The UKIRT Infrared Deep Sky Survey is a set of five surveys of complementary combinations of area , depth , and Galactic latitude , which began in 2005 May . The surveys use the UKIRT Wide Field Camera ( WFCAM ) , which has a solid angle of 0.21deg ^ { 2 } . Here we introduce and characterise the Z Y J H K photometric system of the camera , which covers the wavelength range 0.83 - 2.37 \mu m. We synthesise response functions for the five passbands , and compute colours in the WFCAM , SDSS and 2MASS bands , for brown dwarfs , stars , galaxies and quasars of different types . We provide a recipe for others to compute colours from their own spectra . Calculations are presented in the Vega system , and the computed offsets to the AB system are provided , as well as colour equations between WFCAM filters and the SDSS and 2MASS passbands . We highlight the opportunities presented by the new Y filter at 0.97 - 1.07 \mu m for surveys for hypothetical Y dwarfs ( brown dwarfs cooler than T ) , and for quasars of very–high redshift , z > 6.4 .