Imperfect sensitivity, or imperfect detection, is a feature of all survey methods that needs to be accounted for when interpreting survey results. Detection of environmental DNA (eDNA) is increasingly being used to infer species distributions, yet the sensitivity of the technique has not been fully evaluated. Sensitivity, or the probability of detecting target DNA given it is present at a site, will depend on both the survey method and the concentration and dispersion of target DNA molecules at a site. We present a model to estimate target DNA concentration and dispersion at survey sites and to estimate the sensitivity of an eDNA survey method. We fitted this model to data from a species-specific eDNA survey for Oriental weatherloach, Misgurnus anguillicaudatus, at three sites sampled in both autumn and spring. The concentration of target DNA molecules was similar at all three sites in autumn but much higher at two sites in spring. Our analysis showed the survey method had =95% sensitivity at sites where target DNA concentrations were =11 molecules per litre. We show how these data can be used to compare sampling schemes that differ in the number of field samples collected per site and number of PCR replicates per sample to achieve =95% sensitivity at a given target DNA concentration. These models allow researchers to quantify the sensitivity of eDNA survey methods to optimize the probability of detecting target species, and to compare DNA concentrations spatially and temporarily.