Load parameters for a stationary Gaussian random load are taken as the location, scale and shape parameters of its power spectrum. The centre frequency of a power spectrum is proposed as a measure of fatigue life. A fatigue life function, formulated in terms of the load parameters, is evaluated from the test results obtained by fatigue testing a structural steel under six different power spectral shapes. The concept of a shape operator is employed to correlate fatigue lives under different power spectral shapes.