Gradient
A vector operator that points in the direction of the greatest rate of increase of a scalar field, with magnitude equal to that maximum rate of change.
Governing formula
∇f = (∂f/∂x) î + (∂f/∂y) ĵ + (∂f/∂z) k̂
SI unit
[Scalar Field Unit] / m
In depth
Calculates local spatial rate of change. The gradient vector is perpendicular to scalar field contour lines (equipotential surfaces). In physics, conservative force fields equal the negative gradient of potential energy (F = -∇V).
Examples in the real world
Deriving electric field E = -∇V from scalar electric potential V, or heat flow Q = -k ