The Crop Factor Unmasked

Field of View vs Focal Length on various formats

By PF Staff in Articles and Tips on Jul 23, 2014
The Crop Factor Unmasked

Many of us have cameras with different sensor sizes; this raises the question of which lenses need to be used to get the same field of view on two different formats. Below we provide a table listing focal lengths with equivalent Field of View (FoV) across several sensor sizes.  The actual diagonal field of view (in degrees) is shown on the far right. Click the table to enlarge.

Note that the focal length of a lens (say 50 mm) is an optical property of the lens and remains the same no matter what sensor size camera the lens is mounted on.

In other words, an smc Pentax-A 50mm F1.7 lens as shown to the right is a 50 mm lens when mounted on a Pentax Q7 (1/1.7 inch sensor size), on a Pentax K-3 (APS-C sensor size), or on a Pentax film SLR (aka 24 x 36 mm or full frame). The focal length does not change with the camera. But the field of view which the lens captures does change. And so does depth of field, but that is for another article.

Some manufacturers have the bad habit of marking their lenses not with their true focal length, but with the focal length of the equivalent lens on a full frame (24 x 36 mm) camera. This is confusing. Pentax doesn't belong to that camp; they mark their lenses correctly (i.e. with the true focal length).

Let's look at what is called a "normal" lens. This is a lens with a focal length approximately equal to the diagonal of the sensor. On a 24 x 36 mm camera (aka full frame) that would be 43 mm. On an APS-C camera it would be 29 mm (rounded to nearest whole number), and on a 645Z it would be 55 mm (the green row in the table below). Usually, lenses in the range 40 mm to 50 mm are considered "normal" lenses in the 24 x 36 mm format so we have included 40 mm and 50 mm in our sample table:

Normal Lenses
APS-C
Full frame
645 dig.
27 mm 40 mm 51 mm
29 mm 43 mm 55 mm
33 mm 50 mm 64 mm

The table shows that a 29mm lens on APS-C and a 55 mm lens on 645D have the same field of view as a 43mm lens on full frame. Common terminology is that a 29mm lens on APS-C has an "equivalent" focal length of 43 mm. This terminology can be confusing since its true focal length is 29mm no matter what since that is an optical property related to the lens only and not influenced by the sensor (or film) format.

Anyway, it is common to relate the focal length of a lens/sensor combination to the full frame format so that the lenses better can be compared regarding their field of view. The concept of "equivalent" focal length is thus actually quite useful.

The ratio between the diagonal of a given sensor and the diagonal of a full frame sensor (or 24 x 36 mm negative) is called the crop factor.

Crop factor
Q
Q7
Micro
four-thirds
APS-C
Full frame
645D
645 
6x7 
5.64x 4.66x 2x 1.5x 1x 0.79x 0.62x 0.49x

These crop factors were used to generate the comparison table at the top of this article. Note that a Canon APS-C sensor is slightly smaller than the APS-C sensors used by Pentax/Nikon/Sony and others. The crop factor for a Canon APS-C sensor is 1.6x.

Read on for some background on the origin of the somewhat confusing "crop factor" term.

The Image Circle

A lens forms a circular image of the subject (the image formed on the sensor is actually upside down, but we will ignore that in these illustrations). If the sensor was large enough this is what the image formed on the sensor would look like:

Let's pretend that the above image was formed by the afore mentioned full frame 50 mm lens. If mounted on a camera with a 24 x 36 mm (full frame) sensor only a 24 x 36 mm large part of the image would be captured:

With the same lens on an APS-C camera we can only capture an area 16 x 24 mm which is the size of the APS-C sensor:

 

Magnification and Crop Factor

It gets interesting when we compare the two images captured:

24 x 36 mm (full frame) sensor - 50 mm lens 16 x 24 mm (APS-C) sensor - 50 mm lens

It looks like the magnification of the APS-C image is higher; it appears as if it is captured with a telephoto lens when compared to the 24 x 36 mm image, even though the same lens was used for both images.

While the 50mm lens does not actually deliver more magnification on an APS-C camera, it does have a reduced field of view, and this gives the illusion of "more zoom" when comparing the relative sizes of objects within two images.  This illusion only manifests itself when the two images are scaled to the same size, but this is quite common as you can imagine.

