## How big can a panorama get?

I use the Kolor AutoPano Giga panorama-stitching software, recently acquired by GoPro, but I have yet to produce a gigapixel panorama like those they pioneered. This brings up an interesting question: given a camera and lens, what would the pixel size of the largest 360° stitched panorama be?

Wikipedia to the rescue: using the formula for the solid angle of a pyramid, the full panorama size of a camera with m megapixels on a sensor of a x b using a focal length of f would be:

m * π / arctan(ab / 2f / sqrt(4f^{2} + a^{2} + b^{2}))

For single-strip panoramas of height h (usually a or b), the formula would be:

m * π * h / 2f / arctan(ab / 2f / sqrt(4f^{2} + a^{2} + b^{2}))

(this applies only to rectilinear lenses, not fisheyes or other exotics).

Here is a little JavaScript calculator to apply the formula (defaults are for the Sony RX1RII, the highest resolution camera I own):

The only way I can break through the gigapixel barrier with a prime lens is using my 24MP APS-C Fuji X-T2 with a 90mm lens.

Update (2020-01-21):

Now I could reach 171 gigapixels with my Nikon Z7 and the Nikkor 500mm f/5.6 PF.

Update (2021-01-30):

There was an error in the JavaScript that implements the calculator, it used
4f instead of 4f^{2}, and for telephoto focal lengths, the difference
is dramatic. Thanks to users ZS360 and GerladDXB at DPReview for pointing out
my error.