The energy scale of cosmic rays detected with LOFAR

The LOw-Frequency ARray (LOFAR) measures radio emission from extensive air showers. Precise knowledge of the electric field at each antenna in the $30-80$ MHz range is obtained using a newly developed, frequency-dependent calibration built on knowledge of the Galactic emission and a detailed model of the signal chain. The energy fluence for each event is then determined, allowing for the calculation of the radiation energy of the air shower. The radiation energy, corrected for geometrical effects, scales quadratically with the energy contained in the electromagnetic component of the air shower. These measurements, combined with predictions that rely only on first-principle electrodynamics, provide an energy estimate for the primary particle. In this contribution we present the radio-based energy scale of cosmic rays detected with LOFAR, and compare it to particle-based energy measurements made using the scintillator array located at the LOFAR core.