Newton's Third Law Calculator

Sir Isaac Newton's third law of motion states that for every action, there is an equal and opposite reaction. Mathematically, if object A exerts a force on object B (Action Force, F₁), object B simultaneously exerts an equal magnitude force in the opposite direction on object A (Reaction Force, F₂). This is expressed as F₁ = -F₂. Furthermore, because force equals mass times acceleration (F = m × a), we can equate the two interacting systems as: mass₁ × acceleration₁ = -(mass₂ × acceleration₂). This relationship allows you to solve for any missing variable—whether you need to find an unknown mass, acceleration, or reactive force vector.

Imagine a scenario in physics where a heavy cart with a mass (mass₁) of 20 kg experiences an acceleration (acceleration₁) of 70 m/s². To find the action force and the resulting reaction force, we apply our core formulas step-by-step. First, calculate the action force generated by the first object: Action Force = mass₁ × acceleration₁ = 20 kg × 70 m/s² = 1400 Newtons (N). According to Newton's third law, the reaction force is equal in magnitude but opposite in direction. Therefore, Reaction Force = -(Action Force) = -1400 N. This means the object pushes back with exactly 1400 Newtons of force.

Always maintain consistent metric units throughout your calculations, using kilograms (kg) for mass, meters per second squared (m/s²) for acceleration, and Newtons (N) for force. Pay close attention to negative signs; they represent the direction of the force vector rather than a negative magnitude. When analyzing complex multi-body systems, isolate the specific interaction pair you want to measure to avoid confusing internal forces with external environmental factors like friction.