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Consider a WAV file obtained from a standard redbook CD with 16 bit samples and 44.1 kHz sampling rate. How do you compute the bitrate of the uncompressed stream?

landroni
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  • I don't think there's such a thing as standard redbook FLAC file, as redbook is a standard for pcm audio cds. If the size of a given flac file is X MBytes and it's audio duration S seconds, it's average bitrate in Mbits/s will be (8 * X) / s – audionuma Oct 27 '15 at 17:23
  • @audionuma I now clarified the reference to redbook CDs in the question. Given the info in the question, is there a way to compute the bitrate without knowing the actual size of the FLAC file? – landroni Oct 27 '15 at 19:55

3 Answers3

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Here is how you calculate the constant bitrate (CBR) of uncompressed audio:

 Bits Per Second (bps) = Sample Rate (Hz) * Word Length (bits) * Channel Count

Which for 44.1 KHz, 16 bit, 2 Ch. (stereo) audio gives you:

 44100 * 16 * 2 = 1411200 bps or 1411.2 kbps (kilobits per second, i.e. bps / 1000)

To express that in bytes, kilobytes or megabytes use the following conversions:

 Bits to bytes:      bits / 8             or bits * 0.125
 Bits to kilobytes: (bits / 8) / 1000     or bits * 0.000125
 Bits to megabytes: (bits / 8) / 1000000  or bits * 0.000000125

Which for 44.1 KHz, 16 bit, 2 Ch. (stereo) audio gives you:

 1411200 * 0.125       = 1764000 Bps (bytes per second)
 1411200 * 0.000125    = 176.4 KBps (kilobytes per second)
 1411200 * 0.000000125 = 0.1764 MBps (megabytes per second)

The following tools may be to assistance calculating these numbers:

Michael Hansen Buur
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  • Why does the number of channels enter in the equation? Is it that on recording (i.e. on ADC) the microphone registers two separate streams of audio? – landroni Oct 28 '15 at 09:17
  • Sort of - you have a stream for each side (left and right) in the stereo image. A true mono audio file would only contain one stream. Surround sound comes in several formats with more than two channels, but these are rarely used for music alone. – Michael Hansen Buur Oct 28 '15 at 09:21
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    I thought a kilobyte was 1024 bytes and a megabyte was 1024 kB except in hard drive marketing and packaging. – Todd Wilcox Oct 28 '15 at 11:55
  • @ToddWilcox - Yeah, there is a lot of confusion around that. Take a look at this article for some explanations: https://blogs.gnome.org/cneumair/2008/09/30/1-kb-1024-bytes-no-1-kb-1000-bytes/ – Michael Hansen Buur Oct 28 '15 at 12:11
  • @MichaelHansenBuur That's not an article, it's a blog post expressing an opinion with a request for feedback. However, Wikipedia confirms that you're right that these days, 1 KB = 1024 B is pretty much only used for RAM. Specifically it mentions 1 kB = 1000 B is used for "data transfer rates", which is the topic of this question. I stand corrected. – Todd Wilcox Oct 28 '15 at 12:30
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    @MichaelHansenBuur, that first 441000 should be 44100. (I'd correct it myself, but SE doesn't allow an edit that short.) – Kyralessa Apr 04 '19 at 12:34
  • @Kyralessa - good catch, fixed. – Michael Hansen Buur Apr 05 '19 at 08:33
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Unless I'm getting my math terribly wrong, since standard CDs are stereo these days and there are 44100 samples in a second, each worth 16 bits, then: 

2 * 16 * 44100 = 1411200 bps

Which in turn represents 1411.2 kbps (which is in kbit/s). In bytes, it would be 176.4 kBps.

landroni
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The bitrate of a FLAC encoded file versus the bitrate of the source PCM file depends on the audio content.

In average, depending on the FLAC encoder settings, the ratio FLAC / PCM is around 65 %. See https://xiph.org/flac/comparison.html and http://www.synthetic-soul.co.uk/

So a 1411 kbps audio cd should on average produce an approximately 920 kbps FLAC file.

edit :please notice that this answer was produced before the original post was heavily edited and has in the process removed any reference to flac.

Community
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audionuma
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  • What I'm interested really in the bitrate of the decoded FLAC file, the uncompressed stream. How is that computed? (I realize that my question may be slightly confusing. I tried to make the question clearer still and switched to WAV as example file.) – landroni Oct 27 '15 at 22:31
  • It's a nice answer and provides some good references, but why don't you edit the answer then to match the question? – ZaellixA Mar 29 '21 at 22:23