For well-known and qualified algorithms for the computation of Earth's gravitational potential and its first and second gradients are examined and compared. Their characteristics are analysed with reference to the computational requirements of the global geopotential estimation process from satellite gradiometry. Numerical tests have been performed in order to assess and compare the efficiency, accuracy and precision of the algorithms. The algorithm of Clenshaw has shown to be by far the most efficient and therefore the most suitable for implementation and use when dealing with large amounts of observations.