Newton's Third Law
Calculate action and reaction force pairs using Newton's Third Law: F₁₂ = -F₂₁. Enter mass and acceleration to find the equal and opposite reaction force instantly.
About This Calculator
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This fundamental principle of classical mechanics, first formulated by Sir Isaac Newton in his 1687 work Philosophiæ Naturalis Principia Mathematica, describes how forces always come in interacting pairs. When object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude but in the opposite direction on object A.
This Newton's Third Law calculator uses the equation m₁ × a₁ = -(m₂ × a₂) to compute the missing variable. By entering the mass and acceleration of the first object and the mass of the second object, the calculator determines the acceleration of the second object, the action force (F₁ = m₁ × a₁), and the reaction force (F₂ = m₂ × a₂). The negative sign in the result indicates opposite direction — the forces are always equal in magnitude but opposite in direction.
Newton's Third Law explains countless everyday phenomena. When you walk, your foot pushes backward on the ground (action), and the ground pushes your foot forward (reaction). A rocket engine expels exhaust gases downward at high speed, and the rocket experiences an equal upward thrust. Even at the atomic level, every interaction between particles obeys this equal-and-opposite principle. Understanding this law is essential for students of physics, engineers designing mechanical systems, and anyone curious about how forces shape our physical world.
Regional Notes
Global (SI units): This calculator uses the International System of Units (kg, m/s², N) which is the standard for physics and engineering worldwide. The newton (N) is the SI unit of force, defined as kg·m/s². In the US customary system, force is measured in pound-force (lbf) where 1 N ≈ 0.2248 lbf. The underlying physics is universal — Newton's Laws apply identically regardless of measurement system.
Frequently Asked Questions
What is Newton's Third Law of Motion?
Newton's Third Law states that for every action, there is an equal and opposite reaction. When one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction back on the first object. This is expressed mathematically as F₁₂ = -F₂₁, where F₁₂ is the force exerted by object 1 on object 2.
How do I use the Newton's Third Law calculator?
Enter the mass (in kg) and acceleration (in m/s²) of the first object, and the mass (in kg) of the second object. The calculator uses the formula m₁ × a₁ = -(m₂ × a₂) to compute the acceleration of the second object and both action and reaction forces in newtons (N).
What does the negative sign in the reaction force mean?
The negative sign indicates that the reaction force acts in the opposite direction to the action force. Force is a vector quantity, meaning it has both magnitude and direction. If object 1 pushes to the right, object 2 pushes back to the left with equal strength.
Is the Newton's Third Law calculator free?
Yes, it is completely free to use with no registration required. You can also share your calculation by copying the URL which saves all your input values.
What units does this calculator use?
The calculator uses SI units: mass in kilograms (kg), acceleration in meters per second squared (m/s²), and force in newtons (N). This follows the International System of Units (SI) standard used worldwide in physics and engineering.
What are real-world examples of Newton's Third Law?
Common examples include: a rocket expelling gas downward (action) and moving upward (reaction), a person walking where the foot pushes backward against the ground and the ground pushes the foot forward, and a swimmer pushing water backward to propel themselves forward.
How is Newton's Third Law different from the Second Law?
Newton's Second Law (F = ma) describes how a single force affects an object's motion. Newton's Third Law describes the interaction between two objects — every force comes with an equal and opposite counterpart on the other object. They work together: the Second Law gives the magnitude, and the Third Law gives the pairing.
Can I calculate the action force if I know the reaction force?
Yes. According to Newton's Third Law, the action and reaction forces always have equal magnitude. If you know the reaction force magnitude, the action force magnitude is identical. You only need to know any three of the four variables (m₁, a₁, m₂, a₂) to compute the fourth.