View Full Version : Angle of coverage

Emrehan Zeybekoglu
23-May-2006, 09:13
Greetings ladies and gentlemen:

I'd like to raise a few points regarding focal length and angle of coverage.

It is usually suggested that those of us switching from 35 mm to 4x5 multiply their favorite focal length in that format by 3, and that this will yield the 4x5 equivalents. However, that doesn't seem to be an accurate translation of focal lengths or angles of coverage. For example, a 50mm lens on a 35mm camera has an angle of coverage of 46.8 degrees as the angle of view is determined by focal length and film size. A 150mm lens on a 4x5 camera, on the other hand, gives us 56.145 degrees. A 35mm lens on a 35mm camera has an angle of view of 63 degrees but its triple focal length on a 4x5 camera has almost 75 degrees.

My point is that it is the angle of view that makes us choose a particular lens, although we may express our choice in terms of focal length. Therefore, multiplying a small format camera's focal length by 3 doesn't seem to be satisfactory.

Am I missing something?

tim atherton
23-May-2006, 09:25
for practical purposes, I find this often helps


Ralph Barker
23-May-2006, 09:40
. . . Am I missing something?

Perhaps. The x3 rule of thumb seems to assume a fairly fat thumb, so it's a rough estimate at best. Opinions vary on the best method of determining equivalent focal lengths between formats.

Joe Forks
23-May-2006, 09:40
I think what you are missing is that most of these charts are calculated on the Diagonal axis, yet angle of view implies a width on the horizontal axis only (for a horizontal photo).

If you are concerned only with angle of view on the horizontal axis it might help you to do the calculations using only horizontal comparisons and not diagonals.


23-May-2006, 09:54
50mm is also a little longer then the 43mm diagonal for 35mm. OTOH 150mm is a little shorter then the 162mm diagonal for 4x5. If you use a 4x and consider a 50mm more or less equal to a 210mm how do the angle of view compare?

Oren Grad
23-May-2006, 09:56
My point is that it is the angle of view that makes us choose a particular lens

But which angle of view? Do you key on the horizontal view, the vertical view, or the diagonal? In any case, since aspect ratios are different among the different formats in common use, the visual effects of the various focal lengths are different even if you scale precisely to one of the angular measures. Finally, even for formats that share near-identical aspect ratios (e.g., 4x5 and 8x10, or 3.25x4.25 and 6.5x8.5), size can make a difference too - I'm finding that for negatives intended for contact printing, I lean toward slightly longer focal lengths in the smaller formats, relative to format size, than I do in the larger ones.

The bottom line is that there's no rule that can automatically tell you what your preferred focal length is going to be when you jump from one format to another. When you're getting started in a new format, you make your best guess based on experience and on what you think you want to photograph in the new format, and then you have to just take the plunge and try it for yourself. As with selecting LF cameras, there's a good chance that your first choice won't be what you end up using for the long run.

Daniel Geiger
23-May-2006, 12:01
I think there is a basic confusion about angle of view and angle of coverage.
Angle of view: the angle that is projected on to the film.
Angle of coverage: the angle that is projected by lens in the plane of the film, but extends (with zero movements) beyond the area of the film.

For lenses that allow some movements, angle-of-coverage is larger than angle-of-view. Or, with the same focal length (say a 90 mm Superangulon vs a 90 mm XL) the angle of view will be the same as the focal length is the same, but the angle of coverage is larger in the XL, making the image circle larger, and allowing for more movements.

in 35 mm the difference is not considered, as most lenses do not allow for movements, so that is a new concept when moving from 35 mm to LF.

Gregory Gomez
23-May-2006, 15:56
Oren Grad,

Excellent points and recommendations!

You are absolutely right. If the aspect ratios differ among formats, there is no precise way to compare focal lengths. And even if the aspect ratios are identical (e.g., 4x5 vs. 8x10) oftentimes the size difference among formats makes a subjective but important difference. For example, I really enjoy using a 210mm lens for the 4x5, but prefer a 300mm (equivalent to 150mm for a 4x5) for the 8x10. I can't explain this preference, but not all photographers are going to have this reaction.

