This article presents a method for assessing the radionuclide surface contamination density (SCD) on open sites and in premises of a radiation hazardous facility based on measurements of the ambient dose equivalent rate (ADER). The method is intended for use at the initial stage of the assessment of the radiation environment at facilities. The assessed SCD at a given location on the surface can differ from the directly measured SCD at that location, since sources located on the surface and distributed by the depth contribute to the ADER value. The method makes it possible to estimate SCD with reasonable accuracy without increasing the number of measurements, and thus avoid additional occupational exposure and the use of additional resources. SCD and ADER as spatial variables have different support of measurement data. For ADER, measured at a height of 1 m, the support of measurement data can be taken to be a circle in the centre of which a gamma-ray detector is located, with a radius of several tens of meters. In contrast, SCD has the support of measurement data, close to the overall dimensions of the beta detector (100 cm2). To solve the problem of SCD calculation on the basis of ADER measurements, the method of conversion coefficients (MCC) is usually applied, based on the use of conversion factors; however, this method provides an adequate estimate only under conditions of an SCD with low gradient over the surface. The method proposed in this article is applicable for an arbitrary distribution of SCD, and designed to deal with heterogeneous contamination patterns. The developed method is based on the numerical solution of the Fredholm equation of the first kind. The measurement data always contain an error, therefore, the task of the SCD calculation is an ill-posed problem, and the Tikhonov regularisation method (ridge regression) was used to solve it. The article presents the method developed and examples of use. Validation of the method was performed using 38 measurements of the radioactive contamination from 137Cs in soil. It is shown that the method proposed in the article demonstrates a significant superiority in comparison with the MCC method, because it allows more accurate localisation of areas contaminated with radionuclides and is applicable for an arbitrary distribution of SCD.