Relationships of ultimate and proximate analysis of 4540 US coal samples from 25 states with gross calorific value (GCV) have been investigated by regression and artificial neural networks (ANNs) methods. Three set of inputs: (a) volatile matter, ash and moisture (b) C, H, N, O, S and ash (c) C, H _{exclusive of moisture}, N, O _{exclusive of moisture}, S, moisture and ash were used for the prediction of GCV by regression and ANNs. The multivariable regression studies have shown that the model (c) is the most suitable estimator of GCV. Running of the best arranged ANNs structures for the models (a) to (c) and assessment of errors have shown that the ANNs are not better or much different from regression, as a common and understood technique, in the prediction of uncomplicated relationships between proximate and ultimate analysis and coal GCV.