Ultimate analysis is an important property for fuel utilization. The experimental determination of ultimate analysis is sophisticated, long time consumed, and expensive, on the contrary, the proximate analysis can be run rapidly and easily. A variety of correlations to predict the ultimate analysis of biomass using the proximate analysis have been appeared, while there exists a few number of correlations to estimate the elemental compositions of coal using proximate analysis in the literature but were focused on the predicted model or dependent on the heating value of coal. According to the proximate analysis of four different ranks of coal, this study proposes a series of correlations which are classified to predict carbon, hydrogen, and oxygen compositions through using 300 data points and validated further by another set of 40 data points. These correlations have the R-2 of 0.95, 0.91, and 0.65 corresponding to the measured contents of C, H, and 0 in anthracite, 0.93, 0.83, and 0.67 of C, H, and 0 in high-rank bituminous, 0.86, 0.61, and 0.71 of C, H, and 0 in subbituminous, and 0.92, 0.67, and 0.66 of C, H, and 0 in lignite, respectively. The main merit of the correlations is the ability to estimate elemental composition of different rank coals using the proximate analysis and thus offers a valuable tool to set up a coal-thermal conversion-process model. (C) 2016 Elsevier Ltd. All rights reserved.