what is the formula for force

The basic formula for force in physics is that force equals mass times acceleration: F=m×aF=m\times aF=m×a.

Core idea

• In Newtonian mechanics, a force is any push or pull that can change an object’s motion.

• Newton’s Second Law gives the most common formula:

F=maF=maF=ma

where FFF is force, mmm is mass, and aaa is acceleration.

Units and meaning

• In SI units:
  • Force FFF is in newtons (N)
  • Mass mmm is in kilograms (kg)
  • Acceleration aaa is in meters per second squared (m/s²).

• One newton is the force needed to accelerate a 1 kg mass by 1 m/s².

Other useful equivalent forms

From the same law and from momentum p=mvp=mvp=mv:

• Using change in velocity over time:

a=ΔvΔt⇒F=mΔvΔta=\frac{\Delta v}{\Delta t}\quad \Rightarrow \quad F=m\frac{\Delta v}{\Delta t}a=ΔtΔv​⇒F=mΔtΔv​

• Using momentum ppp:

F=ΔpΔtF=\frac{\Delta p}{\Delta t}F=ΔtΔp​

which says force is the rate of change of momentum.

Quick example

• If a 2 kg object accelerates at 3 m/s², then

F=2×3=6 NF=2\times 3=6\text{ N}F=2×3=6 N

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