dB Tables

Just some lookup tables. More info on Decibel on Wikipedia.

dB

Relative amplitude and power; dB above or below '1';

AmplPowerdB
10.0100 20
7.9463.1 18
5.6231.6 15
3.9815.9 12
3.1610.0 10
2.827.94 9
2.516.31 8
2.245.01 7
2.003.98 6
1.783.16 5
1.582.51 4
1.412.00 3
1.261.58 2
1.121.26 1
1.001.00 0
0.890.79 -1
0.790.63 -2
0.710.50 -3
0.630.40 -4
0.560.32 -5
0.500.25 -6
0.450.20 -7
0.400.16 -8
0.350.13 -9
0.320.10-10
0.250.06-12
0.180.03-15
0.130.02-18
0.100.01-20

The numbers in the above table are relative numbers, not volts or watts;
If you reduce the volume by 3 dB you do get about 71% of the previous amplitude and 50% of the previous power.

dBs and camera stops

The relative amplitudes of the 3 dB steps (-6, -3, 0, ...) almost but not quite correspond with camera f-numbers;
F-numbers are (rounded) multiples of √2. 3 dB steps are close approximations thereof;

StopRatiodB
 22 16 √227.09
 16 1624.08
 11  8 √221.07
  8   818.06
  5.6  4 √215.05
  4   412.04
  2.8  2 √2 9.03
  2   2 6.02
  1.4  √2 3.01
  1   1 0  
  0.7  1/√2‒3.01
  0.5  1/2‒6.02

The difference between the two (3 vs 3.01 dB) is about 0.12%.

dBm

The table below is based on 0 dB is 1 mW in 600 Ω (744.59667 mV).

dBmmV
0775
-1690
-2615
-3548
-4489
-5436
-6388
-7346
-8308
-9275
-10245
-11218
-12195
-13173
-14155
-15138
-1897.5
-2077.5

The telephone audio signal level is -9 dBm or 275 mV. DTMF tones are -7 dBm or 346 mV.
Dial- and other tones are different in each country. Often used values are -12 dBm for dial tones and -20 dBm for busy- and ring-back tones.

dB below clip level

The peek level in this table corresponds with 32767 (the largest possible value of a 16‑bit signed integer).

Peek
dB		Max val
032767
-129203
-226027
-323197
-420674
-518426
-616422
-714636
-813044
-911626
-1010361
-11 9234
-12 8230
-13 7335
-14 6537
-15 5826
-18 4125
-20 3276

The dB values in the above table are accurate for a square wave only. For a pure sine wave the RMS dB values are 3 dB lower (3.01 dB to be exact).

Sine
RMS
dB		Max val
-332767
-429238
-526058
-623224
-720699
-818448
-916441
-1014653
-1113060
-1211639
-1310374
-14 9245
-15 8240
-16 7344
-17 6545
-18 5833
-19 5199
-20 4633

dBm and bits

On the Wikipedia page Digital milliwatt is a description of 1 kHz 0 dBm Alaw and µlaw test signals. Below a translation to 16‑bit signed integers;
A-law 0 dBm grapgh
Of course, the actual analogue signal isn't this 'clunky'. Below a more realistic signal;
A-law 0 dBm signal
It's supposed to be a pure sine wave, but does in fact have some 3rd harmonic distortion.

Note that the 8‑bit values below are hex and the 16‑bit values decimal;

Alaw

Degr8-bit16-bit
202.534 -8960
247.521-20992
292.521-20992
337.534 -8960
22.5b4 8960
67.5a1 20992
112.5a1 20992
157.5b4 8960

Note: The highest value which a Alaw to 16‑bit conversion can produce is 32256 which is 0.14 dB (peek) below 32767.
For a 500 Hz sine of the same amplitude the 0° to 180° values are;

Degr16-bit
0   8
22.5 8960
45  16128
67.520992
90  23040
112.520992
135  16128
157.5 8960
180   8

Note: There is no '0' in Alaw. It's either 8 or -8.
Note: This signal is 0.02 dB (RMS) stronger than the 1 kHz signal.

μlaw

Degr8-bit16-bit
202.51e -8828
247.50b-20860
292.50b-20860
337.51e -8828
22.59e 8828
67.58b 20860
112.58b 20860
157.59e 8828

Note: The highest value which a μlaw to 16‑bit conversion can produce is 32124 which is 0.17 dB (peek) below 32767.
For a 500 Hz sine of the same amplitude the 0° to 180° values are;

Degr16-bit
0   0
22.5 8828
45  15996
67.520860
90  22908
112.520860
135  15996
157.5 8828
180   0

Note: This signal is 0.02 dB (RMS) stronger than the 1 kHz signal.
Note: Some documents may mention a 14‑bit value of 5769 (or 5768) for 90° and 5329 for 67.5°; These correspond to 16‑bit values of 23076 (or 23072) and 21316;
If you encode a signal that is 0.5 * √2 of the maximum µlaw value, you get 0.5 * √2 * 8158 ≈ 5768.577. Rounded this is 5769 and rounded down 5768. This corresponds to 3.05 dB peek below clip level.
However, if you convert these to µlaw and back you end up with 16-bit values 22908 and 20860.

dB Conversion table

For Alaw the 90° value is 23040, for μlaw 22908. These are 3.06 resp 3.11 dB below 32767.
So the peek level is about 3 dB below clip level. Therefore the RMS value of a sine wave is about 6 dB below clip level.
Note: As long as the signal doesn't clip, it's the RMS value that counts!
Below a litte conversion table;

signal levels
dB below
clip level		dBm
PeekRMS
0 -3 3
-3 -6 0
-6 -9 -3
-9-12 -6
-12-15 -9
-15-18-12
-23-26-20

Note that the RMS values in this table apply to pure sinusoidal signals!

You can check the volume of a file with 'sox [File Format] File_Name -n stats'; 

~$ sox -t raw -r 8000 -e signed-integer -b 16 -c 1 File_Name.sln -n stats
DC offset   0.000010
Min level  -0.462158
Max level   0.505310
Pk lev dB      -5.93
RMS lev dB    -27.92
RMS Pk dB     -14.87
RMS Tr dB     -90.69
Crest factor   12.58
Flat factor     0.00
Pk count           2
Bit-depth      15/16
Num samples    2.86M
Length s     357.440
Scale max   1.000000
Window s       0.050

Note that the '-n stats' bit goes after the file name!
The 'RMS Pk dB' of -14.87 corresponds with approximately -9 dBm.