The pressure gradient force is the force resulting from differences in pressure across a distance.

The x component of the pressure gradient force per unit mass is: $-1}{\rho} \frac{dp}{dx$ .

The y component of the pressure gradient force per unit mass is: $-1}{\rho} \frac{dp}{dy$ .

The z component of the pressure gradient force per unit mass is: $-1}{\rho} \frac{dp}{dz$ .

We can express the acceleration more precisely, for a general pressure P as,

$F} = \frac{-1}{\rho$
.


The direction of the resulting force (acceleration) is thus in the direction of the most rapid change of pressure.

Note: In atmospheric dynamics, the pressure gradient force always moves mass from the area of higher pressure to the area of lower pressure.