I just purchased an old large format Speed Graphic camera. It came with a Kodak No. 31 Anastigmat F 4.5 5½ inch lens on a Compur shutter. I was wondering what equivalent mm focal length of this lens would be. I'm not sure if it matters but I have a 120 film back on the camera, with a 2¼ x 3¼ inch mask. As background, I'm used to shooting on a full frame DSLR.
The film back you are using absolutely matters, because this whole concept of "equivalence" is in reference to a given film or sensor size.
You have a 3¼×2¼" mask, so that's the size of your recording medium — about 82×57mm. We're comparing that to the sensor size of a "full-frame" reference DSLR, with a sensor the size of 35mm film — which is 36×24mm.
You'll notice that these aren't quite exactly the same aspect ratio: your mask is a little more square. In this situation, we usually compare the diagonals, which are 99.9mm (let's just say 100!) and 43.3mm, respectively. This 43.3mm/100mm gives us 0.43× as the "crop factor". (That is a strange term sense because we're taking it in the opposite direction of cropping, but I'm going to keep using it anyway because it is the typical term and is even used in this way for digital medium format.)
If the two aspect ratios were really far off — like, if you had a 2¼×2¾" mask — you might need to crop off even more in order to get the formats to match in shape, you might want to calculate that separately. (Like I did here.) But here, we're basically within all reasonable tolerances — so 0.43× is our magic number.
5½" is 140mm, so the 35mm-equivalent focal length of this setup would be simply 140mm × 0.43, which is about 60mm. In other words, you have a slightly-long normal, and a little short for what would normally be used for portraits.
This equivalence holds for angle of view and also holds for depth of field, given some assumptions, like equivalent print size. That is, if you shoot wide open at f/4.5, your depth of field is roughly the same as if you were shooting with an f/1.9 lens on a full-frame DSLR. (This doesn't affect exposure calculation, though!)
If, instead of the 120 back, you were using a Grafmatic Sheet Film Holder with 4x5" film, the frame area would be just a tiny bit smaller than 4×5" — about 96×120mm. If you cropped your DSLR image to the same aspect ratio, you'd have a crop factor of 0.3×. In this case, your 5½" lens's field of view would be equivalent to a 42mm lens on the DSLR — still in the "normal" range, but at the wide side rather than the long one.
The Kodak 5 ½ inch lens 31 was usually mated to a camera that sported film size 3 ¼ x 4 ¼. This 1945 lens has a focal length in millimeters of 5.5 X 25.4 = 140mm. Lenses are customarily fitted to cameras based approximately on the measure of the diagonal of the format. This format is 82.5mm wide by 108mm long and the diagonal measure is 136mm.
If you fit a lens to a camera with a focal length that about matches the diagonal, the lash-up is deemed to deliver a view that matches the “human view”. The industry labels this lash-up a “normal” as to focal length.
The compact digital with a 30mm lens mounted is also considered “normal”. This format is 16mm wide by 24mm long and the diagonal measure is 28.9. The full frame 35mm film camera’s format is 24mm wide by 36mm long. The diagonal measure of this format is 44mm. By custom this value is rounded up to 50mm.
Another definition of “normal”: A lash-up that delivers a diagonal field of view about 53°.
The horizontal field of view is about 45°.
The 5 ½ lens on a 3 ¼ X 4 ¼ film fits this definition
A 30mm on a compact digital fits this definition.
A 45mm on a 35mm fits this definition.
A 50mm on a 35mm nearly fits this definition.
A wide-angle is about 70% of “normal or shorter.
A telephoto is about 200% of “normal or longer.
A portrait lens is about 200% thru 250% of normal.
There are no “normal” in art, you are free to follow your heart.