To determine the wavelength of waves within a random, isotropic wave field, we introduce the observable of wave coherency measured with plasma wave interferometers. We show generally that within a random direction wave field, wavelengths large compared to the interferometer length produce large coherency (nearly 1), but wavelengths the order of a few times the interferometer length, or smaller, produce small coherency (close to zero). We apply this principle first to examining auroral hiss and lower hybrid waves measured by the Physics of Auroral Zone Electrons (PHAZE) 2 and Topside Probe of the Auroral Zone (TOPAZ) 3 experiments and show that the implied wavelengths are consistent with the expected dispersion relations and with other, different estimates of wavelength for these modes. Next, we apply the principle to broadband extra low frequency (BB-ELF) electric fields observed in both experiments and conclude that the wavelengths are small. In one case we calculate the coherency of BB-ELF electric fields, using an ensemble average of 7889 data samples, and demonstrate that the coherency near the oxygen gyrofrequency is very small (≅0.15), corresponding to wavelengths of 10 m and the order of the ion gyroradius. We conclude that because of the short wavelengths, previous satellite measurements of BB-ELF electric fields may have underestimated the electric field amplitudes, unless ion gyroradii are substantially larger than the case for these rocket measurements. Although the wavelengths and frequencies of BB-ELF electric fields are now known, we are unable to assign the wave to a known, normal mode of homogeneous plasmas. This suggests that inhomogeneities may be essential for describing BB-ELF electric fields. ¿ 2000 American Geophysical Union