# Newton’s Third Law Calculator

URL: https://speedycalculator.com/calculators/physics/newtons-third-law/
Last updated: 2026-10-30

> The Newton's third law calculator shows that action and reaction forces are equal and opposite: from the mass and acceleration of one body it finds the force pair and the resulting acceleration of the other body.

## Inputs

- Mass m₁ (kg, g, mg, t, lb, oz)
- Acceleration a₁ (m/s², ft/s², g, cm/s²)
- Mass m₂ (kg, g, mg, t, lb, oz)

## Results

- Action force on body 2 (= reaction on body 1)
- Acceleration of body 2 (opposite direction)
- Acceleration ratio a₁/a₂

## Formula

```
F₁₂ = −F₂₁,  m₁·a₁ = m₂·a₂
```

## Explanation

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

FieldWhat to enterMass m₁Units: kg, g, mg, t, lb, ozAcceleration a₁Units: m/s², ft/s², g, cm/s²Mass m₂Units: 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)30604590601207515090180120240

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)