# Surface integrals, positive or negative normal?

I'm unsure how to decide whether the normal should be positive or negative in $$\hat{n}dS=\pm h_2 h_3 e_1 du_2 du_3$$, where $$h_i$$ are the scale factors, $$e_i$$ are the base vectors, and $$u_i$$ are the curvilinear coordinates.

So for example, in spherical coordinate with $$r, \theta, \phi$$, and $$S: 0. Orientation is given as $$\hat{n} \cdot e_z > 0$$. Here how do I know that $$\hat{n}dS = \pm e_\theta h_r h_\phi dr d \phi = -e_\theta \sin \theta dr d\phi$$, it should be a negative?