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The first flight of the Antarctic Impulsive Transient Antenna (ANITA)experiment recorded 16 radio signals that were emitted by cosmic-ray inducedair showers. For 14 of these events, this radiation was reflected from the ice.The dominant contribution to the radiation from the deflection of positrons andelectrons in the geomagnetic field, which is beamed in the direction of motionof the air shower. This radiation is reflected from the ice and subsequentlydetected by the ANITA experiment at a flight altitude of 36km. In this paper,we estimate the energy of the 14 individual events and find that the meanenergy of the cosmic-ray sample is 2.9 EeV. By simulating the ANITA flight, wecalculate its exposure for ultra-high energy cosmic rays. We estimate for thefirst time the cosmic-ray flux derived only from radio observations. Inaddition, we find that the Monte Carlo simulation of the ANITA data set is inagreement with the total number of observed events and with the properties ofthose events.

Energy and Flux Measurements of Ultra-High Energy Cosmic Rays Observed During the First ANITA Flight