[Proposition 1.2.10](https://books.google.com/books?id=LF6CbQk9uScC&pg=PA11) in "Cohen-Macaulay Rings" by W. Bruns, H.J. Herzog: if $R$ is a Noetherian ring, $I$ an ideal of $R$, and $M$ a finite $R$-module, then
$$\operatorname{grade} (I,M)= \inf \{\operatorname{depth} M_p | p \in V(I)\}.$$