I got into this rabbit hole while trying to replace the speaker wire in my setup. I have speakers with 8 Ω of resistance (Rspeaker) and a maximum input power of 140 Watts, so I wanted wires that would not exceed 140W when considering their gauge and length (looking for 10-16 feet).
I found a table at this site: https://soundcertified.com/what-size-speaker-wire-guide/ which displays the maximum power in the system for the given length, gauge, and speaker resistance. Cool, right? I was able to estimate what I need from it, and for fun I decided to back-calculate the table so I could plug in the different lengths I was looking at and see what gauge would work.
I created the following spreadsheet which shows the given table from the website, a matching table based on the calculation I determined was used, and some various values. Spreadsheet to look at the expressions: https://1drv.ms/x/s!AqQjhMOX3aoJ-RN2iS2C_NCIKuKw?e=dVOrqG, image is attached for initial viewing.
Quick overview of the spreadsheet: the initial table uses feet for the length and gauge for the area. In my calculated table, since I had to use resistivity (Ω*m), I converted that to Ωmm, and all the distances to mm and area to mm^2. The table has four values, each corresponding to a length, for every resistance and area (Ohm and Gauge) pair. At the bottom is the value for the resistivity of copper, the equation for resistance in a wire, and the equation for power as a function of voltage and resistance. I also included the voltage from my system (assumed maximum since volume level will control it).
Figuring out the calculation: Because the values in the table are supposedly wattages, I decided to start with the equation for power using voltage (something I could easily assume and change) and resistance (known) versus current. The total resistance is the sum of the speaker resistance plus the wire resistance (a relatively negligible value) since they are in series (I did the parallel calculation for fun as well and it's an inverse relationship obviously). These wattage values, however, are completely different from anything in the table (~1700W for 8Ω, 20 gauge, and 120V), and the various values per length are very similar because wire resistance is negligible (a pretty obvious conclusion).
So what are the values in the table? After messing around a lot I stumbled upon the relationship: Rspeaker/Rwire. It's the ratio between the resistance of the speaker and the resistance of the wire, which is why the values vary so much considering the small Rwire values. But, this means the values in the table are dimensionless, and not wattages at all! A way to get that relationship is Pwire/Pspeaker (voltages cancel out), but I don't know why this would be done or why the ratio would be useful.
On top of that craziness, the table values and determined relationship are still on the correct order of magnitude for input power into the speaker, and supposedly they make sense (if I assume they're wattages, for my system, 16 gauge wire can be used for 16', and if I want shorter wires I should use 18 gauge to not exceed 140 "watts").
Questions: If the values are dimensionless, how are they supposedly useful for comparing wattage, or it it some fake relationship? If the power calculations that were ~1700W are accurate, why does my speaker have a max input of 140W? Is there a better or proper way of determining this for future reference?