The clear sky UV-index is expressed as a function of two predictable quantities: the solar zenith angle and total ozone. This function is derived by fitting the measurements of total ozone and the UV-index obtained from two instruments, one in the mid-latitudes and one in the tropics. The shape of the function was chosen so that it represents the essentials of the underlying physics. This new function gives good results for all solar zenith angles between 0° and 90° and a wide range of total ozone values. Copyright © 2004 Royal Meteorological Society.