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1080p Math

Let's perform a thought experiment wherein we take a pure, uncompressed 1080p signal. How much bandwidth would it take to display the signal at 60 FPS?

1920 * 1080 = 2073600             number of pixels
2073600 * 24 = 49766400           24-bit color (16.7M colors)
49766400 * 60 = 2985984000        60 frames per second
2985984000 / 8 = 373248000        convert to bytes/sec
373248000 / 1024 = 364500         convert to KB/sec
364500 / 1024 = 355.957           convert to MB/sec

So there you have it: uncompressed 1080p at 60 FPS and 24-bit color would take more than 350 MB/sec bandwidth. HDMI supports 48-bit color, so double the numbers and you're well above half a gigabyte per second of data.

Math like this really impresses upon us all how well modern codecs truly work. For example, a 1920 x 1080 "BBC HD" video I downloaded from Apple clocks in at 24 FPS, 1:33.5, and only 93.10 MB. Scaling 356 MB/sec by a 24:60 factor gives roughly 142 MB/sec. This particular video plays at barely more than 1 MB/sec (8.38 mb/sec), a savings of nearly 99.3%.

3 Responses to "1080p Math"

  1. I believe only the 'i' specs go up to 60fps. 1080p only goes up to 30fps. Recalc in order.

    Reference here.

  2. JW said on November 19, 2006:

    I believe only the 'i' specs go up to 60fps. 1080p only goes up to 30fps. Recalc in order.

    Reference here.

    From that same source:

    If the standard MPEG-2 compression is used, versions with higher frame rate such as 1080p50 and 1080p60 could only be sent over higher-bandwidth channels; to send these over normal-bandwidth channels, a more modern codec such as the H.264/MPEG-4 AVC codec must be used. Higher frame rates such as 1080p50 and 1080p60 are foreseen as the future broadcasting standard for production

    No new math needed. Simply changing to 48-bit color from 24-bit and moving from 60 FPS to 30 keeps the results the same. Otherwise, divide or multiply by two.

  3. An even simpler way of "doing the math":

    *1080p Uncompressed Video Bandwidth*

    1920x1080 resolution = 2,073,600 pixels

    2,073,600 pixels @ 24bpp = 49,766,400 bits (49Mbits)

    49,766,400 bits / 8Mbits (8Mbits per Megabyte) = 6,220,800 bytes (6.2Mbytes)

    So, 6.2Mbytes per frame.

    6,220,800 bytes x 30 fps = 186,624,000 bytes/sec (187Mbytes/sec)
    6,220,800 bytes x 60 fps = 373,248,000 bytes/sec (373Mbytes/sec)

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