Angles-of-View: A Cure for Chronic Millimeter Malaise

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In an earlier chapter of my life I taught photography part-time at a local community college. One of my co-workers, a fellow named Pietr, whose last name I could never pronounce let alone spell, had a novel way of introducing his Photo 101 students to their cameras. He would start off by having them wander about, focus on things that catch their eye, and before pressing the shutter button, peer over the viewfinder and try to visualize where the borders of the image were based on what they saw in the viewfinder.

When he felt they understood the point of this exercise, he gave them their first assignment. But before they left for the day he did one more thing… he covered the viewfinders of each of their cameras with black tape. Like pilots flying a plane in pea soup fog, they had to shoot the assignment by 'feel' (minus the crash-and-burn factor). What was interesting is how many strong images were produced by many of the students, and I attribute it to Pietr's methodology of teaching them to be able to pre-visualize the image based on an understanding of the camera lens's angle-of-view.

In the beginning…

Not long ago, when film was the only game in town the angle-of-view (AOV) of any given lens was a known entity. This was due to the near-universal acceptance of 35mm film as the format of choice among professionals and amateurs alike. Medium-format and larger-format cameras had their place in the world, but for the vast majority of photo enthusiasts, 35mm film was the mother tongue of photography.

As such, it was easy to describe a lens according to its focal length. A 28mm lens was always a wide-angle lens and a 105mm lens was always the ideal portrait lens. Shooting sports? You'll want a lens of at least 300mm, maybe longer. But that logic no longer holds up in practice.

But that was then… and now we're digital

Today the parameters and logic of the traditional 35mm camera system are greatly compromised by the multiple format choices made available by camera manufacturers. Currently there are 5 DSLR sensor sizes; full-frame, APS-H (1.3x), APS-C (1.5x & 1.6x), Foveon (1.7x), and 4/3 (2x). Add to this equation the 5 quirkier-sized sensors found in point-and-shoot digicams (2/3", 1/1.6", 1/1.7", 1/1.8", & 1/2.5") and you wind up with a total of 10 distinct imaging formats.

For the record, only the 5 larger DSLR sensor formats have reliable magnification factors (1.5x, 1.6x, 2x). For the 5 smaller point-and-shoot cameras, it's still the Wild West when it comes to the measurement standards. That said it makes sense to focus on the AOV factor when comparing lenses from one format to another. To better illustrate the differences between the various imaging sensors we've included the following sensor-size comparison chart.

OK… now what?

The result is we can no longer accurately reference lenses in terms of millimeters because depending on which camera you are using, a 100 mm lens, a 50mm lens, and a 17mm lens can produce images with near-identical fields-of-view.

To eliminate all this confusion, perhaps it's time to stop thinking of lenses in terms of millimeters and instead identify lenses in terms of their angles-of-view. Angles-of-view (AOV) are a constant. An 84° AOV will always identify the lens as a wide-angle. On a DSLR containing a full-frame (24x36mm) sensor this would translate into a 24mm lens, while on a Leica M8 (1.3x) it would be closer to an 18mm lens, and a 12mm lens on a 4/3-system camera (2x). There will be subtle differences between each of the resulting images based on the sensor size, but the angle-of-view will always appear the same.

Note- The angle-of-view (AOV) and field-of-view (FOV) of a lens are similar but distinct in the way they describe the measurements (length, width, and/or diameter) of a photographic image. The field-of-view is a linear measurement of the image in feet, inches, meters, etc, while the angle-of-view is the length, width, and/or diameter of the image described in terms of degrees of viewing coverage.

To (hopefully) shed light on the subject, I have assembled the following AOV chart, which illustrates the relationships between the focal lengths of lenses and the 10 format options afforded by our cameras. Because of the variety of point-&-shoot chip sizes – and the way manufacturers measure them – we decided to enter focal-length ranges instead of specific fixed focal lengths because breaking it down to exacting focal lengths would be akin to water boarding.

In a sense, this point-of-view is the opposite of the way manufacturers describe lenses as being 'equivalents of a such-and-such millimeter lens on a 35mm camera'. By letting go of the 35mm reference points you can start thinking of lenses in terms of their respective (and easier to reconcile) angles-of-view regardless of the optic's millimeter ranking.

Click Image to Enlarge

 Note- The AOV of each lens is based the measurement of its diagonal plane, which is also its widest dimension.

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I think there is a small mistake in the table:

The 600mm and 800mm full-frame should have the same angle-of-view as with 375mm and 500mm with a Canon APS-C crop camera (1.6x) - not 400 and 533mm as noted here.

Otherwise great table - thanks for sharing this!