Formal Statement

The flux density is simply defined as the amount of flux passing through a unit-area.

Mathematical Statement

The flux density would essentially be the number of field lines passing through a defined unit-area. These field lines can be produced by anything one cares to imagine but in practical physics they are generally electric field lines, magnetic field lines, or gravitational field lines in some cases. If those field lines pass through a unit area and are 'counted' then they will produce a flux usually denoted and a subscript is generally added for convenience. For example, one generally denotes the magnetic flux (flux attributed to the field) as:

The Flux density is precisely equal to the flux through an area. If we take a and count the amount of flux in that area, we get a new flux which is only technically speaking the 'flux density.' However, depending on your unit-area, flux-density and total flux will always be equivocal. Therefore, flux-density can be stated as either its own unit:



or in the general terms for flux:


where:

• is a vector field
  Vector field
  In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...
  
  
• is the vector area of the surface S, directed as the surface normal
  Surface normal
  A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
  
  ,
•   is the resulting flux.

Bearing in mind that:

• 
• If and only if is the same for both quantities.