We present an analysis of radii of giant stars with 6200 K>= T_eff >= 3800 K based on angular diameters obtained by means of the IRFM and distances computed from Hipparcos parallaxes. In order to asses the reliability of IRFM diameters we have considered a selected sample of stars whose diameters have been directly measured by interferometric techniques with internal errors below 5%. The intercomparison shows a fairly good consistency and no systematic differences against temperature are apparent in the analysis. By averaging the individual values obtained for a sample of approximately 300 stars, we present mean values of linear radii of giants of solar metallicity; the results are tentatively extended to metal-poor giants. We have also devised a method to derive distance moduli of globular clusters complementary to the standard Main Sequence (MS) and Horizontal Branch (HB) fitting. This method is based on the fit of observed linear radii and effective temperatures of Red Giant Branch stars of a given globular cluster to the yields of theoretical isochrones. A careful assessment of the uncertainty on the derived distances is provided. As expected, the distances are critically dependent on the value of the mixing length parameter adopted in the stellar models. We have applied the method to provide a homogeneous distance scale for a representative sample of Galactic globular clusters. The comparison of these distances with the distance scale obtained by means of the MS- or HB-fitting permits a consistent calibration and/or test of the superadiabatic gradient in stellar envelopes, independent of the use of colour-T_eff transformations.