  We measure the energy emitted by extensive air showers in the form of radio
emission in the frequency range from 30 to 80 MHz. Exploiting the accurate
energy scale of the Pierre Auger Observatory, we obtain a radiation energy of
15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV
arriving perpendicularly to a geomagnetic field of 0.24 G, scaling
quadratically with the cosmic-ray energy. A comparison with predictions from
state-of-the-art first-principle calculations shows agreement with our
measurement. The radiation energy provides direct access to the calorimetric
energy in the electromagnetic cascade of extensive air showers. Comparison with
our result thus allows the direct calibration of any cosmic-ray radio detector
against the well-established energy scale of the Pierre Auger Observatory.
