An extrafocal source model has been developed to explain the dependence of head scatter and beam penumbra on field size. In this model, the x-ray source of a medical linear accelerator is described by two components: a small but intense focal component; and a broadly distributed extrafocal component of low intensity. The extrafocal component is so large that it can be "eclipsed" by the field-defining collimators. Extrafocal radiation was found to account for 12% of the energy fluence on the central axis of the 6 MV x-ray beam from a Varian Clinac 2100 c accelerator. Head scatter factors were calculated "in-air" for symmetric, asymmetric, and half-blocked fields. Calculations agreed with measured values to better than 0.5%, on average. However, head scatter factors for asymmetric fields were underestimated by 1.2% when one of the field dimensions was reduced to 4 cm (the minimum jaw setting that was tested). The extrafocal source model was combined with a convolution/superposition dose calculation algorithm to calculate dose-per-monitor-unit calibration (output) factors and beam dose profiles in water. These dose calculations predict the degradation of the field edge as a function of field size, and calculate output factors to within 0.5%, on average. In the most extreme case of a 4 cm field width, output factors were underestimated by 2%. Dose profiles are predicted without the aid of an empirical fit to measured beam penumbra data. The extrafocal source model will be particularly useful for fields defined by independent jaw and multileaf collimation systems.