A comprehensive revision of the basis of the 1959 Rank(S) scale of Suggate uses the van Krevelen diagram (axes of atomic O/C and H/C), and a complementary diagram with axes of calorific value and volatile matter, to demonstrate the progress of rank increase in coals of differing coal types. Both type and rank (maturity) are significant in hydrocarbon generation. The Late Cretaceous and Cenozoic New Zealand coals, which have an almost complete rank range from peat to semi-anthracite, are used to exemplify medium to high hydrogen coals, and Paleozoic coals from the Northern Hemisphere and Australia provide data for lower hydrogen coals. A line of progressive coalification of "average-type" coal, which typifies that of Type III kerogen, is identified. Systematic analytical variation in isorank coals allows the determination of the pattern of isorank lines on the diagrams. These lines are then spaced to provide a scale of equal increments of rank increase, which is accepted as being dependent on temperature at the time of maximum burial. The 1959 supposition that geothermal gradients did not vary widely between subsiding basins is abandoned, and in its place it is now assumed that the geothermal gradient in each basin was uniform with depth. The spacing of isorank lines to provide the Rank(S r ) scale, which ranges from 0 in peat to >20 in anthracite, follows study of individual sequences in deep coalfield boreholes and in oil exploration wells.