What is crop factor and how does it relate to focal length?

I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.

Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera?

You can find detailed definition of Crop Factor in Wikipedia there is also a good explanation on dpreview site where it is referred to as "Focal Length Multiplier"

In short in your scenario if you have one full frame camera (crop factor 1) with 80mm lens and a second camera with 1.6 crop factor and 50mm when taking photos from the same position you will get the same frames (80 x 1 = 50x1.6 = 80)

That does not mean however that the photos will be identical. The depth of field for example if shooting with the same aperture will be different as it is still dependent on the (actual) focal length of the lens, that is the reason why people who are interested in achieving shallow depth of field tend to use full frame cameras.

Also the camera with crop factor 1.6 has a smaller sensor (see crop factor definition) - so assuming the both have same resolution say 10 Mega Pixels, and use the same technology the full frame camera will have bigger pixels, each would capture more light and that would usually translate into better high iso performance and better dynamic range.

More details in linked articles:

Crop Factor is sometimes referred as "Field Of View Crop" ("FOV Crop"), "Magnification Factor", "Focal Length Factor", or "Focal Length Multiplier".

As pointed out correctly by Rowland Focal Length Multiplier and other terms that mention focal length are not correct and can be confusing as the focal length does not really change here. Those terms are however still being used in some camera reviews or specifications.

• Thank you. I guess my question wasn't very clear, but it was the depth of field difference (and anything else there may have been) that I was interested in. – Mark Jul 16 '10 at 0:22
• It should never be known as the "Focal Length Multiplier" as there is no multiplication of focal length going on. It is purely a crop factor, to work out the equivalent focal length for the same field of view on a 35mm sized sensor/film – Rowland Shaw Jul 16 '10 at 7:05
• @Rowland - I personally use the "Crop Factor" term but the "Focal Length Multiplier" term is widely used as well that is the reason I mentioned it here – kristof Jul 16 '10 at 7:12
• So is it accurate to say that background compression is unaffected by crop factor? – Flimzy Jun 20 '11 at 19:00
• @Flimzy It depends on all of the other variables: same shooting distance/different framing or same framing/different shooting distance, different magnification/same display size or same magnification/different display size, etc... – Michael C Apr 15 '15 at 5:30

That difference is because the angle of view of the APS-C sensor is smaller than the 35mm Full frame sensor. Basically the change of focal length is only considered as a change of angle of view.

APS-C sensor has a crop factor of 1.6 of the full frame sensor. ie Anything viewed with the APS-C sensor will be cropped 1.6 times the Full frame sensor.
Hence 300x1.6 = 480 mm

To understand more easily, in order to get the image of 300mm focal length on a APS-C sensor a 480mm focal length will be needed for a full frame sensor.
Consider the following image:

The red frame is the view on Full frame. And blue frame is the view of same focal length on a APS-C sensor.The angle of view of APS-C is more minimized than on a Full frame.

More Physics explanation is here:

As said in the comments, its just a saying, but the same can be achieved with Full frame by simply cropping the photo.

• Now that's an answer! @user88975 I would add that a lot of photographers think the smaller sensor gives them more reach with their lenses, but be aware that the same thing can be achieved by simply cropping post capture with a larger sensor camera (if qualities are similar). The only true benefit is visualizing the image in zoomed in in the viewfinder vs. having to think it through. – Idistic Sep 12 '12 at 17:30
• Isn't pixel density greater on cropped sensors? If you look at the Canon 1DX it's 18MP and full frame and the 60d is 18MP and cropped frame. So if you attempted to crop a full frame picture to simulate having used a cropped sensor you would have far less pixels in the cropped image than you would if you used a cropped sensor to begin with. – tenmiles Sep 13 '12 at 6:03
• @tenmiles ya.. wat i said is with compromise to resolution.. – vivek_jonam Sep 13 '12 at 6:36

Focal length is focal length - it doesn't change between sensor sizes. However, due to the dominance of the 35mm format, focal length has come to also represent the field of view resulting from use of that focal length on 35mm film or FX-sized DSLR. Crop factor lets you translate field of view from one sensor size to another (and usually one of those sensor sizes is implicitly 35mm/FX).

