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This paper generalizes a result of Lynn on the "degree" of an equivariantcohomology ring $H^*_G(X)$. The degree of a graded module is a certaincoefficient of its Poincar\'{e} series, and is closely related to multiplicity.In the present paper, we study these commutative algebraic invariants forequivariant cohomology rings. The main theorem is an additivity formula fordegree: $$deg(H^*_G(X)) = \sum_{[A,c] \in\mathcal{Q'}_{max}(G,X)}\frac{1}{|W_G(A,c)|} \deg(H^*_{C_G(A,c)}(c)).$$ We alsoshow how this formula relates to the additivity formula from commutativealgebra, demonstrating both the algebraic and geometric character of the degreeinvariant.

A Degree Formula for Equivariant Cohomology Rings