Closed-circular, superhelical DNA from simian virus 40 (SV40 DNA I) was treated with an excess of DNA-relaxing enzyme in the presence of increasing amounts of ethidium bromide (EtdBr). After removal of the ethidium, each sample consisted of a group of close-circular DNA molecules differing in their number of superhelical turns (tau) around a mean value of tau in a Gaussian-like distribution. The DNA samples were analyzed by electrophoresis in agarose gels under conditions where the electrophoretic mobility was a function of the number of superhelical turns. Since the distributions around tau of DNA molecules of different samples overlappped, the difference in the mean number of superhelical turns from sample to sample, delta tau, could be determined and used to measure the mean number (tau) for native SV40 DNA I. By this criterion, SV40 DNA I contains a Gaussian-like distribution of molecules differing by integral numbers around a mean value of tau = -24 +/- 2 at 37 degree C [in 0.2 M NaC1, 10 mM Tris-HC1 (pH 7.9), and 0.2 mM EDTA]. The heterogeneity in tau is probably a consequence of thermal fluctuations in the DNA helix at the time when the last phospholiester bond is closed in vivo. When correlated to the buoyant shift of completely relaxed SV40 DNA in a CsC1-propidium diiodide gradient, the number of delta tau = 24 +/- 2 of superhelical versus relaxed DNA implies an unwinding of the DNA helix by 26-28 degree upon intercalation of one molecule of EtdBr.