In this article we present tables of values of the climbing constantβ̂=3α1+2α2,whereα1andα2are the parameters of the second‐order approximation to the stress in a slow, slowly varying flow of any simple non‐Newtonian fluid. The parameterβ̂arises in the analysis of rod climbing, and it is proportional to the height of climb in slow steady flow. A method is presented for computing the first normal stress difference and the extensional viscosity at low rates of deformation, usingβ̂alone. This method is useful for all fluids whose unknown second normal stress is nonpositive at low rates of shearing.