The assessment of multi-junction solar cells often relies on numerically intensive computations. Specifically, the power conversion efficiency strongly depends on the interplay between optical and electrical properties of different materials. Here, a compact and highly accurate analytical framework is proposed, facilitating the analysis of multi-junction solar cells; explicit yet simple analytical equations allow to assess the power conversion efficiency as a direct function of the cell's parameters, without restrictive assumptions. They are first used to compare the performance of the industrial state-of-the-art to multi-junction approaches. Therefore, minute data products are obtained from free satellite-services for different climatic zones over 14 years. Any variations in the operating temperature, sunshine duration, Sun's position, meteorological condition or atmospheric chemistry are thereby accounted for. Similarly, a strong site dependency is found for perovskite-on-silicon tandem cells under real-world conditions. For this, a scattering-matrix treatment is formulated based on incoherent sunlight as the relevant case. While this study gives new theoretical insights about the impact of the cell's parameters on the conversion efficiency, it also presents a powerful analytical tool for the design and assessment of more efficient solar cells in the outdoors. Crown Copyright (c) 2020 Published by Elsevier Ltd. All rights reserved.