When you push on a wall, the wall pushes back on you just as hard. When two skaters push apart, both feel the same force – but the lighter one accelerates more. Rockets, swimming and walking all rely on this action–reaction pair.
How to use the Newton’s Third Law Calculator
- Mass m₁
- Acceleration a₁
- Mass m₂
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the mass and acceleration of body 1 and the mass of body 2. The force on body 1 equals the force on body 2 in size; body 2’s acceleration is that force divided by its mass, in the opposite direction.
Inputs explained
| Field | What to enter |
|---|---|
| Mass m₁ | Units: kg, g, mg, t, lb, oz |
| Acceleration a₁ | Units: m/s², ft/s², g, cm/s² |
| Mass m₂ | Units: kg, g, mg, t, lb, oz |
What each result means
- Action force on body 2 (= reaction on body 1) = [Mass m₁]×[Acceleration a₁]
- Acceleration of body 2 (opposite direction) = [Mass m₁]×[Acceleration a₁]÷[Mass m₂]
- Acceleration ratio a₁/a₂ = [Mass m₂]÷[Mass m₁]
Example values
How the main result changes when Mass m₁ changes and everything else stays at the example values above:
| Mass m₁ (kg) | Action force on body 2 (= reaction on body 1) (N) |
|---|---|
| 30 | 60 |
| 45 | 90 |
| 60 | 120 |
| 75 | 150 |
| 90 | 180 |
| 120 | 240 |
Formula
F₁₂ = −F₂₁, m₁·a₁ = m₂·a₂
Worked example
Inputs — Mass m₁: 60 kg; Acceleration a₁: 2 m/s²; Mass m₂: 90 kg.
Results — Action force on body 2 (= reaction on body 1) = 120 N; Acceleration of body 2 (opposite direction) = 1.3333 m/s²; Acceleration ratio a₁/a₂ = 1.5.
Key terms
- Action–reaction pair
- Two equal and opposite forces acting on different bodies.
Frequently asked questions
If forces are equal, why do objects move differently?
The same force accelerates a lighter object more.
Do action and reaction cancel?
No – they act on different objects.
How does a rocket move in space?
It pushes exhaust backwards; the exhaust pushes the rocket forwards.
Is the Earth pulled up by a falling apple?
Yes, with the same force, but its acceleration is negligible.