T. Fukui introduced an invariant for the blow-analytic equivalence of real singularities. For a nondegenerate analytic function (germ) f, he discovered a formula for computing the one-dimensional invariant, denoted by A(f) := A1(f). We find a formula for A(f) for any f (real or complex, degenerate or not). We then define, and characterise, various notions of stability of A(f), using the formula. For real analytic f, the Fukui invariant with sign is defined, and computed by a similar formula. In the case where f is an analytic function of two complex variables, A(f) can also be computed using the tree-model of f.
