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A simple estimate of the photometric redshift would prove invaluable toforthcoming continuum surveys on the next generation of large radio telescopes,as well as mitigating the existing bias towards the most optically brightsources. While there is a well known correlation between the near-infraredK-band magnitude and redshift for galaxies, we find the K-z relation to breakdown for samples dominated by quasi-stellar objects (QSOs). We hypothesise thatthis is due to the additional contribution to the near-infrared flux by theactive galactic nucleus (AGN), and, as such, the K-band magnitude can onlyprovide a lower limit to the redshift in the case of active galactic nuclei,which will dominate the radio surveys. From a large optical dataset, we find atight relationship between the rest-frame (U-K)/(W2-FUV) colour ratio andspectroscopic redshift over a sample of 17,000 sources, spanning z ~ 0.1 - 5.Using the observed-frame ratios of (U K)/(W2-FUV) for redshifts of z > 1,(I-W2)/(W3-U) for 1 < z < 3 and (I-W2.5)/(W4-R) for z > 3, where W2.5 is the8.0 micron magnitude and the appropriate redshift ranges are estimated from theW2 (4.5 micron) magnitude, we find this to be a robust photometric redshiftestimator for quasars. We suggest that the rest-frame U-K colour traces theexcess flux from the AGN over this wide range of redshifts, although the W2-FUVcolour is required to break the degeneracy.

QSO redshift estimates from optical, near-infrared and ultraviolet colours