  Let $B/F$ be a quaternion algebra over a totally real number field. We give
an explicit formula for heights of special points on the quaternionic Shimura
variety associated with $B$ in terms of Faltings heights of CM abelian
varieties. Special points correspond to CM fields $E$ and partial CM-types
$\phi \subset \mathrm{Hom}(E, \mathbb{C})$. We then show that our height is
compatible with the canonical height of a partial CM-type defined by Pila,
Shankar, and Tsimerman. This gives another proof that the height of a partial
CM-type is bounded subpolynomially in terms of the discriminant of $E$.
