The discovery of naturally occurring enzymes which cleave DNA at sites specific to particular nucleotide sequences has had a great impact on molecular biology. The function of these enzymes in uivo is to protect bacterial cells from viral invasion by degradation of foreign DNA. Several hundred of these “restriction” enzymes are known and they are a very common tool both for analysis and manipulation of DNA. The overwhelming majority of restriction enzyme recognition sites are four or six nucleotides in length and have the remarkable property of internal symmetry with respect to nucleotide sequence (i.e. diad symmetry). A major practical offshoot of the characterization of restriction enzymes has been their use in DNA cloning. In addition, comparison of restriction enzyme cleavage patterns has been used analytically to assess the similarity of DNA from related organisms-particularly mitochondrial DNA. As an aid in these studies, a number of statistical methods have been devised to analyze data generated by comparison of restriction enzyme digestion patterns. The first of these studies was carried out by Upholt (1977) and Upholt & Dawid (1977). This work was revised by Nei & Li (1979) and by Gotoh et al. (1979). The intent of this note is to add practical detail to these analyses. One of the parameters addressed in the studies referenced above is an estimate of the average spacing of restriction enzyme cleavage sites in a molecule of DNA. This issue is of importance in selecting enzymes with which to analyze a particular DNA and also in assessing the randomness of site distribution within a given DNA sequence. If the distribution of sites is random, the average spacing is a function of (1) the particular nucleotide recognition sequence and (2) the G-C/A-T content of the DNA, which varies significantly in DNA from different sources. Deviation from the expected distribution of restriction sites may indicate the presence of distinctive sequence features such as those discussed below. The derivation of an equation which predicts the average spacing of cleavage sites is relatively simple if we make three assumptions of a nature common in probability problems: (1) the sites occur randomly along the DNA strand; (2) the strands are very long, comprising many nucleotides; (3) the occurrence of any given base pair on the strand may be considered