How to Calculate Force with Newton's Second Law

Calculates force with Newton's second law F = mass × acceleration. Mass is in kilograms, acceleration in m/s², and force in newtons (N).

Explanation

The force acting on an object follows from its mass and the acceleration that force gives it. This is Newton's second law, and it is where mechanics starts.

F = m a

$F$ is the force, in newtons (N)
$m$ is the mass, in kilograms (kg)
$a$ is the acceleration, in metres per second squared (m/s²)

One newton is the force that gives a 1 kg object an acceleration of 1 m/s², so 1 N = 1 kg·m/s². Apply the same force to two objects and the heavier one picks up speed more slowly. That is what it means for something to be hard to get moving.

Example

The defaults are a mass of 2 kg and an acceleration of 3 m/s².

F = 2 \times 3 = 6\,\mathrm{N}

The force is 6 N. To find the weight of that same 2 kg object instead, enter the acceleration of gravity, 9.8 m/s², as the acceleration: 2 × 9.8 = 19.6 N.

Notes

$F$ is the net force: every force on the object, added up with its direction. If friction, air resistance or gravity are also acting, add them in first. The push you apply on its own is usually not the whole story.

No acceleration means no net force. An object sitting still and an object gliding in a straight line at a steady speed are in the same state, with the forces on them cancelling out.

Keep the units SI. Divide grams by 1000 for kilograms, and cm/s² by 100 for m/s², before entering them.