A new method is proposed for the evaluation of the capacity of flat laminae of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Specific approximate formulae are derived for evaluating the capacity of a polygon, a triangle, a rectangle, a rhombus, a circular rector and a circular segment. All the formulae are checked against the solutions known in the literature, and a good accuracy is confirmed. No similar formulae have ever been reported.