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Convenient and inclusive tables for the demagnetization factors of general ellipsoids are calculated by an APL program using the mathematical framework of Osborn [Phys. Rev. 67, 351 (1945)] along with elliptical integral function tables of Spenceley and Spenceley [Smithsonian Elliptic Function Tables, 109, 3863 (1947)]. The new demagnetization tables have immediate application to magnetic and superconductor studies of present day prominence. For an ellipsoid of major axes a≥ (R18)b≥ (R18)c the range of variables is from 1≥ (R18)(c/a)≥ (R18)0.0001, and 1≥ (R18)(b/a)≥ (R18)0.01; appropriate approximations are indicated for smaller values of these ratios. In addition details of the mathematical calculation are included so that those interested may duplicate the procedure. Methods of applying this ‘‘ellipsoidal’’ approximation to other shapes such as parallelopipeds are also indicated.