Length of copper wire in 1 lb spool
Find a function of length depending on mass

Conversion factors:


$2.54 ~\mathrm{\frac{cm}{in}}$
$454 ~\mathrm{\frac{g}{lb}}$


Constants:


Wire diameter $d = 0.129~\mathrm{cm}$
Density of copper $\rho = 8.92~\mathrm{g\, cm^{-3}}$


Thus, our function $l(m)$ for the wire length from the wire mass in pounds reads:
$$ l(m) = m \cdot 454~\mathrm{\frac{g}{lb}} \cdot \frac{1}{\pi d^2 \rho}$$

Evaluate the function

Since I'm too lazy to evaluate something like this by hand (and since I somehow had to record this thought process and did not want to waste the processed remnants of a dead tree) there is a small python script available to do this for you, which you can find here and which, if you run it using the command python3 wires.py, will give you the following output:


  Wire length of 1.00 lb of 16-gauge wire: 9.71 m




(Bonus: You can run the command as python3 -i wires.py and will then be dropped into an interactive python shell, where you can call the wirelength function as many times as you wish using different masses for the wire.)