The Maths of Pixels.

June 7, 2012 § 2 Comments

This is a fairly short post, just to describe the maths behind “size” of video files, specifically in their uncompressed form.  Obviously, the number here have no real world application, but I find it interesting.

Specifically, we’re looking at something running at 24fps, and running on what wikipedia says is 2k resolution for cinemas, 1998 × 1080, which is a 1.85:1 aspect ratio, not that that’s related, oh, and let’s say we’re dealing with a 2 hour long movie, which is running in 3D.

So, if we have a 1998 x 1080 screen, we’re dealing with 2,157,840 pixels on screen.

Let’s assume that each pixel is running in 32 bit colour, so we have 69,050,880 bits on each frame, which is (divided by eight to get) 8,631,360 bytes in each frame(obviously, the simpler equation is just to multiply the bits by 4 to get 32 bits as bytes).

There are 48 frames every second(24 frames, twice, to deal with 3D), which means we have 414,305,280 bytes every second.

With sixty seconds in every minute, we have 24,858,316,800 bytes every minute.

With one-hundred and twenty minutes in two hours, we have 2,982,998,016,000 bytes for the whole film.

There are 1024 bytes in a kilobyte, so if we divide by 1024 we have 2,913,084,000 kilobytes.

The same applies for kilobytes into megabytes, so it’s 2,844,809 megabytes.

Funnily enough, the same as above applies to get gigabytes, so it’s 2,778 gigabytes, or 2.7 terabytes.

Unless I’ve made a mistake in my maths here, which is entirely possible.

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