The problem of inferring the internal inductance from external magnetic measurements in tokamaks is considered. It was practically resolved in JET (Barana O et al 2002 Plasma Phys. Control. Fusion44 2271), but several questions remain to be addressed before extrapolation of that method on other tokamaks. These naturally arise because of the integral nature of determined by unknown distribution of the magnetic field inside the plasma. Without universal solutions, the quality of approximations should be examined along with potential experimental enforcements of the existing procedures. This is the main goal of the study that is fully analytical. Several relevant quantities are calculated for the large-aspect-ratio plasma with elliptical shifted magnetic surfaces. Usually the plasma elongation is mentioned as a key factor in the task. Here it is explicitly shown that not only , but its radial derivative too plays a role. The latter parameter did not appear in the JET scaling and in the accompanying discussions. It is also shown that the -dependent term representing there the first iteration actually brings a systematic error. Therefore, several improvements to that scaling can be proposed. The study is based on the use of virial relations for the toroidal axisymmetric configurations.