If you care about cameras you probably like learning about interesting new (and old) lenses. They’re described by two numbers: How wide they open (also: aperture, brightness, speed), and how long they are (also: focal length). That first number is generally comparable across lenses: Lower is better. The aperture unit, “F-stop”, is hardly intuitive, but whatever. Focal lengths are hard to compare, because how much the lens sees depends on how big the sensor behind it is, and there are lots of different sensor sizes.
Generally, focal lengths are expressed as “35mm equivalent”, meaning “If we stuck this lens in front of a sensor the size of traditional photographic film, which is the same size used in modern expensive digital cameras, here’s what the focal length would be.”
Which is dumb and irritating, because that’s not the number printed on the side of the lens, and anyhow, the number itself doesn’t really mean anything. So I was thinking of some uniform ways to express what focal length means.
Focal angle · What you really care about is how much of the scene in front of you the lens can take in. There’s a nice smooth trade-off: The less it takes in, the more magnification you get, and the further away you can see. The terminology is broadly “wide-angle”, “normal”, and “telephoto”.
The math isn’t hard. If your sensor is W mm wide and your lens is L mm long, your focal angle is:
Angle = 2 × arctan(W / 2×L))
Of course, that’s in radians, which most of us don’t think in. So the most obvious way to present them to humans would be as degrees, with extreme wide-angle lenses pushing toward 180° and huge telephotos getting down into the single digits.
I suppose that’s OK, but if we assume that the maximum practical field of view is 180°, why not just give the answer as a percentage of that? It turns out that if you think of 75% as 0.75, that is also a direct measurement of the angle, if you think the natural unit to describe angles is “π radians” (well, d’oh, of course it is).
Without further ado, here’s how that would work.
|iPhone 7 Plus (4.8mm sensor, 3.99mm)||62.1°||34.5%|
|Nexus 6P (6.17mm sensor, 4.67mm)||66.9°||37.2%|
|Micro Four Thirds (17.3mm sensor)|
|Olympus OM-D E-M1, Olympus M.Zuiko 8mm F1.8||94.5°||52.5%|
|Olympus OM-D E-M1, Leica Summilux 25mm F1.4||38.2°||21.2%|
|Olympus OM-D E-M1, M.Zuiko 300mm F1.8||3.3°||1.8%|
|APS-C (23.6mm sensor)|
|Fujifilm X-T1, XF 10-24 F4 at 10||99.4°||55.2%|
|Fujifilm X-T1, XF 35mm F1.4||37.3°||20.7%|
|Fujifilm X-T1, XF 100-400 F4.5-5.6 at 100||13.5°||7.5%|
|Fujifilm X-T1, XF 100-400 F4.5-5.6 at 400||3.4°||1.9%|
|Full frame (36mm sensor)|
|Sony a7 II, Rokinon 8mm F3.5||131.8°||73.2%|
|Leica M10, Summilux 50mm F1.4||39.6°||22.0%|
|Canon 1DX, EF 200-400mm F4 at 200||10.3°||5.7%|
|Canon 1DX, EF 400mm F2.8||5.2°||2.9%|
|Medium format (645) (43.8mm sensor)|
|Pentax 645z, FA645 35mm F3.5||64.1°||35.6%|
|Pentax 645z, FA645 120mm F4||20.7°||11.5%|
Problem? · It’s a little weird that as lenses get longer, the numbers get smaller. I think marketers like thumping their chests about shipping a big-ass 300mm lens, so they might be unhappy.
I actually considered using inverse angles or percentages to counteract that, but it looked lame.
Notes on the cameras · Finding the specs on the phone sensors was a little tough; in each case, the focal length is what they report in the EXIF data.
The Micro Four Thirds combined with the Olympus 300mm lens, is actually the biggest telephoto you can get. But both Oly and Fuji ship tele-extenders if you want to go completely insane.
The Leica is sort of the canonical example of a “normal” lens. The Sony/Rokinon combo is the widest off-the-shelf combo that exists, as far as I know. The Canon combos are those big light-grey lenses you see clustered around the edges of the soccer pitch or football field on TV.
There actually are larger sensor formats than 645, but very rare in the field.