The main theorem of this paper is a combinatorial formula for the spin character (or projective character) for the symmetric group ζ π λ . A simpler formula for the case when λ has two parts is also given. These formulae are stated in terms of objects called “complete separations of the partition π” corresponding with a composition. A complete separation of π is an ordered set-partition of the numbers in π such that the block sums are determined by the composition. The character formulas are proved using several identities for Schur Q-functions. In addition to the authors’ proofs, Theorems 3.5 and 2.2 have appeared in Section 1 of an article by P. Pragacz [Algebro-geometric applications of Schur S- and Q-polynomials, Topics in invariant theory (Paris 1989/1990), Lect. Notes Math. 1478, 130-191 (1991; Zbl 0783.14031)].