The diagonal field of view on APS-C is 1.5x smaller than full frame and this number is what is called the "crop factor". This unfortunate term stems from the fact that the APS-C sensor captures a smaller, or cropped, part of the image circle as illustrated in the previous section.

The Bottom Line

At the end of the day, there is one and only one implication of the crop factor: the field of view is narrower on APS-C compared to full frame given the same lens.

The crop factor itself is found by dividing the length of the diagonal of the 24 x 36 mm sensor (43 mm) with the length of the diagonal of the APS-C sensor (28.8 mm): 43 / 28.8 = 1.5.

"Equivalent" Focal Length

To get the same field of view with a 24 x 36 mm camera as we have with the APS-C sensor we'd have to use a longer focal length on the 24 x 36 mm camera, namely a lens that is longer by the crop factor. So a 75 mm lens would yield the same field of view on full frame as a 50 mm lens yields on APS-C.  Similarly, a 33.3 mm lens on APS-C would yield the same field of view as a 50mm on full-frame.

24 x 36 mm (full frame) sensor - 75 mm lens 16 x 24 mm (APS-C) sensor - 50 mm lens

When comparing lenses for different sensor formats it has become common practice to convert the focal length of a given lens on a given camera to the "equivalent" focal length. Unless qualified further "equivalent" focal length means the focal length one would need on a full frame camera in order to get the same field of view (or same magnification) as produced by the given lens on that other (smaller or larger format) sensor.

As an example a 50 mm lens on APS-C has an "equivalent" focal length of 75 mm.

The Bottom Line

The main thing to take away from all this is simple: larger formats are better-suited for wide-angle photography, while smaller formats make telephoto shooting easier, as they don't require monster lenses for the same tight field of view.

Animated Demo

The animation below shows the effect of the crop factor.

Aperture and Bokeh

Aperture is a constant for each lens, so regardless of the format you're shooting, you'll get the same light transmission (i.e. exposure) with the same lens.  Thus, there is no benefit in using larger-format lenses on smaller sensors as far as exposure goes.

Some say that larger sensor formats can offer "better" bokeh.  This is true in the sense that it's easier to obtain a strong background blur with larger formats in typical shooting scenarios, since longer focal lengths deliver wider fields of view than they would on smaller formats.  Recall that as focal length increases, the depth of field decreases and thus it's easier to obtain a background blur.  It is therefore advantageous when longer focal lengths can still deliver a relatively wide field of view.

This is easier to understand through an example: on a Pentax Q, one would need a 9.3mm lens to get the same field of view as a 35mm on an APS-C Pentax K-3.   At the same aperture setting and focusing distance, the photo taken with the K-3 would have considerably shallower depth of field.

If you were to mount the 35mm lens on a Pentax Q, you would in fact get the same background blur as with the 35mm on the K-3: but you'd only see a fraction of the frame, as your field of view would be a mere 12 degrees, rather than 44!

Geometric Distortion

We'll touch on one last concept before letting you go: distortion.  This is a relatively advanced concept, but it can still have an impact on your photos.

Suppose that we have a full-frame camera with a 50mm lens and an APS-C camera with a 33.3mm lens.  Images shot with both cameras will have the same field of view, and we'd like to shoot some portraits. Will they look the same from either camera?

At first sight, the images might look the same.  But if you look closer, you might see subtle variations in curves and edges caused by the lens's geometric distortion.  The wider a lens, the more likely it is to require a more complex optical formula.  This can lead to distortion, particularly near the edges and corners of the image, that might not be present in a simpler (or more expensive) lens.  When distortion manifests itself, lines that are straight in real life will appear curved in your image.

Distortion is unwanted in a variety of applications, including portraits, product photography, and architecture.  While it can usually be corrected in software, this comes at the expense of time and can result in a reduced field of view or in a loss of detail. 

On an unrelated note, distortion can also be caused by the perspective: i.e. where you are standing and what lens you're using. We invite you to continue on to our in-depth guide on perspective distortion to learn more.

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