Force Calculator (F = m·a)

Newton's second law: enter mass and acceleration, get force in newtons. Step-by-step working and pound-force conversion shown.

Inputs

In kilograms (kg).

In metres per second squared. Earth gravity ≈ 9.81 m/s².

Result

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General calculation reads

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How to use this calculator

  • Enter the mass of the object in kilograms.
  • Enter the acceleration in m/s². Use 9.81 for objects in free fall near Earth.
  • Read force in newtons, plus pound-force and CGS unit conversions.

About this calculator

Newton's second law states that the force on an object equals its mass times its acceleration. F = m·a is the foundation of classical mechanics: pushing a 10 kg box at 2 m/s² requires 20 N; lifting a 1 kg book against gravity requires 9.81 N. The unit of force, the newton, is defined exactly as the force needed to accelerate 1 kg at 1 m/s². For everyday intuition: 1 N is roughly the weight of a small apple. This calculator returns force in newtons, pound-force (engineering use), and dynes (CGS / particle physics).

Frequently asked

What is one newton in everyday terms?+
1 newton is roughly the weight of a small apple (~100 g) under Earth gravity. It is the force needed to accelerate 1 kg at 1 m/s².
How does this differ from weight?+
Weight is the specific case where the acceleration is gravity (g ≈ 9.81 m/s² on Earth). Weight = m × g. Force is the more general F = m × a for any acceleration.
Why pound-force as well as newtons?+
US engineering work — automotive thrust, structural specs, aircraft loads — is still quoted in lbf. 1 lbf ≈ 4.448 N.
Does this account for friction or air resistance?+
No — F = m·a is the net force. If friction or drag is acting, you must subtract those to get net acceleration before computing.
Can I use negative acceleration?+
Yes. A negative result means the force points opposite to the chosen positive direction (i.e. it is a decelerating force).
What about relativistic speeds?+
Newton's second law is a low-velocity approximation. Above ~10% of light speed you need the relativistic form F = dp/dt with p = γmv. For ordinary objects, F = m·a is essentially exact.

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