The instrumental resolution function for the Daresbury 9.1 high-resolution powder diffractometer has been measured as a function of wavelength, slit width and specimen geometry. It has been demonstrated that the effects of size and strain from the sample of annealed barium fluoride used as a reference material were negligible, and that it is a suitable standard for studying instrumental broadening. The results of considering the angular dependence of the Lorentzian and Gaussian components of the integral breadths of instrumental line profiles are in excellent agreement with those predicted by the receiving-slit width and the known wavelength spread in the incident beam. The measured instrumental resolution function was found to be dependent on the slit dimensions at low and intermediate angles, and to be dominated by the effects of angular dispersion at higher angles. The line shapes are predominantly Gaussian at low angles and for a flat sample tend to a pure Lorentzian shape at 180°. The line profiles for a capillary sample are similar at low and intermediate angles and tend to an intermediate Gaussian/Lorentzian form at high angles.