Newton's Third Law Calculator

For every action there is an equal and opposite reaction.

How the Math Works

Newton's Third Law states that for every action force, there is an equal and opposite reaction force. The formula 'reaction = -action' mathematically represents this principle, where the negative sign indicates opposite direction. When object A exerts a force on object B (action), object B simultaneously exerts a force on object A (reaction) with the same magnitude but opposite orientation. This means the two forces in the pair are equal in size, opposite in direction, and act on different objects, forming a fundamental relationship in force interactions.

Practical Applications

To apply this calculation, first identify the action force acting on an object, such as a 500 N thrust from a rocket engine. Using the formula, the reaction force would be -500 N, indicating an equal and opposite force exerted by the expelled gases. This is critical in engineering for designing structures that can withstand paired forces, analyzing collisions between vehicles, or calculating propulsion systems. Engineers use this principle to ensure safety margins in bridges and aircraft by accounting for both action and reaction forces in their designs.

Day-to-Day Use

This law explains everyday phenomena like walking—your foot pushes backward against the ground (action), and the ground pushes you forward (reaction). Similarly, when you row a boat, your oar pushes water backward (action), and the water pushes the boat forward (reaction). Even holding a book involves this law: the book's weight (action) is countered by your hand's upward force (reaction). Understanding these paired forces helps explain how we move, stay balanced, and interact with our environment in seemingly simple ways.

Worked example

Push a wall with 40 N and it pushes back with 40 N.

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