  We measure the distribution function of rotational velocities phi(V_c) of
late-type galaxies from the HIPASS galaxy catalogue. Previous measurements of
the late-type velocity function are indirect, derived by converting the galaxy
luminosity function using the relation between galaxy luminosity and rotation
velocity (the Tully-Fisher relation). The advantage of HIPASS is that space
densities and velocity widths are both derived from the same survey data. We
find good agreement with earlier inferred measurements of phi(V_c), but we are
able to define the space density of objects with V_c as low as 30 km/s. The
measured velocity function is `flat' (power-law slope alpha ~ -1.0) below V_c =
100 km/s. We compare our results with predictions based on LCDM simulations and
find good agreement for rotational velocities in excess of 100 km/s, but at
lower velocities current models over-predict the space density of objects. At
V_c=30 km/s this discrepancy is approximately a factor 20.
