Newton's third law states that when one object exerts a force on another object, the second object simultaneously exerts a force of equal magnitude and opposite direction on the first object. It is commonly expressed as, for every action there is an equal and opposite reaction, although this wording can sometimes create the misconception that the two forces occur sequentially. They do not. The two forces are simultaneous and constitute an interaction between two bodies.
If object A exerts a force on object B, object B exerts a force of the same type and magnitude back on object A, with the directions opposite to one another. Mathematically, if the force of A on B is represented as F_AB, then the force of B on A is F_BA = -F_AB. The negative sign indicates opposite direction. The law applies to gravitational, electromagnetic, contact, tension, frictional, and other interaction forces. It is one of the three laws of motion formulated by Isaac Newton in his 1687 work Principia Mathematica and forms a central part of classical mechanics.
The most important feature of Newton's third law is that the two forces act on different objects. This distinguishes a third law force pair from two forces that happen to act on the same object. For example, when a person pushes a wall, the person exerts a force on the wall and the wall exerts an equal and opposite force on the person. The forces do not cancel each other because they are applied to different bodies.
If the forces are represented in a free body diagram for the person, only the force exerted by the wall on the person belongs on that diagram. The person's force on the wall belongs on a separate diagram for the wall. This distinction is essential in mechanics because an object's acceleration depends on the net force acting on that particular object, not on forces acting elsewhere in the interaction. The same principle applies when a foot pushes the ground, when a tyre pushes a road, when a rocket expels gas, or when two magnets attract or repel one another.
Newton's third law can be understood more deeply through momentum. In an isolated two body interaction, the forces exerted on the bodies have equal magnitude and opposite direction, so the changes in momentum of the two bodies are equal and opposite. If the interaction lasts for a time interval, the impulses delivered to the two bodies are also equal and opposite. Consequently, the total momentum of the interacting system remains constant when there is no external net impulse.
This provides a close connection between Newton's third law and the conservation of momentum. For two bodies A and B, F_AB = -F_BA means that the internal forces cancel when considering the two bodies together as one system. They do not cancel when considering either body individually. This system level distinction explains why internal forces can change the individual velocities of objects while leaving the total momentum of an isolated system unchanged.
The law applies to everyday contact interactions but is not limited to objects physically touching. A book resting on a table illustrates a contact force pair. The book pushes downward on the table through its weight and contact interaction, while the table exerts an upward normal force on the book. More precisely, the gravitational force of Earth on the book has a third law partner consisting of the gravitational force of the book on Earth.
The normal force exerted by the table on the book has a corresponding force exerted by the book on the table. These are different third law pairs. A common mistake is to identify the upward normal force and downward gravitational force on the book as a third law pair. They are not, because both act on the same object. Similarly, the force of an engine on a car and the resistive force on the car are not automatically a third law pair. Correct identification requires asking which two objects are interacting and whether the forces are opposite members of the same interaction.
Newton's third law explains propulsion and locomotion. A swimmer pushes water backwards and the water exerts a forward force on the swimmer. A bird pushes air downward and backwards with its wings, while the air exerts forces that contribute to lift and forward motion. A person walking pushes the ground backwards through static friction, and the ground exerts a forward frictional force on the person.
A rocket pushes combustion products out of its engine and the expelled gases exert a force on the rocket in the opposite direction. Importantly, a rocket does not require air to push against. Its propulsion results from momentum transfer between the rocket and the exhaust gases, so rockets operate in vacuum.
The Earth also experiences a force from a walking person, swimmer, bird, or rocket, but because Earth's mass is enormous compared with the moving object, its acceleration is usually extremely small. The equal force does not imply equal acceleration because Newton's second law gives acceleration as force divided by mass.
Newton's third law is also important in gravitational interactions. If Earth attracts an apple gravitationally, the apple simultaneously attracts Earth with a force of equal magnitude and opposite direction. The force magnitudes are equal because gravitational interaction is mutual. The accelerations are not equal because Earth has vastly greater mass. The apple therefore experiences a noticeable acceleration toward Earth, while Earth's acceleration toward the apple is extremely small.
The same principle applies to the Earth and Moon, the Sun and Earth, binary stars, and interacting galaxies. In a two body gravitational system, both objects orbit their common centre of mass rather than one body being completely stationary in an exact physical description. Newton's law of universal gravitation and Newton's third law therefore work together to describe mutual gravitational interactions, although precise orbital dynamics at extreme speeds or gravitational fields require general relativity rather than classical Newtonian mechanics.
There are important limits to the simple textbook formulation of Newton's third law. Classical mechanics treats forces as interactions between identifiable bodies and assumes an appropriate inertial reference frame. In electromagnetic systems, especially when fields carry significant momentum, a simple mechanical description involving only instantaneous forces between material objects can become incomplete. Electromagnetic fields themselves can store and transport energy and momentum, and a fully relativistic treatment accounts for momentum carried by fields.
General relativity also changes the classical conception of gravity by describing gravity through spacetime geometry rather than an ordinary Newtonian force. Nevertheless, within its domain of validity, Newton's third law remains extraordinarily useful. Engineering, structural mechanics, vehicle dynamics, orbital mechanics at ordinary velocities and many everyday mechanical systems can be analysed successfully using Newtonian force interactions. The law should therefore be understood as a foundational principle of classical mechanics rather than as an unrestricted description of every physical interaction in nature.
Newton's third law is ultimately a statement about mutual interaction and is closely associated with the structure of classical mechanics. It provides the conceptual basis for analysing collisions, recoil, propulsion, contact forces, friction, tension, gravitational interactions and many other phenomena. During a collision, each object experiences a force from the other with equal magnitude and opposite direction, although their accelerations and changes in velocity can be very different because their masses differ.
During recoil, a projectile and launcher exchange momentum through equal and opposite interaction forces. In engineering, identifying third law pairs helps prevent incorrect free body diagrams and incorrect calculations of net force. The most reliable method is to name the two objects involved, identify the force exerted by the first on the second, and then identify the corresponding force exerted by the second on the first. The forces must be of the same interaction type, equal in magnitude, opposite in direction, simultaneous, and applied to different objects.
