hip to be square
what's "normal," anyway?
first published 2018 Feb 23, updated 2023 Jun 20
The aspect ratio of a photograph – the ratio between the image's width and height – only draws attention when it's pushed to an extreme. The Xpan, for instance, is famous for it's ultrawide 65:24 frames, and 6x17cm cameras are known for creating powerful, expansive panoramas. These are worthy techniques, but far more versatile and dynamic is the aspect ratio that lies on the total opposite extreme. I am referring to the pinnacle of nature's geometric perfection:
the square
In the beginning, square photos were the default. All photos were square. It was only with the success of Leica and its 35mm film that the 3:2 aspect ratio became popular, kicking off the descent into all sorts of 4:3 and 7:6 nonsense. Yet, after years of squares quietly fading into the background, Instagram – that obnoxious social media service – spurred a resurgance in square photos. As soulless as an Instagram shot may be, there's no denying the intense beauty in squares, the fascinating dynamism and powerful honesty in a well-composed square photo.
The dilemma
Our digital cameras are designed to work in non-square aspect ratios. Lens focal lengths are given in "35mm equivalent", as if the 3:2 ratio and 35mm frame size are the gold standard. But what if we want a different standard, a 6x6 square standard? Can we come up with a "6x6 equivalent" focal length? Yes, indeed we can.
So let's talk about focal lengths.
Let's talk about focal lengths
The focal length of a camera, usually expressed in millimeters, is calculated based on the sum of light's path through the lens barrel. It's a virtual number – e.g. a 50mm lens does not necessarily have any element 50mm from the film plane. To a photographer, the focal length number is useful only relative to other focal length numbers: a smaller focal length indicates a wider field of view, and a higher number indicates a longer (narrower) view.
A small focal length captures a large portion of what's in front of the camera, whereas a higher focal length captures only a long, narrow view.
Between the long and wide lies the "normal." It's the field of view which is neither zoomed in nor zoomed out. Wide angles distort subjects, stretching them in one dimension and not another. Long angles compress subjects, making objects look closer together than they actually are. A "normal" field of view, however, does neither – it's a balancing point between the extremes. It's a field of view where the objects photographed look... uh... normal.
To calculate exact field-of-view from focal length, you must also know the camera's sensor size (or film frame size). For instance, a lens with a 50mm focal length will give the "normal" field-of-view on a 35mm "full frame" camera, while simultaneously giving a long field of view on a small-sensor camera and a wide field-of-view on a large-sensor camera. In one sense, the smaller sensor sizes (or film frame sizes) "crop" out parts of the image that a larger sensor size does not.
the relative frame sizes are here overlayed
This is all to say that to create a new "equivalent" we must disregard everything we've learned about 35mm equivalence. We will be needing to pretend that our 3:2 and 4:3 digital sensors are actually 1:1 square sensors, and we will be doing this by disregarding the part of the sensor that falls outside of a square crop.
Math will save us
We can use math to solve this riddle. Content warning for mathematicians: photography math if fuzzy. It turns out, the focal length of a normal lens is somewhat equal to the diagonal of the frame size. The 35mm "normal" is 50mm, and the diagonal of a 35mm frame (using the handy dandy Pythagorean theorem) √(362 + 242) = 43mm (close enough to 50mm for photographers). The same is true for 6x6cm frames and 80mm lenses – because everything in photography is a lie, a 6x6cm frame is actually 56mm square, or a diagonal of √(562 + 562) = 79mm.
Therefore, if we determine the ratio between diagonals of 6x6cm frames and those of a smaller sensor cropped square, we will also know the ratio between their "normal" lenses.
The digital sensor sizes I'll be calculating here are the GFX digital medium format's 43.8x32.9mm, the "full frame" 36x24mm, and the "crop frame" 23.8x15.6mm (i.e. "APS-C" cameras such as Fujfilm X and Canon EF-S). For each, we are ignoring the part of the sensor beyond the square cropping, effectively disregarding the full length of the longer edge of the sensor and pretending it's equal in length to the short edge. And then we'll solve for the "6x6cm-equivalent" crop factor multiplier where: diagonal × crop factor = 79mm.
6x6cm equivalence crop factor
| Sensor/Frame size | Size (square) (mm) | Diagonal | 6x6 Crop Factor |
|---|---|---|---|
| 6x6cm film | 56 x 56 | 79mm | 1x |
| digital medium format | 32.9 x 32.9 | 47mm | 1.68x |
| full frame | 24 x 24 | 34mm | 2.32x |
| crop frame | 15.6 x 15.6 | 22mm | 3.59x |
Remember that the "crop factor" is only for determining equivalent fields of view, and that a 50mm lens renders depth-of-field and sharpness like a 50mm lens no matter the sensor size. The full complexities of how focal length and frame size interweave are fascinating, but beyond the scope of this page.
6x6 equivalency extrapolated
Using the above crop factors, we can extrapolated to the full range of focal lengths for each of the sensor sizes. The first row are the focal lengths of popular 6x6cm Hasselblad V-system lenses. The three rows following are the focal lengths required to achieve the same field-of-view while shooting square frame on a digital camera of that row's size sensor.
| Sensor/Frame size | Very wide | Wide angle | Normal | Short telephoto | Long telephoto |
|---|---|---|---|---|---|
| 6x6cm film | 40mm | 60mm | 80mm | 150mm | 250mm |
| medium format (1.68x) | 24mm | 35mm | 47mm | 90mm | 150mm |
| full frame (2.32x) | 17mm | 26mm | 34mm | 65mm | 108mm |
| crop frame (3.59x) | 11mm | 16mm | 22mm | 42mm | 70mm |
So there we have it. We are now prepared to go forth into the world, shooting our square frame photos on any camera system we so choose, having recalibrated our thinking away from 35mm film and it's vestiges, instead picking the more beautiful 6x6cm film as our basis. Below, find some examples.
photo shot on digital medium format at focal length of 145mm, or 6x6 equivalent of 250mm
photo shot on digital medium format at focal length of 30mm, or 6x6 equivalent of 50mm