3rd Law of Motion Calculator

Calculator

Newton’s third law states: if A pushes on B, then B pushes on A with equal magnitude and opposite direction.

Example Data Table

Tip: signs and angles define direction. Reaction is always opposite.

Formula Used

• F_{A on B} = −F_{B on A}
• Magnitude: |F_{A on B}| = |F_{B on A}|
• Components: (R_x, R_y, R_z) = (−F_x, −F_y, −F_z)
• Impulse (average force): F_avg = Δp / Δt

This tool reports the equal-and-opposite reaction for any action force representation.

How to Use

1. Select a method: magnitude+angle, components, or impulse.
2. Choose your preferred unit for force (and time for impulse).
3. Enter the action values, including sign or direction information.
4. Press Calculate to view reaction values instantly.
5. Use the CSV or PDF buttons to export results.

Newton’s Third Law: Practical Notes

1) What the law actually says

Newton’s third law pairs forces: when object A exerts a force on object B, object B exerts an equal force on A in the opposite direction. The two forces act on different bodies, so they do not cancel each other on one object.

2) Action–reaction is simultaneous

The action and reaction occur at the same time. If your input is 120 N at 30°, the reaction is 120 N at 210°. This calculator shows that relationship directly, including component sign flips.

3) Typical force sizes you can expect

Everyday pushes range from about 20–200 N for light tasks. A firm door push often falls near 50–150 N. A person weighing 70 kg exerts about 686 N on the ground while standing (70×9.81), and the ground exerts the same upward force.

4) Working with components (Fx, Fy, Fz)

Many problems are easiest in components. If you enter Fx = 80 N and Fy = 60 N, the reaction becomes −80 N and −60 N. The magnitude is found by √(Fx²+Fy²+Fz²), so for (80,60,0) it is 100 N.

5) Angles and direction data

Angle input is measured from the +x direction counterclockwise. A 0° force points right, 90° points up, and 180° points left. The reaction angle is always θ + 180° (wrapped into 0–360°).

6) Impulse mode connects force and momentum

In collisions and braking, average force can be estimated using F_avg = Δp/Δt. For example, a 24 N·s momentum change over 0.20 s gives 120 N average action force; the reaction is −120 N. Shorter stopping time means a larger force.

7) Units and quick conversions

This tool supports N, kN, and lbf. Remember: 1 kN = 1000 N, and 1 lbf ≈ 4.448 N. Converting units does not change the physics; it only changes how the same force is reported.

8) Common interpretation mistakes

A frequent confusion is thinking action and reaction cancel, so “nothing moves.” Motion depends on the net force on each object. Also, friction and normal forces each have their own action–reaction partners with equal magnitude and opposite direction.

FAQs

1) Do action and reaction cancel each other?

Not on a single object. They act on different objects, so each body can still have a nonzero net force and accelerate.

2) Why does a rocket move forward?

Exhaust gases are pushed backward, and the gases push the rocket forward with an equal and opposite force. The rocket’s net force is forward.

3) What if I enter a negative force in impulse mode?

A negative sign represents direction in 1D. The calculator keeps the sign in Fx and flips it for the reaction, showing the opposite direction.

4) How does the calculator find magnitude from components?

It uses the vector length: √(Fx² + Fy² + Fz²). The reaction has the same magnitude because each component is multiplied by −1.

5) Why is the reaction angle 180° different?

Opposite direction means the vector is rotated by 180°. In 2D, adding 180° (and wrapping within 0–360°) gives the reaction direction.

6) Can the reaction force be on a different object?

Yes—always. The reaction is exerted by the object being pushed or pulled, acting back on the original object with equal magnitude.

7) Is the third law the same as “equal forces, equal acceleration”?

No. Equal forces can cause different accelerations because acceleration also depends on mass (a = F/m). The law only states forces are equal and opposite.