The calculation of diffuse horizonthal illuminance D(V) outdoors is generalized and interrelated to parameters that characterize the sky luminance distribution function. The derived analytical formula for D(V,rel) which is D(V) normalized using luminance in the zenith can be commonly applicable to all IS ISO-standardized sky types. This makes the modelling of all 15 skies more uniform than ever before. The presented analytical solution is simplified enough because the set of 60 parameters B(1), C(1), D(1), E(1) - B(15), C(15), D(15), E(15) scaling the diffuse illuminance is no more necessary in the new solution. In addition, the analytical formulae substituting the empirical ones are valid for all solar altitudes gamma(S) (including the situations with sun in zenith). On the contrary, the empirical formulae may become inapplicable for gamma(S) > 75 degrees and fail when gamma(S) approaches 90 degrees. Compared with detail numerical integration the analytical formula guarantees more rapid calculation of D(V,rel). (C) 2010 Elsevier Ltd. All rights reserved.