It's ratio of size of your sensor to regular 35mm film frame. Canon 7D has 23×15mm sensor size, so if you use "normal" 50mm lens on it, the resulting image will be smaller (the projection is going to stay the same, but smaller sensor will get just the center part).

Since 7D has 1.6 crop factor, resulting image from 50mm lens will look like you'd use a 80mm lens on a regular film DSLR.

• Which is a good thing as you'll get the goodness of 85mm for the price of a 50mm :P – Rish Nov 1 '10 at 6:26

Just a technical nitpick on kristof's answer (since I can't leave comments yet):

Depth of field is not directly affected by focal length, but rather the working distance between the camera and the subject. It is tied to perspective distortion.

With a full frame camera, you will stand closer to the subject, comparatively exaggerating distances (compared to longer focal lengths) and creating a more shallow depth of field.

It is the same reason why Olympus and 4/3rd cameras can simulate FF depth of field by simply standing closer and stitching. This user simulates sub f1 images on different gear:

Focal length is a physical measurement, but is nothing more than magnification. It is the same as simply cropping an image or adding a teleconverter. When you crop a 50mm f/2 image by 1.4x, you will get the same depth of field as a 70mm f2.8, with the loss in pixel resolution associated.

This is precisely why they call it a crop factor, as that is what a smaller sensor is effectively doing.

• good points, already voted on your answer. The main difference between shooting with teleconverter on full frame body compared to using the same lens on crop body (or cropping the results from full frame) is that adding teleconverter makes the lens darker, while cropping does not affect the speed of the lens but the result in terms of DOF is as if the lens was stepped down. – kristof Jul 24 '10 at 11:20
• Good points, but I do want to note that while adding a teleconverter makes the lens darker, cropping makes the noise greater. For the same ISO, you will get a faster shutter by cropping, but effectively cropping will bring you closer to the noise, as if you had higher ISO anyway (like 4/3rds vs APS-C vs FF). With the TC, the noise would be averaged by all the pixels and have less noise when resolution normalized. A (good) TC works better than cropping if the lens is out-resolving the resolution of the sensor by an amount greater than the degradation of the TC. – eruditass Jul 24 '10 at 15:45

The crop factor of a sensor has to do with its size in relation to a full-frame camera (i.e. a 35mm film camera or a top-end DSLR with a 35mm sensor.) There are a variety of crop factors, and depending on the camera manufacturer, they differ.

Canon generally has three sensor sizes in its DSLR camera: full-frame (1x), APS-H (1.3x), and APS-X (1.6x). Most of canon's cameras make use of an APS-C style sensor, and have a 1.6x crop factor. Few of canon's cameras use an APS-H or FF sensor.

Crop factor, while interesting from a sensor size perspective, has a more useful meaning. If you take a shot of a scene with the same lens in the same location with both a FF and an APS-C camera, the 1.6x crop factor causes the photo from the APS-C to appear "more zoomed". If we assume that you took the photo with a 50mm lens, the FF 1x image would appear correct for a 50mm lens, but the APS-C 1.6x image would appear as though it was from an 80mm lens. (Simply multiply the real focal length by the crop factor to get the effective focal length.) This simple effect can be useful in some scenarios, such as say photographing birds at a great distance. The cropped sensor gives the appearance of being closer to your subject.

Crop factor is dependent on your camera's sensor. Focal length is dependent on your lens.

Combine them to get the effective focal length, which is stated in 35mm-frame-size terms. This will let you "talk the same language" as the 35mm/full-frame folk (which is by and large the standard).

For example, if you hear someone state that "85mm is a good focal length for a portrait lens", (and you know they're referring to a 35mm/full frame scenario), you could divide that number by your camera's crop factor (1.5x on my D90) and get the real focal length that will give you the same effect. 85mm / 1.5x = 57mm, so I can use my 50mm lens and get close to the same results.

