## How do you compute the bitrate of a WAV file?

5

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?

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 – 2015-10-27T17:23:59.717

@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 – 2015-10-27T19:55:01.620

10

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:

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 – 2015-10-28T09:17:27.247

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 – 2015-10-28T09:21:13.707

1I thought a kilobyte was 1024 bytes and a megabyte was 1024 kB except in hard drive marketing and packaging. – Todd Wilcox – 2015-10-28T11:55:10.873

@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 – 2015-10-28T12:11:33.570

@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 – 2015-10-28T12:30:13.223

1@MichaelHansenBuur, that first 441000 should be 44100. (I'd correct it myself, but SE doesn't allow an edit that short.) – Kyralessa – 2019-04-04T12:34:47.337

@Kyralessa - good catch, fixed. – Michael Hansen Buur – 2019-04-05T08:33:19.543

0

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.

0

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.

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 – 2015-10-27T22:31:14.050