The systematic errors inherent in the numerical evaluation of the various moments of an experimental paramagnetic resonance line are discussed as a function of the choice of the shapes and the arbitrary cutoff of wing contributions. Lorentzian and Gaussian first derivative shapes are used as models. Expressions for the zeroth, second, and fourth moments of these shapes are derived in generalized coordinates with an arbitrary cutoff. The generalized coordinates, which contain parameters related to easily measured experimental quantities, permit application of the results to any line of the Lorentzian or Gaussian shape.