As with curves, to say that two surfaces have the same shape means simply that they are congruent. And just as with curves , we will justify our infinitesimal measurements by proving that two surfaces with "the same" shape operators are, in fact, congruent. The algebraic invariants (determinant, trace,...) of its shape operators thus have geometric meaning for the surface M. We investigate this matter in detail and find efficient ways to compute these invariants, which we test on a number of geometrically interesting surfaces.