We measure the distribution function of rotational velocities φ(Vc) 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 H i Parkes All Sky Survey is that space densities and velocity widths are both derived from the same survey data. We find good agreement with earlier inferred measurements of φ(Vc), but we are able to define the space density of objects with Vc as low as 30 km s−1. The measured velocity function is ‘flat’ (power-law slope α≈−1.0) below Vc≈ 100 km s−1. We compare our results with predictions based on Λ cold dark matter simulations and find good agreement for rotational velocities in excess of 100 km s−1, but at lower velocities current models over-predict the space density of objects. At Vc= 30 km s−1, this discrepancy is approximately a factor of 20.