  Cosmic rays are routinely measured at LOFAR, both with a dense array of
antennas and with the LOFAR Radboud air shower Array (LORA) which is an array
of plastic scintillators. In this paper, we present two results relating to the
cosmic-ray energy scale of LOFAR. First, we present the reconstruction of
cosmic-ray energy using radio and particle techniques along with a discussion
of the event-by-event and absolute scale uncertainties. The resulting energies
reconstructed with each method are shown to be in good agreement, and because
the radio-based reconstructed energy has smaller uncertainty on an
event-to-event basis, LOFAR analyses will use that technique in the future.
Second, we present the radiation energy of air showers measured at LOFAR and
demonstrate how radiation energy can be used to compare the energy scales of
different experiments. The radiation energy scales quadratically with the
electromagnetic energy in an air shower, which can in turn be related to the
energy of the primary particle. Once the local magnetic field is accounted for,
the radiation energy allows for a direct comparison between the LORA
particle-based energy scale and that of the Pierre Auger Observatory. They are
shown to agree to within (6$\pm$20)% for a radiation energy of 1 MeV, where the
uncertainty on the comparison is dominated by the antenna calibrations of each
experiment. This study motivates the development of a portable radio array
which will be used to cross-calibrate the energy scales of different
experiments using radiation energy and the same antennas, thereby significantly
reducing the uncertainty on the comparison.
