Convert A weighted voltage output into sound pressure
I am assuming your output is also driving an amplifier and then some loudspeakers.

If that's the case the best way to calibrate your vu meter is put some pure tone in the amp and measure the spl with a microphone nicely placed.

You can also search for a parameter called "sensitivity", the manufacturer of your loudspeakers should be able to tell you it. Sensitivity is measured in \$\frac{\text{dB}}{\text{W}\cdot\text{m}}\$, i.e. is the spl in decibel the loudspeaker outputs for each watt of power you give to it, measured at a distance of 1m. Problem is that sensitivity depends on frequency and on the enclosing and probably other parameters.