An electric field can pass through a surface at different strengths and angles. Electric flux measures the net field passing through an oriented surface.

For a small surface element with area vector $d\mathbf A$,

$$d\Phi_E=\mathbf E\cdot d\mathbf A.$$

For a complete surface,

$$\Phi_E=\int_S\mathbf E\cdot d\mathbf A.$$

Orientation matters

The area vector is perpendicular to the surface. A field normal to the surface contributes maximally, while a field tangent to the surface contributes zero flux.

Reversing the chosen surface orientation reverses the sign of the flux.

Closed surfaces

For a closed surface, the conventional area vector points outward. Positive flux represents net field leaving the enclosed region; negative flux represents net field entering it.

Electric flux is not the amount of electric field 'stored' in a surface. It is a geometric measure combining field strength, surface area and orientation, and it is the quantity that connects enclosed charge to Gauss's law.