FFMPEG - Get the exact calculated audio filesize after encode - audio

Question

Im trying to guess an audio (mp3) filesize before encode with ffmpeg, afterward, need to have the exact calculated filesize.
Here is the formula im using to predict and calculate the filesize (hope im not wrong) :
( Bitrates x Duration ) / 8) x 1000 = Filesize in Bytes.
Im going to give a real example so that everyone can understand the use case.
Example :
Having an m4a file with the following data :
Name : Assuming xxx.m4a
Filesize : 8 304 014 bytes (8,3 Mo)
Bitrates : 256k
Duration : 260 seconds
Expected filesize : ( (256 x 260) / 8 ) x 1000 = 8 320 000 bytes
Then im running the following ffmpeg command :
ffmpeg -i xxx.m4a -f mp3 -y -minrate 256k -maxrate 256k -bufsize 256k -b:a 256k -fs 8320000 output.mp3
Console output :
ffmpeg version 2.7.2 Copyright (c) 2000-2015 the FFmpeg developers
built with Apple LLVM version 6.1.0 (clang-602.0.53) (based on LLVM 3.6.0svn)
configuration: --prefix=/usr/local/Cellar/ffmpeg/2.7.2_1 --enable-shared --enable-pthreads --enable-gpl --enable-version3 --enable-hardcoded-tables --enable-avresample --cc=clang --host-cflags= --host-ldflags= --enable-opencl --enable-libx264 --enable-libmp3lame --enable-libvo-aacenc --enable-libxvid --enable-vda
libavutil 54. 27.100 / 54. 27.100
libavcodec 56. 41.100 / 56. 41.100
libavformat 56. 36.100 / 56. 36.100
libavdevice 56. 4.100 / 56. 4.100
libavfilter 5. 16.101 / 5. 16.101
libavresample 2. 1. 0 / 2. 1. 0
libswscale 3. 1.101 / 3. 1.101
libswresample 1. 2.100 / 1. 2.100
libpostproc 53. 3.100 / 53. 3.100
Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'xxx.m4a':
Metadata:
major_brand : isom
minor_version : 512
compatible_brands: isomiso2mp41
encoder : Lavf56.36.100
Duration: 00:04:20.53, start: 0.000000, bitrate: 254 kb/s
Stream #0:0(und): Audio: aac (LC) (mp4a / 0x6134706D), 44100 Hz, stereo, fltp, 253 kb/s (default)
Metadata:
handler_name : SoundHandler
Output #0, mp3, to 'output.mp3':
Metadata:
major_brand : isom
minor_version : 512
compatible_brands: isomiso2mp41
TSSE : Lavf56.36.100
Stream #0:0(und): Audio: mp3 (libmp3lame), 44100 Hz, stereo, fltp, 256 kb/s (default)
Metadata:
handler_name : SoundHandler
encoder : Lavc56.41.100 libmp3lame
Stream mapping:
Stream #0:0 -> #0:0 (aac (native) -> mp3 (libmp3lame))
Press [q] to stop, [?] for help
size= 8127kB time=00:04:20.02 bitrate= 256.1kbits/s
video:0kB audio:8127kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.011765%
Problem and Questions :
Can you tell me why im I getting an output with 8 322 546 bytes and
not 8 320 000 as expected ?
Is there something wrong in my formula or the ffmpeg command ?
What solution can you suggest to get the exact predicted filesize ?
Thank you in advance.

Answer 1

Besides the muxing overhead inherent in the container, MP3 audio is stored in frames. And each frame has fixed number of 1152 samples. The encoder will output full frames so for an output sampling rate of 44100, the closest to 260 seconds is
ceiling of (260 x 44100/1152) = 9954 frames = ~260.02285 seconds.
This throws your calculation, by itself, off balance, even if the encoding assumptions were right.
Even then, the bit reservoir may come into play.
Edit:
You can drop the bitrate and add silent padding, but this too isn't precise as muxing overhead comes into play
ffmpeg -i xxx.m4a -f lavfi -t 5 -i anullsrc -lavfi "[0:a][1:a]concat=n=2:v=0:a=1" -f mp3 -y -minrate 224k -maxrate 224k -bufsize 224k -b:a 224k -fs N output.mp3
Here, the fs should be calculated as per MP3 + 5 seconds duration.