Basis of weight lattice in terms of root lattice

Question

Let $\Lambda_R = \bigoplus_{i \in I} \mathbb{Z} \cdot \alpha_i$ be the root lattice of a root system $\Phi$ with simple roots $\alpha_i$ and let $\Lambda_W$ denote the corresponding weight lattice. Is there a way to compute the reals $q_i \leq 1$, s.t. $\Lambda_W = \bigoplus_{i \in I} \mathbb{Z} \cdot (q_i\alpha_i)$? They should exist, right? At least in the $B_n$-case, they should be $\frac{1}{2}, \dots, \frac{1}{2},1$.