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 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 infra-red 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 \mathrm { \mu m } and Spitzer /MIPS at 23.68 and 71.42 \mathrm { \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Results : We have analysed 18 classical TNOs with previously unpublished data and re-analysed previously published targets with updated data reduction to determine their sizes and geometric albedos as well as beaming factors when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-Ilmarë ( 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 \pm 0.1 in the diameter range 100 < D < 500 km .
For dynamically cold classical TNOs we determine q =5.1 \pm 1.1 in the diameter range 160 < D < 280 km as the cold classical TNOs have a smaller maximum size .

Conclusions :