Physics Laws & Theorems
Basic

Newton's Third Law

For every action there is an equal and opposite reaction.

Formula

FAB=−FBAF_{AB} = -F_{BA}

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Variables

F_{AB}Force A on B
F_{BA}Force B on A

Example

A rocket pushes exhaust gas down; the gas pushes the rocket up with equal force.

How it works

This law says forces always come in pairs: if object A pushes or pulls on object B, object B pushes or pulls back on A with the same size force in the opposite direction. The two forces act on different objects, so they do not cancel each other on one object; they are a direct result of interactions like contact, gravity, or magnetic forces. It works because forces arise from mutual interactions, so each body experiences the interaction from the other body equally and oppositely.

When to use it

Use this law whenever two objects interact and you want to identify the paired forces, such as walking, pushing a wall, collision problems, or objects resting on surfaces. It is especially useful for drawing free-body diagrams and keeping the forces on each object separate.

Worked example, step by step

A skater pushes backward on the ice with a force of 120 N. By Newton's Third Law, the ice pushes forward on the skater with an equal and opposite force. F_{ice, skater} = -F_{skater, ice} F_{ice, skater} = -(120 N) = -120 N So the reaction force has magnitude 120 N and points forward. Final answer: the ice exerts a 120 N force on the skater in the opposite direction.

Common mistakes to avoid

  • thinking the action and reaction forces cancel because they are equal and opposite, even though they act on different objects
  • mixing up which object is doing the pushing and which object is receiving the force
  • using Newton's Third Law to find motion directly without also considering the other forces on each object

Did You Know?

Rockets work in the vacuum of space precisely because of this law — they push exhaust one way and fly the other.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026