How do you add the noise level together? Note that there are 10 frequencies... In this presentation, the method to compute (formula and procedure in Excel) the noise level from dB to dB(A), is shared herein.

1. Noise dB to dB(A) Calculation
The Formula and Procedure
Gan Chun Chet (Mr.)
MSc in Operations Management 1997
University of Manchester Institute of Science and Technology UMIST, United Kingdom
BEng (Hons) in Mechanical Engineering 1996
University of Manchester, United Kingdom

2. dB to dBA : A-Weighting Corrections (1)
Noise Level
Frequency (Hz) 31.5 63 125 250 5001kHz 2kHz 4kHz 8kHz 16kHz
Level (dB) 70.9 78.4 83.3 87.6 87.3 93.5 93.8 97 99.9 98.2
Next, Adding A-Weighting Corrections
Frequency (Hz) 31.5 63 125 250 5001kHz 2kHz 4kHz 8kHz 16kHz
A-Weighting Correction (dB) -39.4 -26.2 -16.1 -8.6 -3.2 0 1.2 1 -1.1 -6.6
Result (dB) 31.5 52.2 67.2 79 84.1 93.5 95 98 98.8 91.6
Adding each (respective frequency/components),
raw data, with A-weighting corrections
Measured raw data, in
decibel dB
The result, by adding each (respective frequency/components),
raw data, with A-weighting corrections
Respective frequency of each component

3. dB to dBA : A-Weighting Corrections (2)
• Example of Calculation:-
At 2kHz, measured data is 93.8 dB
By adding the A-weighting at this frequency, which is 1.2 dB, the result in dB for this particular frequency shall
be 95 dB.
However, it is impossible just to sum all the readings for respective frequency and averaging the raw data to
obtain a result in decibel dB. Instead, a procedure to sum all these readings is stipulated in the next slide.

4. o A B C D E F G H I J K
1 Frequency (Hz) 31.5 63 125 250 500 1kHz 2kHz 4kHz 8kHz 16kHz
2 Result (dB) 31.5 52.2 67.2 79 84.1 93.5 95 98 98.8 91.6
3
4 Details
5 A = 10^[dB]/10 - 165958.69 5248074.6 79432823 257039578 2.239E+09 3.162E+09 6.31E+09 7.586E+09 1.445E+09
6 C = 10log(A+B) ; dB(A) - 52.236808 67.336342 79.28643 85.338837 94.117222 97.591302 100.81076 102.93102 103.23946
7 B = 10^[dB]/10 1412.5375 167371.23 5415445.8 84848269 341887848 2.581E+09 5.743E+09 1.205E+10 1.964E+10 -
dB to dBA : The Formula and Procedure (1)
1.1 Divide the ‘result’ in dB by 10
1.2 Then anti-log the ‘value’, which means calculate
10 to the power of the ‘value’. This will give you the
noise intensity only at this particular frequency.
𝑁𝑜𝑖𝑠𝑒 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝐼1
𝐼0
= 10𝐼𝐿1/10
[derived from 𝐼𝐿1 = 10 log(
𝐼1
𝐼𝑜
)]
3.1 Thereafter add the current noise intensity and
preceding noise intensity,
𝐼1+ 𝐼2
𝐼0
=
𝐼1
𝐼𝑜
+
𝐼2
𝐼𝑜
= 10𝐼𝐿1/10+ 10𝐼𝐿2/10
3.2 Log (base 10) the added noise intensity and multiply
by 10, in accordance to the formula to calculate Intensity
Level IL.
𝐼𝐿1+2 = 10 log (
𝐼1+𝐼2
𝐼0
)
Calculations (Steps):-
1.1 : 31.5/10 = 3.15 (31.5Hz)
1.2 : 103.15
= 1.412 x 103
2.1 : 52.2/10 = 5.22 (63 Hz)
2.2 : 105.22
= 1.659 x 105
3.1 : 1.412 x 103
+ 1.659 x 105
= 1.673 x 105
3.2 : 10 * 𝑙𝑜𝑔10 (1.673 x 105
) = 52.23 dB
2.1, 2.2 Then calculate the next noise intensity of
the subsequent frequency by repeating the same
procedure, 1.1 and 1.2
4.1 Repeat until the end for subsequent
frequency.

5. dB to dBA : The Formula and Procedure (2)
o A B C D
1 Frequency (Hz) 31.5 63 125
2 Result (dB) “B2” “C2” D2
3
4 Details (formula) :-
5 A = 10^[dB]/10 - “C5” = POWER(10, "C2"/10) “D5” = POWER(10, "D2"/10)
6 C = 10log(a+b) ; dB(A) - ”C6” = 10*LOG(("B7"+"C5"),10) ”D6” = 10*LOG(("C7"+"D5"),10)
7 B = 10^[dB]/10 “B7” = POWER(10, "B2"/10) “C7” = POWER(10, "C6"/10) … “D7” = POWER(10, "D6"/10)
Formula, in Excel, as shown below