Quantum mechanics ascribes to the ground state of the electromagnetic radiation(1) zero-point electric field fluctuations that permeate empty space at all frequencies. No energy can be extracted from the ground state of a system, and therefore these fluctuations cannot be measured directly with an intensity detector. The experimental proof of their existence therefore came from more indirect evidence, such as the Lamb shift(2,3,4), the Casimir force between close conductors(5,6,7) or spontaneous emission(1,8). A direct method of determining the spectral characteristics of vacuum field fluctuations has so far been missing. Here we perform a direct measurement of the field correlation on these fluctuations in the terahertz frequency range by using electro-optic detection(9) in a nonlinear crystal placed in a cryogenic environment. We investigate their temporal and spatial coherence, which, at zero time delay and spatial distance, has a peak value of 6.2 x 10(-2) volts squared per square metre, corresponding to a fluctuating vacuum field(10,11) of 0.25 volts per metre. With this measurement, we determine the spectral components of the ground state of electromagnetic radiation within the bandwidth of our electro-optic detection.