The decibel (dB) is a dimensionless unit used to express the logarithm of
the ratio of a measured sound quantity to a reference quantity. In acoustics, the decibel is used to describe the level of quantities that are
proportional to sound power. In
mathematical terms, the decibel is expressed as:
L = 10 log_{10} (W_{1}/W_{2})
L = the level in dB
10 = a multiplier
W_{1} and W_{2} = quantities proportional to sound power
Combining Decibels
Decibels are logarithmic values and so it is not proper to add them by normal algebraic addition. For example, 70 dB plus 70 dB does
not equal 140 dB, but only 73 dB. When adding sound pressure levels or sound power levels, the following equation
should be used:
L_{(total)} = 10 log_{10} (S 10^{Li/10})
where L can be sound power level or sound pressure level.
Example: The total sound pressure level of three sources with sound pressure levels of 85, 83, and 88 dB is
calculated as follows:
L_{(total)} = 10 log_{10} (10^{85/10} + 10^{83/10} + 10^{88/10}) = 90.6 dB
A simplified method that can be used for combining decibels utilizes the following table:
Difference in dB Values 
Add to Higher Level 
01 dB 
3 dB 
23 dB 
2 dB 
49 dB 
1 dB 
10 dB or more 
0 dB 
Example: 70 dB + 73 dB = 75 dB (the difference between the values is 3 dB, so add 2 dB to the higher value, so
73 + 2 = 75 dB).
More than two levels
can be combined using the above method by taking the combinations in pairs (any order will work).
Example: Four noise sources with sound pressure levels of 88, 86, 80 and 85 dB would be combined as shown in the
flow chart.
