Calculate Decibel

The logarithmic decibel scale is convenient when calculating resulting sound power levels and sound pressure levels for two or more sound or noise sources.

Adding Equal Sound Power Sources

The resulting sound power when adding equal sound power sources can be expressed as:

L_wt = 10 log(n N / N_o) = 10 log(N / N_o) + 10 log(n)

= L_ws + 10 log(n) (1)

where

L_wt = the total sound power level (dB)

L_ws= sound power level from each single source (dB)

N = sound power (W)

N_o = 10^-12 - reference sound power (W)

n = number of sources

The adding of equal sound power sources can also be expressed graphically as

Adding equal sound power levels

Note! Adding two identical sources will increase the total sound power level with 3 dB ( 10 log(2) ).

The sound power and sound power level is commonly used to specify the emitted noise or sound from technical equipment as fans, pump and other machines. The sound measured with microphones is the sound pressure.

Adding Equal Sound Pressure Levels

The resulting sound pressure level when adding equal sound pressure can be expressed as:

L_pt = L_ps + 20 log(n) (2)

where

L_pt = total sound pressure level (dB)

L_ps = sound pressure level from each single source (dB)

n = number of sources

Number of Sources	Increase in Sound Power Level ( dB)	Increase in Sound Pressure Level dB
2	3	6
3	4.8	9.6
4	6	12
5	7	14
10	10	20
15	11.8	23.6
20	13	26

Adding Sound Power from Sources at different Levels

The sound power level from more than one source can be calculated as:

L_wt = 10 log( (N₁ + N₂ ... + N_n) / N_o) (3)

Adding two sources at different levels can be expressed graphically as

Adding different sound levels

Sound Power Level Difference between two Sound Sources (dB)	Added Decibel to the Highest Sound Power Level (dB)
0	3
1	2.5
2	2
3	2
4	1.5
5	1
6	1
7	1
8	0.5
9	0.5
10 or more	0

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