the image does change because you are using a different lens. Therefore, the images will look slightly different because of the way the shorter focal length lens bends the light.

Take an extreme example to prove this concept: Take a portrait of a person with a full-frame fisheye lens. Stand directly in front of them at close range. The subject's nose will appear huge and their face will be distorted. Then, crop the heck out of that image to simulate a smaller sensor. The big nose and distorted face remain big and distorted even though your field of view has changed.

So, back to portraits: I find that the perspective difference between a 50mm lens and an 85mm lens is not especially noticeable. But, if you search the web, you will find opinions (often stated as fact) from "pros" saying that the perspective of 50mm lenses is completely unsuitable for portrait work. But, if you ask me, I can show you a handful of portraits taken with a 50mm lens on an APS-C camera that not only I was fond of, but the subject was as well.

My latest portrait lens? The Fujinon XF 56mm f/1.2 R lens that has the field of view of an 84mm lens on the APS-C Fujifilm sensor. The portraits I have taken with that have been well received, except for some of my girlfriend as she does not like many pictures of her. But she never said, "The perspective is wrong because you used a shorter focal length lens."

Great question, jerry. I hope this long answer clears it up for you! Thank you for reading!

Well said. Don't know why this is so confusing for folks. A 50mm lens has a fixed focal length and perspective., regardless of sensor size.

The other big thing, that may be covered in your FF vs. DX article, is that actual portrait length lenses have a more flattering perspective and faster DOF fall off. When we pro shooters left medium format film for the early pro DSLRS with DX sensors, the lenses left much more in focus. If one wants to create separation between subject and background, a larger sensor helps.

Unless you're shooting at f/1.2 with that Fuji 56mm :-)

Hey John,

Thanks for the comments! It's only a confusing topic when people fill the internet with talk about how crop sensor changes focal length and aperture! We have gotten several comments on other articles lately asking why we didn't apply crop factor to lens aperture thanks to misleading information circulating the interweb.

I wont disagree with you about perspective, but, as I wrote above, when you get into the "flattering perspective" discussion, opinion is likely to enter the fray!

That Fujinon lens is amazing for portraits. I do wish, however, that it could focus a little bit closer than it does. Maybe I should get an extension tube and shoot it MF! 

Thanks for reading!

Great Article!  Thanks

You are very welcome, Aimee! Thanks for reading!