An algorithm for analyzing difference scaling results is described. Frequency data on ordered categories that represent perceived differences for a unidimensional psychological attribute are modeled according to Thurstone’s judgment scaling model. The algorithm applies the gradient method for the maximum likelihood estimation of the model parameters. Two ways to calculate the start configuration for the model parameters are elaborated. The algorithm also provides asymptotic values for the standard errors of the estimates and three measures for the goodness of the model fit. An additional feature of DifScal is that it is suited to analyze incomplete data.