The Stacks project

Remark 100.12.4. If $\mathcal{X}$ is a nonempty stack of finite type over a field, then $\dim (\mathcal{X})$ is an integer. For an arbitrary locally Noetherian algebraic stack $\mathcal{X}$, $\dim (\mathcal{X})$ is in $Z\cup \{ \pm \infty \}$, and $\dim (\mathcal{X}) = -\infty$ if and only if $\mathcal{X}$ is empty.