In physics, a force is a push or pull that can cause an object with mass to change its velocity. Force has both magnitude and direction, making it a vector quantity. Newton's second law states that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass. Equivalently, the net force on an object equals the rate at which its momentum changes. See also thrust.

Forces acting on three-dimensional objects may also cause them to rotate or deform, or result in a change in pressure or even change volume in some cases. The tendency of a force to cause changes in rotational speed about an axis is called torque. Deformation and pressure are the result of stress forces within an object.e.g. ; .University Physics, Sears, Young & Zemansky, pp18–38

Since antiquity, scientists have used the concept of force in the study of stationary and moving objects. However, descriptions of forces by Aristotle incorporated fundamental misunderstandings, which, despite advances made by the third century BC philosopher Archimedes from studies of simple machines, persisted for many centuries. By the seventeenth century, Sir Isaac Newton corrected these misunderstandings with mathematical insight that remained unchanged for nearly three hundred years. By the early 20th century, Einstein in his theory of general relativity successfully predicted the failure of Newton's model for gravity by ushering in the concept of a space-time continuum.

The recent theory of particle physics known as the Standard Model associate forces at the level of quantum mechanics. The Standard Model predicts that exchange particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.

Pre-Newtonian concepts

Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the natural world held four elements that existed in "natural states". Aristotle believed that it was the natural state of objects with mass on Earth, such as the elements water and earth, to be motionless on the ground and that they tended towards that state if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. The place where forces were applied to projectiles was only at the start of the flight, and while the projectile sailed through the air, no discernible force acts on it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path provided the needed force to continue the projectile moving. This explanation demands that air is needed for projectiles and that, for example, in a vacuum, no projectile would move after the initial push. Additional problems with the explanation include the fact that air resists the motion of the projectiles.