A simple expression is derived for the linear growth rate of R-X mode, auroral kilometric radiation under the assumptions of cold plasma wave dispersion and &ohgr;pe2<<&OHgr;e2, where &ohgr;pe and &OHgr;e are the electrons plasma frequency and gyrofrequency, respectively. The result is valid for all wave normal angles and all frequencies above the right-hand cutoff frequency. With this expression, it is not necessary to evaluate the full dispersion tensor, and variations of the growth rate with plasma parameters are easily obtained. Corrections to a previously employed, equivalently simple, expression for the growth are also easily obtained, the previous expression being valid only for nearly perpendicular wave propagation and frequencies well above the cutoff. Applying to new expression, we find that kilometric radiation growth rates &ggr; are strongly dependent upon the magnitude of the magnetic field-aligned potential difference V∥, with &ggr;∝V∥2, and that significant growth of radiation at harmonics of the fundamental is unlikely in regions where &ohgr;pe2<<&OHgr;e2.