Within the framework of the Planck satellite polarization calibration, we present a study of the Crab Nebula spectral energy distribution (SED) over more than six decades in frequency ranging from 1 to 10 6 GHz (from 299 to 2.99× 10− 4 mm). The Planck satellite mission observes the sky from 30 to 857 GHz (from 9.99 to 0.3498 mm) and therefore we focus on the millimeter region. We use radio and submillimeter data from the WMAP satellite between 23 and 94 GHz (from 13 to 3.18 mm), from the Archeops balloon experiment between 143 (2.1 mm) and 545 GHz (0.55 mm), and a compendium of other Crab Nebula observations. The Crab SED is compared to models including three main components: synchrotron that is responsible for the emission at low and high frequencies, dust that explains the excess of flux observed by the IRAS satellite, and an extra component on the millimeter regime. From this analysis, we conclude that the unpolarized emission of the Crab Nebula at microwave and millimeter wavelengths is the same synchrotron emission as the one observed in the radio domain. Therefore, we expect the millimeter emission of the Crab Nebula to be polarized with the same degree of polarization and orientation as the radio emission. We set upper limits on the possible errors induced by any millimeter extra component on the reconstruction of the degree and angle of polarization at the percent level as a maximum. This result strongly supports the choice by the Planck collaboration of the Crab Nebula emission for performing polarization cross-checks in the range 30 (299 mm) to 353 GHz (0.849 mm).