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Newton’s Third Law — Two-Body Force & Acceleration

Relate a force pair and the resulting accelerations of two positive masses along a shared coordinate axis.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

If mass one is 2 kg and its interaction acceleration is 3 m/s², the force is 6 N. Mass two of 3 kg has force −6 N and acceleration −2 m/s².

F₁ = m₁a₁; F₂ = −F₁; m₁a₁ = −m₂a₂

Worked example

Enter these known values and leave the other values blank.

Mass of body one
2 kg
Body-one acceleration from this interaction
3 m/s²
Mass of body two
3 kg
Body-two acceleration from this interaction
-2 m/s²
Force on body one
6 N
Force on body two
-6 N

Assumptions and limitations

  • Masses are positive and constant. The force pair is resolved along a common axis in an inertial frame.
  • The accelerations entered here are due to this interaction alone. They equal total accelerations only when other force components along the axis sum to zero.
  • Equal force magnitudes do not require equal acceleration magnitudes when the masses differ.

Common questions

Why are the accelerations different?

Acceleration is force divided by mass. Equal and opposite forces produce smaller acceleration magnitude on the more massive body.

Do the two forces cancel on one object?

No. The pair acts on different objects. Include the forces actually acting on each object in its own force balance.

References

Bookify accepts the zero-force pair with both interaction accelerations zero. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor. The pound-force uses the exact international pound and standard gravity instead of the rounded captured factor.

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