• So if I had two cameras with different sensor sizes, but the same effective focal length (due to lenses with different real focal lengths), the picture would look exactly the same, all other things being equal? – Mark Jul 15 '10 at 20:48
• Yes, they would. Note that in general, the larger the sensor the more sensitive the sensor, so the pictures would never really look the same. – Josh Goldshlag Jul 15 '10 at 20:56
• No. The DoF would be different, as that is based on actual focal length. The crop factor does just crop the image, so you get "the same amount of stuff in the picture" as if you'd used the longer lens, but it still has the perspective of the lens it was actually taken with. – Edd Jul 22 '10 at 14:00
• Er, why the downvote? Is there something wrong with what I've written? – Craig Walker Jul 23 '10 at 15:36
• I didn't downvote, but: this answer could be significantly improved by explaining why one would want to get an "effective focal length". – mattdm Jan 13 '11 at 4:54

When the sensor is smaller, you get only a portion of the produced image from the lens, you get a small 'crop' from center of the actual image that lens can produce, the image will look like if you used a longer lens on a full frame.

Take a look at Nikon's lens simulator to get a feel about this, compare DX and FX lens and bodies. http://imaging.nikon.com/lineup/lens/simulator/

If you're using a a modern DSLR you then get the crop factor (sometimes mis-described as a focal length multiplier), but for a camera with an APS-C sized sensor, you have a crop factor of 1.6; and if you have a 100mm lens attached to it, then it will have the same field of view as a 160mm lens on a 35mm camera; in reality, the focal length is still 100mm though.

The above answers are correct but they do not point out that the focal length is exactly the same. The conventions in photography sometimes makes a machine vision dude like myself want to pull my hairs out :) FOV = 2*atan(size/(2*f))

size is the size of the actual chip. You compute it for height and width separately, like 36mm and 24mm (for full frame) and 25.1mm and 16.7mm for your std issue "crop camera", or 4.8 x 3.6mm for your std issue 1/3 inch machine vision camera with c-mount.

If you start to linguistically code it as "having a longer focal length" then you might believe that it gives a larger magnification, which it doesn't. I also noticed that the joyful world of photography even try to fix that by introducing a virtual "35mm eq. magnification", which makes no sense either, since M is based on the physical size of of the projection and not dependent on sensor size at all.

A third term to be vary about is circle of confusion which is about how focused the light rays are through the lens onto the sensor. You will find calculators that calculates the the lowest COC (e.g. for depth of field) based on what can be detected by the human eye as a point. I'm not going to look at the projection through the lens on a wall, am I :) If I look at a zoomed in digital photo on the screen, or an algorithm process machine vision VGA image I want it to be sharp within a pixel cell size (e.g. 6um) and not some print human based measure that will never apply to the images I take. And then the depth of field suddenly becomes much narrower than those calculators show, as they consider the coc limit to be 29um for full frame and 18um for aps-c.

So in conclusion, you need to keep the terms seperate. "crop sensors" affect the FOV (because you change 1 out of 2 factors in the formula), not the focal length. Since focal length affects more than FOV, you cannot convert the focal length.

This is the way I mentally picture the situation:

Take the full frame lens, put it on your APS-C sensor camera, set the aperture, zoom and take a picture.

Now, take this lens off your camera and put it on a full frame body. Take a photograph with the same settings. Open the image in your favorite image editing software and crop the image to about 1/1.5 of the original.

The image you get will be about the same as the one you took on your APS-C camera. As mentioned above, the focal length is the focal length is the focal length... But on the APS-C, it crops to 1/1.5 so it appears as if it were taken with a longer focal length lens.

The mental image you can use is to take a photograph on a 35mm film frame, with your full frame lens, then take a pair of scissors and cut out a piece of the film about 24mm x 16mm.