It is found that the energy density of electromagnetic fields at the surface of the Earth follow a scaling law that extends over 16 orders of magnitude from 10-9 Hz to 107 Hz. The temporal variability of the field can be described with an 1/f2, or Brownian, noise power spectrum which reflects the superposition of numerous transient source processes. To the best of our knowledge, the spectral extent of this straightforward scaling law is unparalleled and outperforms any other scaling law in physics which describes a time dependent observable. The frequency dependence of the energy density can be approximated with the analytic description u(f) = u0(f0/f)2 where u 0 = 10-16 Jm-3Hz-1, f0 = 1 Hz is a scaling constant, and f is the frequency of the electromagnetic field. The corresponding frequency dependence of the magnetic field is B(f) = B 0(f0/f) where B0 = 10-11 T/Hz 1/2.