  The aim of this paper is to characterize the radial structure of the star
formation rate (SFR) in galaxies in the nearby Universe as represented by the
CALIFA survey. The sample under study contains 416 galaxies observed with IFS,
covering a wide range of Hubble types and stellar masses. Spectral synthesis
techniques are applied to obtain radial profiles of the intensity of the star
formation rate in the recent past, and the local sSFR. To emphasize the
behavior of these properties for galaxies that are on and off the main sequence
of star formation (MSSF) we stack the individual radial profiles in bins of
galaxy morphology and stellar masses. Our main results are: a) The intensity of
SFR shows declining profiles that exhibit very little differences between
spirals. The dispersion between the profiles is significantly smaller in late
type spirals. This confirms that the MSSF is a sequence of galaxies with nearly
constant intensity of SFR b) sSFR values scale with Hubble type and increase
radially outwards, with a steeper slope in the inner 1 HLR. This behavior
suggests that galaxies are quenched inside-out, and that this process is faster
in the central, bulge-dominated part than in the disks. c) As a whole, and at
all radii, E and S0 are off the MSSF. d) Applying the volume-corrections for
the CALIFA sample, we obtain a density of star formation in the local Universe
of 0.0105 Msun/yr/Mpc^{-3}. Most of the star formation is occurring in the
disks of spirals. e) The volume averaged birthrate parameter, b'=0.39, suggests
that the present day Universe is forming stars at 1/3 of its past average rate.
E, S0, and the bulge of early type spirals contribute little to the recent SFR
of the Universe, which is dominated by the disks of later spirals. f) There is
a tight relation between the intensity of the SFR and stellar mass, defining a
local MSSF relation with a logarithmic slope of 0.8.
