When the thickness becomes so small as in the case of the trailing edge of the propeller blade or when the curvature of the surface varies rapidly as in ship stem, the existing panel method employing a flat-surface panel, obtained by collapsing the original non-planar surface into its mean location, suffers the leakage problem and also gives inaccurate induction upon the field point very close to the panel. The hyperboloidal panel deals with the induction from the dipole distributed on the non-planar surface without approximation, overcoming the defects of the flat-surface panel. This paper introduces two distinct derivations of the formulae to compute the integral for the potential induced by a dipole of uniform density distributed on a non-planar hyperboloidal surface element. One method is based on the Gauss-Bonnet theorem and the other is based on the transformation of the surface integral into a line integral.