The freely available Multiwfn program (http://sobereva.com/multiwfn) fully supports the fchk file generated by PSI4, using Multiwfn to calculate molecular volume is fairly easy and quick. Boot up Multiwfn, then input commands like below
h2o.fchk // Example file
12 // Main function 12: Quantitative analysis of molecular surface
6 // Start analysis without considering mapped function
Then you will see below output:
Volume: 177.09406 Bohr^3 ( 26.24264 Angstrom^3)
Estimated density according to mass and volume (M/V): 1.1399 g/cm^3
Overall surface area: 154.10915 Bohr^2 ( 43.15496 Angstrom^2)
Note that the volume estimated in this way (see J. Mol. Graph. Model., 38, 314 (2012) for detail) has evidently higher numerical accuracy than the “volume” keyword in Gaussian, which employs Monte Carlo method.
By default, isosurface of electron density of 0.001 a.u. is used for defining molecular surface, you can alter this setting by using option “1 Select the way to define surface” in main function 12 of Multiwfn.
Multiwfn also supports calculating volume via Monte Carlo method based on molecular structure and atomic van der Waals radii (via subfunction 3 of main function 100).
If you simply need to calculate grid data, you can use main function 5 of Multiwfn. Multiwfn supports more than 100 real space functions, including electron density. After calculation, the grid data can be exported to cube file via corresponding option in the menu.