Newton's Third Law Calculator

Newton's third law states: 'For every action, there is an equal and opposite reaction.' 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. These two forces always act on different objects, which is why they do not cancel each other out.

The equation is F_action = −F_reaction. The negative sign indicates that the reaction force is equal in magnitude but opposite in direction to the action force. In vector terms, if Object A pushes Object B with force F at angle θ, then Object B pushes back on Object A with force F at angle (θ + 180°).

Using Newton's second law, the action force is F = m × a = 20 kg × 70 m/s² = 1400 N. By Newton's third law, the reaction force is equal in magnitude: 1400 N, acting in the opposite direction. You can verify this with our calculator by entering a force magnitude of 1400 N.

Action and reaction forces act on different objects — the action force acts on Object B, while the reaction force acts on Object A. Since they apply to separate bodies, they cannot cancel. Cancellation of forces only occurs when two forces act on the same object.

Yes — this is one of the most important insights of Newton's third law paired with his second law (F = ma). Although the forces are equal in magnitude, if the two objects have different masses, they will experience different accelerations. A less massive object accelerates more than a heavier one under the same force.

Classic examples include a rocket expelling gas downward (action) and being propelled upward (reaction), a swimmer pushing off a wall, a gun recoiling when fired, and Earth and an apple gravitationally attracting each other with equal forces. Even walking relies on the ground pushing back on your foot as you push down.

The force angle is measured in degrees from the positive x-axis (standard mathematical convention, 0–360°). The reaction force angle is automatically calculated as (action angle + 180°) mod 360°, ensuring it points in the exact opposite direction. The x and y components of the force are also broken down using trigonometry.

Newton's First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion, unless acted upon by an external force. Newton's Second Law: Force equals mass times acceleration (F = ma). Newton's Third Law: For every action force, there is an equal and opposite reaction force.