I can think of two ways you can make an approximation. Neither of them are great, but I can’t think of any better options.

The first thing you can do is make the assumption that the Leq spectrum is similar in shape to the L90 spectrum. This is not a reliable assumption to make, since the L90 spectrum can be quite different from Leq, depending on what sounds you were measuring. Subtract the difference between your unweighted (overall) Leq and A-weighted Leq from your unweighted L90 and that will approximate the A-weighted Leq.

L90 (dBA, approx) = L90 (unweighted) – [Leq (unweighted) – Leq (dBA)]

If you don’t have the unweighted Leq already, you can calculate it by adding up the 1/3-octave or octave bands using decibel addition.

The other approach you can take is to do some research and dig up some Ln spectra for a similar measurement. L90 captures a good representation of background, ambient noise, so if you can find a measurement done in a similar location chances are decent the background spectrum will be similar to what it was for your measurement. Again, approximate the A-weighted L90 for your data by subtracting the difference between the unweighted and A-weighted numbers for your reference measurement.

Hopefully you weren’t in an unusual environment. If you were somewhere typical, like an outdoor rural area, then comparing your data to a measurement in a similar environment should yield decent results.

I’ve got the percentile formula working in Excel now. Just as a point of interest for those trying it, the syntax is:

PERCENTILE(Range,xValue)

Because of the way the formula works, For L90 the xValue is 0.1, for L10 it is 0.9. The only Ln value that is the same as the xValue obviously is L50.

Another perspective that might help you understand the process is to consider that finding L50 is the same process as finding the median. The median value of any group of data falls below 50% and above 50% of the group. The L90 value falls below 90% and above 10% of the samples.

It is the “percentile” function.

It’s really a matter of counting more than a matter of calculating. Ln values are called statistical measurements because they’re a result of analyzing a group of samples, rather than performing a calculation. During a measurement the sound level meter continuously adds the current SPL to a histogram. The interval between samples is constant and internal to the meter, and certainly less than a second. L10 then becomes the value that is lower than 10% of the measurements and higher than 90% of the measurements.

Here’s a very simplified example. Suppose we turn on our SLM long enough for it to collect 20 samples and we ask it to tell us the L20 of the measurement. The samples it collects, in chronological order, are:

58, 59, 58, 57, 56, 55, 55, 56, 56, 57, 58, 59, 60, 61, 62, 62, 61, 62, 63, 64

To determine L20, we look for the value that is below 20%, or 4 out of 20, of the samples. The easiest way to do this is to sort the samples in descending order:

64, 63, 62, 62, 62, 61, 61, 60, 59, 59, 58, 58, 58, 57, 57, 56, 56, 56, 55, 55

L20 will be the value below the top 4 values and above the bottom 16. The 4th and 5th samples (in descending order) are 62 and 62, so L20 is 62. In other words, 20% of the time, the measured sound level was above 62 dB.

We can also determine the L50 (or any other Ln from our data) by using a similar analysis. Instead of the top 20% of samples, we would instead determine the top 50%, or 10 out of 20. The 10th and 11th samples, in descending order, are 59 and 58. So the L50 is somewhere between 58 and 59 dB.

The only way you could really do this calculation in Excel is if you had access to frequent periodic samples of the measured sound level meter. Generally the only way you can collect that type of data is with an advanced sound level meter, and such a meter will almost certainly have Ln functionality built in, so it’s sort of pointless to do it yourself. In a real Ln measurement the SLM will collect far more than 20 samples, so doing it by hand in a spreadsheet could be quite an undertaking.

If you had a quick pencil, you could approximate Ln values by watching a simple SLM and recording the value at regular intervals; every 10 seconds for an hour, to use your example, would work well, giving you 360 samples. You would watch a clock with a second hand and every 10 seconds write whatever value was on the SLM at that moment. You would then enter all of your samples into a spreadsheet and sort them in descending order. You could then determine your approximate L10 by seeing what value had 10% (36 out of 360) of the samples above it.

-Joshua

Thanks