Newtons Third Law Calculator - Action and Reaction Force Pairs

A newtons third law calculator turns "for every action there is an equal and opposite reaction" into numbers you can read directly. Enter the mass and acceleration of two interacting bodies; the calculator applies F = m · a to each, then checks whether the two net forces form an isolated third-law pair. The rule in symbols is F_AB = -F_BA, and the calculator shows that relationship without forcing you to draw a free-body diagram.

• • Checking homework and lab reports: Confirm two measured forces on two carts, springs, or pucks form an action-reaction pair before submitting.
• • Rocket and propulsion estimates: A 10 kg rocket losing 1 kg/s of exhaust sees an equal-magnitude, opposite-direction thrust force.
• • Teaching collisions and contact forces: When two objects touch — foot on ground, bat on ball, hand on wall — the force each applies on the other is what the third law describes.
• • Verifying a video-tracking experiment: Pull two accelerations from a motion video, enter them with the two masses, and see whether the force pair satisfies the third law.

The newtons third law calculator works on any pair of real bodies, from a hand pushing a wall to a magnet pulling on a fridge. The two bodies must interact through a single contact or field, and the action and reaction forces act on opposite bodies, so you can read the pair directly from the result panel.

If you want to see how the action and reaction forces in an interaction relate to the motion each body actually undergoes, pair this tool with our forces and Newton's laws calculator, which solves F = m · a for any single body.

The calculator applies Newton's second law to each body, then checks whether the two net forces form an isolated third-law pair. The third law always says action and reaction are equal in magnitude and opposite in sign, but it does not, on its own, predict motion — each body's acceleration is set by its own net force. The calculator reads those net forces from F = m · a and flags a third body in the system when |F_A + F_B| ≠ 0.

• m_A, m_B: Mass of objects A and B in kilograms. Both must be greater than zero.
• a_A, a_B: Linear acceleration of each body in m/s² along the chosen axis. The sign carries the direction.
• F_A, F_B: Net force on each body from F = m · a. In an isolated pair, F_A is the reaction B exerts on A and F_B is the action A exerts on B.
• F_AB, F_BA: Action A exerts on B and reaction B exerts on A. Third law: F_AB = -F_BA, flagged by |F_A + F_B| = 0.

A non-zero pair difference does not mean the third law is broken — it means a third body (a wall, a floor, a rope, friction) is acting on one of the objects. The third-law pair is still present; the calculator just cannot recover its magnitude from the accelerations alone.

According to Wikipedia, Newton's laws of motion, Newton's Third Law states that for every action force A exerts on B, B exerts an equal and opposite reaction force on A, written F_AB = -F_BA.

According to MIT OpenCourseWare 8.01 Classical Mechanics, the course presents the third law as action and reaction always coming in equal-magnitude, opposite-direction pairs acting on two different bodies, with F_AB = -F_BA as the canonical statement.

Four ideas make every result the newtons third law calculator shows easier to interpret.

If you want to see what those forces do to the motion of the system as a whole, the conservation of momentum calculator uses the same pair in integrated form and is a natural follow-up.

Five short steps give you a reliable action-reaction force pair.

1. 1 Enter the mass of object A: Type m_A in kilograms into the first field. Use the actual mass, not the weight in newtons.
2. 2 Enter the acceleration of object A: Type a_A in m/s². Pick a direction along an axis and use a positive or negative sign.
3. 3 Enter the mass and acceleration of object B: Repeat for the second body. For a clean pair, a_B should have the opposite sign of a_A scaled by m_A / m_B.
4. 4 Read the net forces on each body: The result panel shows net force on A and net force on B from F = m · a. Compare their signs and magnitudes first.
5. 5 Check the action-reaction pair status: Use the pair difference row and pair status line to see whether the accelerations form an isolated third-law pair.

A 0.05 kg model rocket expelling 0.01 kg/s of exhaust at 200 m/s experiences about 2 N forward (rocket) and 2 N backward (exhaust). Enter m_A = 0.05, a_A = 40, m_B = 0.01, a_B = -200 to confirm a near-zero pair difference.

When the two bodies in your experiment are vehicles rather than carts, the car crash force calculator applies the same F = m · a and F_AB = -F_BA reasoning to a real-world collision.

A purpose-built newtons third law calculator makes the third-law relationship obvious.

• • Pairs action and reaction in one view: The result panel shows action and reaction side by side with explicit signs, so the equal-magnitude, opposite-direction relationship is visible without a free-body diagram.
• • Verifies the third-law relationship automatically: The pair difference row and pair status line convert F_AB = -F_BA into a single check, faster than recomputing forces on paper.
• • Works in either direction: Start from the action force and read the reaction, or start from observed accelerations and read the implied pair.
• • Supports classroom and lab use: Use it during a lab to confirm two carts on a track form a true action-reaction pair, or during a lecture to demonstrate the third law with one shared example.
• • Keeps units and signs consistent: Applies F = m · a with kilograms, m/s², and newtons, with a consistent sign convention so the pair matches your free-body sketch.

For a non-contact third-law example that uses the same pair logic, the buoyant force calculator shows the equal and opposite pair between a submerged object and the displaced fluid.

Three variables determine the result, and two limitations tell you when to interpret the pair carefully.

• • The calculator assumes a one-dimensional interaction along a single axis. Two-body interactions at angles need to be decomposed into components first.
• • A non-zero pair difference only flags that the pair is not isolated. It does not identify which third body is responsible; you still need to inspect the physical setup.

If the accelerations you entered come from a vertical drop, keep the gravitational acceleration consistent with your other physics tools.

According to Omni Calculator, Newton's Third Law, the page frames the calculation as finding the reaction B exerts on A given the action A exerts on B, and shows the magnitudes must match while the directions are exactly opposite.

If the accelerations you entered come from a vertical drop or a free-fall experiment, the free fall time calculator keeps the gravitational acceleration consistent across both calculations.