We use deep 70, 100 and 160 μm observations taken with PACS, the Photodetector Array Camera and Spectrometer on board of Herschel, as part of the PACS Evolutionary Probe (PEP) guaranteed time, to study the relation between star formation rate and environment at redshift ~ 1 in the GOODS-S and GOODS-N fields. We use the SDSS spectroscopic catalog to build the local analog and study the evolution of the star formation activity dependence on the environment. At z ~ 1 we observe a reversal of the relation between star formation rate and local density, confirming the results based on Spitzer 24 μm data. However, due to the high accuracy provided by PACS in measuring the star formation rate also for AGN hosts, we identify in this class of objects the cause for the reversal of the density-SFR relation. Indeed, AGN hosts favor high stellar masses, dense regions and high star formation rates. Without the AGN contribution the relation flattens consistently with respect to the local analog in the same range of star formation rates. As in the local universe, the specific star formation rate anti-correlates with the density. This is due to mass segregation both at high and low redshift. The contribution of AGN hosts does not affect this anti-correlation, since AGN hosts exhibit the same specific star formation rate as star forming galaxies at the same mass. The same global trends and AGN contribution is observed once the relations are studied per morphological type. We study the specific star formation rate vs. stellar mass relation in three density regimes. Our data provides an indication that at M/M&sun; > 1011 the mean specific star formation rate tends to be higher at higher density, while the opposite trend is observed in the local SDSS star forming sample.