Recent R-matrix calculations of electron impact excitation rates in K v are used to derive the nebular emission line ratio R = I(4122.6 A)/I(4163.3 A) as a function of electron density (N(e)). This ratio is found to be very sensitive to changes in N(e) over the density range 10(3) to 10(6) cm(-3), but does not vary significantly with electron temperature, and hence in principle should provide an excellent optical N(e) diagnostic for the high-excitation zones of nebulae. The observed value of R for the planetary nebula NGC 7027, measured from a spectrum obtained with the Hamilton Echelle spectrograph on the 3-m Shane Telescope, implies a density in excellent agreement with that derived from [Ne iv], formed in the same region of the nebula as [K v]. This observation provides observational support for the accuracy of the theoretical [K v] line ratios, and hence the atomic data on which they are based. However, the analysis of a high-resolution spectrum of the symbiotic star RR Telescopii, obtained with the University College London Echelle Spectrograph on the 3.9-m Anglo-Australian Telescope, reveals that the [K v] 4122.6 A line in this object is badly blended with Fe ii 4122.6 A. Hence, the [K v] diagnostic may not be used for astrophysical sources that show a strong Fe ii emission line spectrum.