Context : Trans-Neptunian objects ( TNO ) represent the leftovers of the formation of the Solar System .
Their physical properties provide constraints to the models of formation and evolution of the various dynamical classes of objects in the outer Solar System .

Aims : Based on a sample of 19 classical TNOs we determine radiometric sizes , geometric albedos and beaming parameters .
Our sample is composed of both dynamically hot and cold classicals .
We study the correlations of diameter and albedo of these two subsamples with each other and with orbital parameters , spectral slopes and colors .

Methods : We have done three-band photometric observations with Herschel /PACS and we use a consistent method for data reduction and aperture photometry of this sample to obtain monochromatic flux densities at 70.0 , 100.0 and 160.0 \mathrm { \mu m } .
Additionally , we use Spitzer /MIPS flux densities at 23.68 and 71.42 \mathrm { \mu m } when available , and we present new Spitzer flux densities of eight targets .
We derive diameters and albedos with the near-Earth asteroid thermal model ( NEATM ) .
As auxiliary data we use reexamined absolute visual magnitudes from the literature and data bases , part of which have been obtained by ground based programs in support of our Herschel key program .

Results : We have determined for the first time radiometric sizes and albedos of eight classical TNOs , and refined previous size and albedo estimates or limits of 11 other classicals .
The new size estimates of 2002 MS _ { 4 } and 120347 Salacia indicate that they are among the 10 largest TNOs known .
Our new results confirm the recent findings that there are very diverse albedos among the classical TNOs and that cold classicals possess a high average albedo ( 0.17 \pm 0.04 ) .
Diameters of classical TNOs strongly correlate with orbital inclination in our sample .
We also determine the bulk densities of six binary TNOs .

Conclusions :