Abstract. We explore two new modifications of the magnetotail magnetic flux (F) calculation algorithm based on the Petrinec and Russell (1996) (PR96) approach of the tail radius determination. Unlike in the PR96 model, the tail radius value is calculated at each time step based on simultaneous magnetotail and solar wind observations. Our former algorithm, described in Shukhtina et al. (2009), required that the "tail approximation" requirement were fulfilled, i.e., it could be applied only tailward x ∼ −15 R_E. The new modifications take into account the approximate uniformity of the magnetic field of external sources in the near and middle tail. Tests, based on magnetohydrodynamics (MHD) simulations, show that this approach may be applied at smaller distances, up to x ∼ −3 R_E. The tests also show that the algorithm fails during long periods of strong positive interplanetary magnetic field (IMF) B_z. A new empirical formula has also been obtained for the tail radius at the terminator (at x = 0) which improves the calculations.