How to convert apparent visual magnitude to SI units? How do I convert the apparent visual magnitude of astronomical objects to SI units (lumens)?
I found this from Wikipedia:

$$\mathrm{illuminance} = 10^{(-14.18 - M_\mathrm{V})/2.5}~\mathrm{lx}$$

https://en.wikipedia.org/wiki/Illuminance#Astronomy

Looks to be right.  I checked the formula with the luminous flux of Sol given by Wikipedia as 3.75&times;1028 lumens, with an (extraterrestrial) luminance at 1 AU of
$$\frac{3.75 \times 10^{28}~\mathrm{lm}}{4\pi~\mathrm{au}^2} = 133000~\mathrm{lm/m^2}$$
The formula above gives instead a (terrestrial) illuminance of 105700 lm/m2 for an apparent visual magnitude of -26.74 (which makes sense since there would be less illuminance on the surface beneath an atmosphere).

https://en.wikipedia.org/wiki/Sun