As to what angle of view should be used? The answer depends upon which angle is most important to the photographer. For many of us, according to Fred Picker, it is the horizontal angle of view that matters most; for others, it might be the vertical angle. For me, I have always relied upon the diagonal angle of view of the entire film area described by Michael K. Davis in his second table in the attachment provided by Tim Atherton. Why? Because the diagonal angle of view takes into consideration both the horizontal and vertical angles, which also corresponds well with my experience of using multiple formats. I prefer to use the image area diagonal of the film as opposed to the pint area diagonal (Davis's first table) because I make most of my compositional decisions in the field, and I prefer not to crop during the printing process if I can help it. (But cropping is always an option, which, in effect, narrows the angle of view as if a longer focal length were employed.) For other photographers, this series of choices may not provide a satisfactory solution. Then I would suggest either using the horizontal angle (image area or print area), or simply use trail and error, which can get expensive.

If one were to use the diagonal angle of the entire image area, then the common denominator between 35mm and 4x5 would be 3.54965357967, rounded to 3.55, according to the numbers listed in Davis's second table (i.e., 153.7 for 4x5 divided by 43.3 for 35mm). With this common denominator, one can construct the following table comparing common 35mm optics with 4x5 glass:


1. 20mm; 71mm (72mm or 75mm closest equivalent)

2. 24mm; 85.2mm (80mm or 90mm closest equivalent)

3. 28mm; 99.4mm (no equivalent with adequate coverage)

4. 35mm; 124.25mm (120mm or 125 closest equivalent)

5. 45mm; 159.75mm (no equivalent )

6. 50mm; 177.5mm (180mm closest equivalent)

7. 85mm; 301.75 (300mm closest equivalent)

8. 105mm; 372.75mm (360mm closest equivalent)

4x5; 35mm

1. 135mm; 38mm (no equivalent)

2. 150mm; 42.25mm (45mm closest equivalent)

3. 210mm; 59.15mm (Zeiss 60mm macro for Contax cameras)

4. 240mm; 67.6mm (no equivalent)

5. 250mm; 70.42 (popular focal length in 35mm zoom lenses)

I have used the 3.55x rule (where x = the 35mm focal length) and the x/3.55 rule (where x = the 4x5 focal length) quite successfully for all my lens purchases. Maybe it will work for you too. :)



Leonard Evens
23-May-2006, 16:59
First of all, a multiplier of 3 has no justification whatsoever in actual measurments. As others have pointed out, the multiplier can be anything from 3.333 to 4, depending on which dimension in the film plane you choose to define the angle of view.

Second, it may be a quibble, but dimensions like 4 x 5 and 8 x 10 are simplifications. The actual frame sizes are a bit smaller. For example, the actual exposed area for my 4 x 5 film holders is more like 95 x 120 mm, give or take half a mm in either dimension. With those dimensions, the diagonal is just about 153 mm, not the 162 mm one would get from using 4 x 5 inches as the dimensions.

Finally, as someone already pointed out, 50 mm is only considered "normal" for 35 mm format because of historical accident. In principle, the "normal" focal length is the diagonal of the format, which for a 24 x 36 mm frame is about 43 mm.

Emrehan Zeybekoglu
24-May-2006, 13:26
Oren Grad:
"But which angle of view?" Well, I actually had the diagonal in mind, and my calculations were based on that.

Daniel Giger:
"I think there is a basic confusion about angle of view and angle of coverage. " Yes, you're right. I was sloppy in my usage of the terms. I meant "angle of view" based on the diagonal.

Gregory Gomez, I'm not sure what angle of view I "prefer" while taking photographs. I can't tell, but I find myself using the vertical quite often - it comes naturally, and I may be using it more often in 4x5 than in 35mm. Also the common denominator of 3.55 makes more sense.

The aspect ratio makes a difference. For the 4x5 I also end up using the 210 mm lens quite a lot, but for my 35mm there is no equivalent. Even if there were I'm not sure if I'd go for it.

The bottom line is, as some of you suggest, there seems to be a subjective element that drives us toward a particular lens.

Thank you all for your input.