Given a complex vector subspace V of Cⁿ, the dimension of the amoeba of V ∩(C^∗)ⁿ depends only on the matroid that V defines on the ground set {1, . . ., n}. Here we prove that this dimension is given by the minimum of a certain function over all partitions of the ground set, as previously conjectured by Rau. We also prove that this formula can be evaluated in polynomial time.