We present a theoretical study of the absorption of light in periodic arrays of InP nanowires. The absorption in the array depends strongly on the diameter and the length of the nanowires, as well as the period of the array. Nanowires of a length of just 2 m are able, after an appropriate choice for the other parameters, to absorb more than 90% of the incident energy of TE and TM polarized light, with photon energies almost all the way down to the band gap energy and an incidence angle up to 50 degree. This high total absorption arises from a good coupling of the incident light into the nanowire array at the top interface between air and the array and absorption inside the array before the light reaches the interface between the nanowires and the substrate. We find that for a given photon energy there exists a critical nanowire diameter above which a dramatic increase in the absorption occurs. The critical diameter decreases for increasing photon energies, and is directly related to the dispersion of waveguiding modes in single isolated nanowires. A characterization showed that the absorption characteristics of the nanowire arrays are very promising for photovoltaic applications.