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In this paper, formulas are proposed for the self- and mutual-inductance calculations of a helical toroidal coil by direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann's equation, and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental, empirical, and numerical results for inductance, using the direct and the indirect methods, indicates that the proposed formulas have high reliability. It is also shown that the self-inductance and mutual inductance could be calculated in the same way, provided that the radius of curvature is greater than 0.4 of the minor radius and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of the helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor's mass, the elimination or the balance of stress in certain coordinate directions, and the attenuation of leakage flux could be considered.