For a normal functor ${\cal F}$ and a point $\xi\in{\cal F}(Y)$ ($Y$ is a compact metric space) we define lower and upper metric orders $\underline{o}(\xi)$ and $\overline{o}(\xi)$ as a speed of approximation of $\xi$ by points $\xi_n\in{\cal F}_n(Y)$. If ${\cal F}$ is the exponential functor $\exp$ then $\underline{o}(\xi)$ and $\overline{o}(\xi)$ coinside, respectively, with classical lower and upper capacitarian dimensions $\underline{\dim}_B\xi$ and $\overline{\dim}_B\xi$ of a closed subset $\xi\subset Y$. We establish some properties of $\underline{o}(\xi)$ and $\overline{o}(\xi)$ and pose several questions, concerning, in particular, metric orders in superextension $\lambda(Y)$.