In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a vector quantity. Newton's second law, F=ma, can be formulated to state that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass, an approximation which breaks down near the speed of light. Newton's original formulation is exact, and does not break down: this version states that the net force acting upon an object is equal to the rate at which its momentum changes.^[1]

Related concepts to accelerating forces include thrust - any force which increases the velocity of the object, drag - any force which decreases the velocity of any object, and torque - the tendency of a force to cause changes in rotational speed about an axis. Forces which do not act uniformly on all parts of a body will also cause mechanical stresses,^[2] a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume.^[3][4]

Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force, due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion.^[5] Some of these misunderstandings were corrected during the Middle Ages; for example, Al-Baghdadi's version of the theory of impetus correctly theorized that force is proportional to acceleration.^[6] Most of the previous misunderstandings about motion and force were eventually corrected by Sir Isaac Newton; with his mathematical insight, he formulated laws of motion that remained unchanged for nearly three hundred years.^[4] By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the "forces" produced by gravitation and inertia.