# Calculate dBA from Octave Band Sound Levels

This post is an answer to a question that was posted on our blog recently.

The questions was “**Is it possible to calculate the overall dB(A) value from a set of 1:1 octave band values**?”.

The answer to this is yes, but there are a few things to consider in terms of how the data has been measured and what it is being compared to.

The first is that the octave band data values should have been measured at the same time using a real-time octave band sound level meter such as the CR:162C optimus red or CR:171A optimus green instruments. If the data has not been measured using a real-time sound level meter, the comparison between the overall LAeq and the calculated values should be done with caution.

The second is that the octave bands have been measured as Leq (rather than sound level). This is important as it allows us to gather all of the noise energy together to calculate an overall dB(A) value.

The third is to consider that the data gathered by the octave bands is not be the same as that used to calculate the overall dB(A) value in the sound level meter. The calculation of the LAeq in a sound level meter uses an A-weighting filter that spans from 10Hz to 20kkHz whereas the octave band filters may only cover centre frequencies from 63Hz to 8kHz in some circumstances. If the noise measured contains significant amounts of noise outside of these bands, the calculated values can be significantly different to the measured values.

Also consider that the A-weighting curve used for the overall values in the sound level meter has tolerances which are not taken into account when calculating a dB(A) from octave bands.

**What do we need?**

We need the values of each of the octave bands, ideally from 31Hz to 16kHz, and we need to know if these have been frequency weighted in any way.

The best way to measure 1:1 or 1:3 octave bands is to not use any frequency weighting and then to apply any corrections after the measurement. This avoids any issues with overload or under-range in the instrument during the measurement.

This was often an issue with older sound level meters where the dynamic range of the instrument was limited.

Modern sound level meters such as the Cirrus optimus instruments often have a dynamic range is excess of 120dB and so this type of error is much less common.

We also need to know the corrections for A-weighting at each of the frequencies for which we have data. This post, What are A, C & Z Frequency Weightings?, describes what these frequency weightings are and gives the corrections for each at the different frequencies.

Frequency (Hz) | 31.5 | 63 | 125 | 250 | 500 | 1kHz | 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 |

In the example below, we will use values from 31Hz to 16kHz taken from a measurement made with an optimus red sound level meter and downloaded into the NoiseTools software.

**An example calculation**

Below are the noise levels, measured as LZeq or Leq dB(Z) by the optimus sound level meter:

Frequency (Hz) | 31.5 | 63 | 125 | 250 | 500 | 1kHz | 2kHz | 4kHz | 8kHz | 16kHz |

Level (dB) | 70.9 | 78.4 | 83.3 | 87.6 | 87.3 | 93.5 | 93.8 | 97.0 | 99.9 | 98.2 |

The next step is to add the A-weighting corrections to the measured levels:

Frequency (Hz) | 31.5 | 63 | 125 | 250 | 500 | 1kHz | 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 |

Level (dB) | 70.9 | 78.4 | 83.3 | 87.6 | 87.3 | 93.5 | 93.8 | 97 | 99.9 | 98.2 |

Result (dB) | 31.5 | 52.2 | 67.2 | 79 | 84.1 | 93.5 | 95 | 98 | 98.8 | 91.6 |

Now we need to take each of the resulting values and do a calculation on each one. Firstly we need to divide each value by 10 and then anti-log each value. The simplest way to do this is to use the formula 10 ^(L/10) where L is the value in each cell.

Now we add all of these values together, log this value and multiply it by 10 to give the final dB(A) value.

These steps allow us to calculate the overall dB(A) value of this noise measurement and the value that we end up with is 103.2dB(A).

This is the same as the overall LAeq value that the optimus sound level meter measured.

I hope this answers the question but if you’d like to know more or if you have a question that you’d like answering, just drop an us email or use the form at the top of the page.

### James Tingay

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