The IBA-Scanditronix NACP-02, IBA-Wellhöfer PPC-40 and PPC-05 plane-parallel ionization chambers have been simulated with the Monte Carlo code PENELOPE to obtain their chamber- and quality-dependent factors f(c,Qo) for a (60)Co gamma beam. These are applicable to the determination of k(Q) beam-quality factors for the dosimetry of electron, protons and heavier charged particles beams based on standards of absorbed dose to water. The factor f(c,Q) is equivalent to the product s(w,air)p, but it is not subject to the assumed independence of perturbation factors and stopping power (Sempau et al 2004 Phys. Med. Biol. 49 4427-44). The calculations have been carried out using three different (60)Co source models: a monoenergetic point source, a point source with a realistic (60)Co spectrum and the simulated phase space from a radiotherapy (60)Co unit. Both the detailed geometries of the ionization chambers and of the (60)Co unit have been obtained from the manufacturers. In the case of the NACP-02 chamber, values of f(c,Qo) have been compared with those in the IAEA TRS-398 Code of Practice and from other authors, results being in excellent agreement. The PPC-05 and PPC-40 chambers are of relatively new design, and their values have not been calculated before. Within the estimated uncertainty, computed at the 2sigma level (95% confidence limit), the results for each of the three chambers appear to be independent of the degree of sophistication of the (60)Co source model used. For the NACP-02 chamber this assumption is justified by the excellent agreement between the various models, which occurs at the level of one standard uncertainty. This suggests the possibility of adopting the mean value of the three source models, weighted with the inverse of their corresponding uncertainties, as a better estimate of f(c,Qo). A consequence of the above conclusions is that the estimated uncertainty of k(Q) beam-quality factors of all charged particles referred to (60)Co can potentially be decreased considerably using our approach. For example, the estimated relative standard uncertainty of the denominator of k(Q), given in TRS-398 as 1.6% for plane-parallel ionization chambers, can be reduced to 0.06% for a NACP chamber using the mean value of f(c,Qo) given in this work. Similar reductions could be obtained for the combined standard uncertainty of the k(Q) beam-quality factors of all charged particles, notably electrons.