The number of distinct functional classes of single-stranded RNAs (ssRNAs) and the number of sequences representing them are substantial and continue to increase. Organizing this data in an evolutionary context is essential, yet traditional comparative sequence analyses require that homologous sites can be identified. This prevents comparative analysis between sequences of different functional classes that share no site-to-site sequence similarity. Analysis within a single evolutionary lineage also limits evolutionary inference because shared ancestry confounds properties of molecular structure and function that are historically contingent with those that are imposed for biophysical reasons. Here, we apply a method of comparative analysis to ssRNAs that is not restricted to homologous sequences, and therefore enables comparison between distantly related or unrelated sequences, minimizing the effects of shared ancestry. This method is based on statistical similarities in nucleotide base composition among different functional classes of ssRNAs. In order to denote base composition unambiguously, we have calculated the fraction G+A and G+U content, in addition to the more commonly used fraction G+C content. These three parameters define RNA composition space, which we have visualized using interactive graphics software. We have examined the distribution of nucleotide composition from 15 distinct functional classes of ssRNAs from organisms spanning the universal phylogenetic tree and artificial ribozymes evolved in vitro. Surprisingly, these distributions are biased consistently in G+A and G+U content, both within and between functional classes, regardless of the more variable G+C content. Additionally, an analysis of the base composition of secondary structural elements indicates that paired and unpaired nucleotides, known to have different evolutionary rates, also have significantly different compositional biases. These universal compositional biases observed among ssRNAs sharing little or no sequence similarity suggest, contrary to current understanding, that base composition biases constitute a convergent adaptation among a wide variety of molecular functions.