Torque ($\vec{\tau}$) measures the effectiveness of a force $\vec{F}$ in causing rotation about an axis. The magnitude of torque $\tau$ is defined as the product of the force magnitude $F$ and the lever arm $r_\perp$.

The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force: a theoretical line extending infinitely along the force vector.

Geometrical analysis shows that the lever arm relates to the position vector magnitude $r$ and the angle $\theta$ between the position and force vectors by $r_\perp = r \sin(\theta)$. Substituting this into the definition yields the general formula:

Equivalently, torque is the product of the radial distance $r$ and the component of force perpendicular to $r$, denoted $F_{\perp} = F \sin(\theta)$.