What is magnetic force measured in?

Hint: The term magnetic force was first coined after observing magnets. These are some magnificent objects that create around themselves an invisible area of magnetic force. This invisible area is also termed a magnetic field. When a magnetic object is brought near the magnet, it is either attracted or repelled depending on the poles of the two objects.

Complete answer:
The magnetic force is observed by a moving charge in a magnetic field and not by a stationary charge. This could be understood by the equation of magnetic force which is given by:
$\Rightarrow \overrightarrow{{{F}_{M}}}=q\left( \overrightarrow{v}\times \overrightarrow{B} \right)$
Where,
$\overrightarrow{{{F}_{M}}}$ is the magnetic force.
‘q’ is the charge which is experiencing the magnetic force.
‘$\overrightarrow{v}$’ is the velocity vector of the charge. And,
‘$\overrightarrow{B}$’ is the magnetic field vector.
Thus, we can see that the magnetic force is a product of charge, velocity and magnetic field.
In SI base units, the unit of magnetic force will be equal to $N{{A}^{-1}}{{m}^{-1}}$. This term is known as “Tesla” and it is the measuring unit of magnetic force. Also, we can write the dimensional formula of magnetic force using this SI base unit as $\left[ M{{T}^{-2}}{{I}^{-1}} \right]$.
Hence, the standard unit in which magnetic force is measured is Tesla.

Note:
The unit of any quantity be it force, momentum, acceleration, torque, mass, etc. is not a specific quantity. People around the globe use different unit systems. For example, the Europeans generally use the metric system while calculating mass of an object whereas the Americans use the CGS system. This is why a standard system was developed known as the SI system of units which is accepted all over the globe.