A mathematical formalism for the quantitative analysis of X-ray photoelectron spectroscopy (XPS) intensities for supported, multiphase catalysts is presented. Such powdered catalysts are modeled as spherical support particles, covered in regions (islands) by different stratified layers of phases. It specifically considers the variation in photoelectron take-off angle over the surface of the particles, by integrating the signal over the particle’s volume. The evaluation of this integral can be done numerically, but for certain particle sizes it is simplified by a new approximation to the exponential integral function presented here, which introduces an error of <4%. The results show that the common assumption of normal emission usually leads to large errors (factors of 2-5). A simpler approximation to this new formalism, using the unweighted average take-off angle of photoelectrons from the local surface normal of 57.3 degrees, introduces an error of <23% except for species whose main intensity arises from an underlayer that is buried by another phase of average depth greater than 1.3 lambda (lambda is a photoelectron’s inelastic mean free path). It is useful for the initial optimization of parameters when searching for structural models of catalysts that are consistent with their XPS spectra. These formalisms are also applicable in treating other shapes of catalysts than those treated explicitly here, provided the phase’s surface-to-volume ratio is the same as chosen in this model and that the BET surface area is less than about 35 m(2)/g. More complex expressions which treat higher surface area samples are also presented. The formalisms can also be used in quantitative Auger electron spectroscopy (AES), if the XPS sensitivity factors are replaced by AES sensitivity factors.