Definition of Torque:
The Torque on an object about some pivot point is due to the action of a force on the object.

Magnitude of the Torque:

t = "Force" times the "Lever Arm"

= (Component of the Force perpendicular to Lever Arm) x (Lever Arm - the distance between the pivotal axis and the point where the force is applied) = F_p l
See Zero Torque example.

= (Force) x (Perpendicular line of action lever arm - the shortest distance between the pivot point and the line of action of the force through the body) = F l_p
See Same Torque example.

= (Force) x (Lever Arm) x sin(angle between the two) = F l sin(q)

The more exact definition is that the torque is that the torque is the cross product of the lever arm with applied force.
The torque's direction is perpendular to both the direction of the lever arm and the direction of the force. The direction can be found using the right hand rule.

SI Units: N m

* These are the same units as a Joule, but nobody uses Joules. There must be some deep connection which nobody has yet discovered. Any ideas ?

Torque on a Body
A force is applied to an irregular shaped body on a frictionless, horizontal surface. The location the point of application of the force can be altered by dragging the application-point. The magnitude and direction of the applied force can be altered by dragging its tail. Displayed are the torque, the magnitude and direction of the force, the lever arm, and the angle between the force and the lever arm. Also displayed are the perpendicular values of the applied force and the lever arm.