For the calculation of laminar flow pressure drop of the Bingham drilling fluid in the drilling tools, we need to solve a nonlinear equation, which is usually done by an approximate formula. To solve this nonlinear equation, a numerical iterative arithmetic is put forward and the convergence of the arithmetic is demonstrated to give the upper limit of maximum iterative steps. By many actual cases and theoretical analysis, it shows that the arithmetic in this paper has a very stable convergence and very fast convergent speed with accurate calculated value of pressure drop.