Adding Decibels

The logarithmic decibel scale is convenient calculating sound power levels for two or more sound sources

Adding Equal Sound or Noise Power Sources

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

Lwt =  10 log(n N / N0)

    = 10 log(N / N0) + 10 log(n) 

    = Lws + 10 log(n)         (1)


Lwt = the total sound power level (dB

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

N = sound power (W)

N0 = 10-12 - reference sound power (W)

n = number of sources

Adding Equal Sound Power Calculator

N - sound power (W)

N0 - reference sound power (W)

n - number of sources

Sound Power Level (dB) :  

Lws - sound power level (dB)

n - number of sources

Sound Power Level (dB) :  

Adding of equal sound power sources can be expressed graphically

adding equal sound level sources

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

Sound power and sound power level are often used to specify the noise or sound emitted from technical equipment like fans, pumps or other machines.

Sound measured with microphones or sensors are sound pressure

Number of SourcesIncrease in Sound Power Level
2 3
3 4.8
4 6
5 7
10 10
15 11.8
20 13

Adding Sound Power from Sources with different Sound Powers 

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

Lwt =  10 log( (N1 + N2 ... + Nn) / No)    (3)

Adding two sources at different levels can be expressed graphically as

adding different sound levels diagram

Sound Power Level Difference between
two Sound Sources
Added Decibel to the Highest Sound Power Level
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 0.5
> 10 0

Related Topics

  • Acoustics - Room acoustics and acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation
  • Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems

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