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The max rectangle area that can be enclosed in a circle is actually a square. This means that ideally a 1:1 aspect-ratio sensor would be able to collect more information than any other aspect ratio sensor.

On my phone, the highest resolution (in terms of pixel count) is obtained for 4:3 aspect ratio. Does it mean that the camera sensor is physically designed with 4:3 ratio? This seems weird since camera lenses are circular, and optical images have circular symmetry, so a 1:1 aspect ratio sensors would provide the most information.

Then why the max pixel count is not for 1:1 ratio? What exactly a 4:3 ratio is optimized for?

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That is the shape of the sensor. Whenever you shoot at a non-native aspect ratio, you must crop either from top and bottom or from left and right, so resolution drops.

This is not specific to smartphones. Nearly all digital cameras have a native aspect-ratio which gives the highest resolution. A few cameras such as the Panasonic LX100 have a larger than necessary sensor whose corners fall out of the imaging circle of the lens. Hence, it always crops but manages to keep the same resolution for 4:3, 3:2 and 16:9, although there is a drop at 1:1.

The reason for sensors being like this is not only historical but has a history in asthetics. People tend to prefer rectangular images and so, even from the days of film, images were most often developed as rectangles. There are several aspect-ratios, not just 4:3, but that and 3:2 became most popular.

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  • \$\begingroup\$ i would be interested to see some documentation to support your assertion that "most people tend to prefer rectangular images" and if its true, why. Do they prefer them because that's what they are used to or is it because of psychology or some connection to the laws of nature and physics? \$\endgroup\$
    – Alaska Man
    Commented May 10, 2017 at 21:43
  • \$\begingroup\$ There is an entire other question related to this. It's a whole other discussion. \$\endgroup\$
    – Itai
    Commented May 10, 2017 at 22:35
  • \$\begingroup\$ btw, has the 4:3 ratio anything to do with golden ratio? \$\endgroup\$
    – user152435
    Commented May 11, 2017 at 11:58
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The max rectangle area that can be enclosed in a circle is actually a square. This means that ideally a 1:1 aspect-ratio sensor would be able to collect more information than any other aspect ratio sensor.

That is not actually correct. See http://www.scantips.com/mpixels.html

1:1 (1:1) 4899x4899 pixels, 24 mp

4:3 (1.33:1) 5657x4243 pixels, 24.003 mp

3:2 (1.5:1) 6000x4000 pixels, 24 mp

It's default example is for 24 megapixels. It is not about pixel size. Using units of "one pixel", the math just finds the maximum "numbers" of each aspect ratio that can multiply to be 24 megapixels (which is exactly area, and always exactly equal). Where 3:2 is wider but less tall, 1:1 is, well, more square. But both have exactly the same area which exactly fits into the circumscribed circle of the same diagonal. Aspect ratio is merely an arbitrary choice.

We could argue that the square is less efficient, not fitting any rectangular print paper as fully, like 4x6, 5x7, or 8x10.

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  • \$\begingroup\$ I don't understand this calculation. In particular, if I'm inputting 24mp, how come one of the outputs is larger than 24mp? \$\endgroup\$
    – Sparkler
    Commented May 10, 2017 at 21:34
  • \$\begingroup\$ ? It is rounding. That 24.00265 megapixels of 5657x4243 pixels is the best fit to 24 megapixels. If we subtract one pixel of width, to be 5656x4243, then that does not exceed 24, but it subtracts 4243 pixels in all the rows, which is is only 23.998 megapixels. That calculator provides that option if important to you. And frankly, your camera rounds worst cases than this. :) \$\endgroup\$
    – WayneF
    Commented May 10, 2017 at 23:34
  • \$\begingroup\$ This calculations are totally wrong. If you have a 6000px sensor, you would have a 6000x6000=36Mpx sensor to use the full extent of the projected image. This question has nothing to do with Megapixels, but geometry alone. \$\endgroup\$
    – Rafael
    Commented May 11, 2017 at 1:04
  • \$\begingroup\$ Not wrong in any way. 36 megapixels could also be 4:3 6928x5196 pixels, 35.998 mp, or 3:2 7348x4899 pixels, 35.998 mp, or 16:9 8000x4500 pixels, 36 mp. All the same area of 36 megapizels (all with same diagonal to fit the lens shape). Square has no advantage, only disadvantage of matching our paper shapes. \$\endgroup\$
    – WayneF
    Commented May 11, 2017 at 1:17
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    \$\begingroup\$ Wayne, we've had this discussion before. For a given image circle and pixel size a square aspect ratio gives the most area and thus the most pixels. Your calculator is not wrong, but it's calculating the wrong thing. \$\endgroup\$
    – Mark Ransom
    Commented May 11, 2017 at 16:35

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