This paper proposes to compute the electrical behavior, including electromagnetic and electromechanical parameters, of a single-turn toroidal coil which is fed by a transient pseudo-harmonic current pulse at low or medium frequency. Solutions adapted to the specificity of the pulsed high magnetic fields technology are given, including original performance characteristics, independent on the current source, but still taking eddy currents and the skin effect into account. The finite element analysis is carried out progressively; first with time harmonics, then in the transient working condition, and finally by coupling the electromagnetic calculations to the equivalent electrical circuit of the coil. The aim of this study is to first evaluate the accuracy of a 2D axi-symmetrical numerical model by comparing it to 3D reference calculations. The reliability is valued according to measurements. The method then makes it possible to very quickly compute the main interesting coils characteristics, namely the equivalent resistance, inductance, maximum induction coefficient and finally the self and mutual force coefficients. These last new parameters are also defined in the present paper and provide important performance criteria. Finally, a sensitivity analysis will be performed to understand the impact of the main usual parameters (frequency, coil length, coil radius, airgap, electrical conductivity). The 2D model allows to save time and to build an approximate but reliable solution that might make either the transient calculation or the coupling with electrical, mechanical and thermal physics easier. After an introduction (part 2), part 3 gives the model geometry, physics and meshing. Magneto-harmonic calculations of fields and coils' parameters and a complete sensitivity analysis are performed in part 4. Transient computations are carried out on a single-turn coil made of steel without a field-shaper and are compared to experimental results in parts 5. Finally, an innovative single-turn coil with a field-shaper, both made of a non-standard copper alloy (siclanic (R)), has been also calculated, tested and measured in part 6. To conclude, the 2D model provides the main interesting intrinsic coil's characteristics and a fast sensitivity analysis as a function of several parameters, such as the pulse natural frequency. These parameters are needed to couple the electromagnetic process to an electrical circuit or a mechanical workpiece deformation. The present study can estimate if, in given conditions, the forming coil can ensure electromagnetic forces high enough either to initiate the process or to end it with an assembling static pressure.