Newton's Third Law Calculator — Action and Reaction Forces
Enter the action force and, optionally, the mass of each object. The calculator shows the equal-and-opposite reaction force and each object's resulting acceleration, and draws the force pair as opposing vectors.
N
kg
kg
Equal in magnitude, opposite in direction — acts on object A
- 1
Action force on object B
F = 50 N = 50 - 2
Acceleration of B (F ÷ m_B)
50 ÷ 70 = 0.7143 - 3
Reaction force on object A (Newton's 3rd law)
|−F| = 50 = 50Equal in magnitude to the action force, opposite in direction — acts on the object that applied the force.
How does this calculator work?
Newton's third law: F_action = −F_reaction. Both forces have equal magnitude; they act on different objects and never cancel. Enter the force (N) and each object's mass (kg) to get the reaction force and the acceleration each body experiences (a = F/m). The vector diagram shows the symmetric force pair.
Formula
How this is calculated
Newton's third law states that when object A exerts a force on object B, object B simultaneously exerts a force on object A that is exactly equal in magnitude and opposite in direction. These two forces always come in pairs — there is no action without a reaction. Crucially, the two forces act on different objects, so they never cancel each other out.
Because the reaction force has the same magnitude as the action force but is applied to a different mass, the resulting accelerations (a = F/m, Newton's second law) can differ greatly. A skater pushing off a wall exerts the same magnitude of force the wall pushes back, but the wall — effectively infinite mass — has negligible acceleration while the skater moves away. Similarly, when a rocket engine burns, equal and opposite forces propel the exhaust backward and the rocket forward.
This calculator reports the action and reaction forces and, when masses are supplied, the acceleration each object experiences. The vector diagram shows both force arrows originating symmetrically from the contact point, illustrating the equal-and-opposite relationship. Leave a mass field blank (or zero) to omit the corresponding acceleration.
Frequently asked questions
Because they act on different objects. Cancellation only applies to multiple forces on the same object. Object A experiences the reaction force and accelerates accordingly; object B experiences the action force. Neither object feels both at once.
Yes. A book on a table pushes down on the table (gravitational interaction) and the table pushes up on the book (normal force). A separate action-reaction pair exists between the table legs and the floor. All pairs obey the law regardless of whether any object is moving.
Newton's third law guarantees the contact forces are equal in magnitude during the collision. The difference in outcome comes from Newton's second law: the same force acting on the car's much smaller mass produces a far greater acceleration (deceleration) than it does on the truck.
Also known as
TG we-Calculate Editorial Team. (2026). Newton's Third Law Calculator — Action and Reaction Forces [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/newtons-third-law-calculator
TG we-Calculate Editorial Team. "Newton's Third Law Calculator — Action and Reaction Forces." TG we-Calculate. 2026. https://we-calculate.com/calculator/newtons-third-law-calculator.
TG we-Calculate Editorial Team, "Newton's Third Law Calculator — Action and Reaction Forces," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/newtons-third-law-calculator
@misc{wecalculate_newtons_third_law_calculator, title = {Newton's Third Law Calculator — Action and Reaction Forces}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/newtons-third-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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