For the first time the high-energy gamma-ray continuum emission from the Crab Nebula has been measured in overlapping energy bands with the Fermi Large Area Telescope (LAT) and imaging air Cherenkov telescopes (IACTs). Following the phenomenological approach presented by Hillas et al. (1998) a model of the spectral energy distribution is presented which accurately describes the broadband emission from the nebula where the Fermi/LAT measurements are used to calculate the magnetic field inside the nebula. The results are compared to predictions of the magnetohydrodynamic flow model of Kennel & Coroniti (1984). Since a better description of the data is achieved by the phenomenological model it is used to derive energy-calibration factors for the IACTs. As a first application of this cross calibration an upper limit on the diuse gamma-ray emission between 250 GeV and 1 TeV is obtained.