Context. The Kuiper belt is formed of planetesimals which failed to grow to planets and its dynamical structure has been affected by Neptune. The classical Kuiper belt contains objects both from a low-inclination, presumably primordial, distribution and from a high-inclination dynamically excited population. Aims. Based on a sample of classical trans-Neptunian objects (TNOs) with observations at thermal wavelengths we determine radiometric sizes, geometric albedos and thermal beaming factors for each object as well as study sample properties of dynamically hot and cold classicals. Methods. Observations near the thermal peak of TNOs using infrared space telescopes are combined with optical magnitudes using the radiometric technique with near-Earth asteroid thermal model (NEATM). We have determined three-band flux densities from Herschel/PACS observations at 70.0, 100.0 and 160.0 mu m and Spitzer/MIPS at 23.68 and 71.42 mu m when available. We use reexamined absolute visual magnitudes from the literature and ground based programs in support of Herschel observations. Results. We have analysed 18 classical TNOs with previously unpublished data and re-analysed previously published targets with updated data reduction to determine their sizes and geometric albedos as well as beaming factors when data quality allows. We have combined these samples with classical TNOs with radiometric results in the literature for the analysis of sample properties of a total of 44 objects. We find a median geometric albedo for cold classical TNOs of 0.14(-0.07)(+0.09) and for dynamically hot classical TNOs, excluding the Haumea family and dwarf planets, 0.085(-0.045)(+0.084). We have determined the bulk densities of Borasisi-Pabu (2.1(-1.2)(+2.6) g cm(-3)), Varda-Ilmare (1.25(-0.43)(+0.40), g cm(-3)) and 2001 QC(298) (1.14(-0.30)(+0.34) g cm(-3)) as well as updated previous density estimates of four targets. We have determined the slope parameter of the debiased cumulative size distribution of dynamically hot classical TNOs as q = 2.3 +/- 0.1 in the diameter range 100 \textless D \textless 500 km. For dynamically cold classical TNOs we determine q = 5.1 +/- 1.1 in the diameter range 160 \textless D \textless 280 km as the cold classical TNOs have a smaller maximum size.