In physics, a couple is a pair of forces that are equal in magnitude but opposite in their direction of action. A couple produce a pure rotational motion without any translational form.

The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". The forces have a turning effect or moment called a torque about an axis which is normal (perpendicular) to the plane of the forces. The SI unit for the torque of the couple is newton metre.

If the two forces are F and −F, then the magnitude of the torque is given by the following formula: $${\displaystyle \tau =Fd}$$ where

The magnitude of the torque is equal to F • d, with the direction of the torque given by the unit vector ${\displaystyle {\hat {e}}}$, which is perpendicular to the plane containing the two forces and positive being a counter-clockwise couple. When d is taken as a vector between the points of action of the forces, then the torque is the cross product of d and F, i.e. $${\displaystyle \mathbf {\tau } =|\mathbf {d} \times \mathbf {F} |.}$$

The moment of a force is only defined with respect to a certain point P (it is said to be the "moment about P") and, in general, when P is changed, the moment changes. However, the moment (torque) of a couple is independent of the reference point P: Any point will give the same moment. In other words, a couple, unlike any more general moments, is a "free vector". (This fact is called Varignon's Second Moment Theorem.)

The proof of this claim is as follows: Suppose there are a set of force vectors F₁, F₂, etc. that form a couple, with position vectors (about some origin P), r₁, r₂, etc., respectively. The moment about P is

Now we pick a new reference point P' that differs from P by the vector r. The new moment is

Now the distributive property of the cross product implies