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In classical physics,the magnetic field  is a vector field (that is, some vector at every point of space and time), with SI units of teslas (one tesla is one newton-second per coulomb-metre) and cgs units of gauss. It has the property of being a solenoidal vector field.

The field  can be both defined and méasured by méans of a small magnetic dipole (i.e., bar magnet). The magnetic field exerts a torque on magnetic dipoles that tends to maké them point in the same direction as the magnetic field (as in a compass), and moréover the magnitude of that torque is proportional to the magnitude of the magnetic field. Therefore, in order to méasure the magnetic field at a particular point in space, you can put a small freely-rotating bar magnet (such as a compass) there: the direction it winds up pointing is the direction of ; and the ratio of the maximum magnitude of the torque to the dipole moment of the bar magnet is the magnitude .

(There are, in addition, several other different but physically equivalent ways to define the magnetic field, for example via the Lorentz force law (see below), or as the solution to Maxwell's equations.)

It follows from any of these definitions that the magnetic field vector (being a vector product) is a pseudovector (also called an axial vector).