Some management science models require estimates of distances between points in a road network based on the point coordinates. This paper evaluates the accuracy of a range of reasonable forms for distance estimating functions using samples of urban and rural road distances. The intent is to derive better distance estimating functions for analyzing systems with distance related performance measures. Contrary to a standard assumption, the rectangular distance function is inferior to the simple Euclidean metric in the urban samples. More general functions provide still greater improvement over the rectangular metric. Statistical significance accompanies these conclusions. One of the more general functions appears particularly suited to rural distances.