The spatial arrangement and abundance of the elements: C, H, N, O, S often correlate or directly influence a plethora of coal properties. For >90 years, attempts have utilized the ultimate (elemental) analysis of coal to predict a wide variety of properties such as: calorific value (higher heating value), volatile matter, vitrinite reflectance (mean maximum), Hardgrove grindability index, helium density, aromaticity, etc. While many relationships resulted in graphical plots that have utility even today, numerical values can also be directly calculated utilizing the correlations. These have the potential to allow rapid predictions and low-cost approaches to coal property determination. Here the many correlations addressing multiple coal properties were reviewed and where possible evaluated against a sampling of the Pennsylvania State University Coal Sample Bank and Database for vitrinite-rich (>80% by point counting) United States coals. Over 42 correlations were found in the literature. While some correlations, such as calorific value predictions are accurate over a wide range of compositions, others are restricted in applicability to a select rank range. For many correlations, there are challenges to predict the property accurately, over a wide range, but may capture the trends. (C) 2014 Elsevier B.V. All rights reserved.