Power From Force Velocity⚠ unverified

Physics / Mechanics · Compute instantaneous mechanical power from force and velocity

Parameters

Input	Symbol	Unit	Default	Description
force	force	N	1.0	Force applied along the direction of motion
velocity	velocity	m/s	1.0	Velocity of the point of application

Output	Symbol	Unit	Description
result	P	W	Instantaneous power, in watts (W)

$F$ — only the component parallel to motion does power; static forces with $v = 0$ do zero power.
$v$ — higher speed at the same force means higher power (and usually higher energy use rate).
$P$ — $1\,\text{N}\times 1\,\text{m/s} = 1\,\text{W}$.

Work $dW = F\,ds$ for collinear force. Divide by $dt$:

$$P = \frac{dW}{dt} = F\frac{ds}{dt} = F v.$$

Equivalently from Power $P = dW/dt$ and $v = ds/dt$. Rotational analogue: $P = \tau\omega$.

$P = Fv$ is the workhorse relation for vehicle tractive effort, cutting forces, and actuator sizing — the mechanical twin of electrical $P = VI$.

Related Concepts: Power, Work Constant Force, Torque, Watt's Law, Motor Power

Notes: Registry calculator power-from-force-velocity (unverified). Collinear $F$ and $v$ only.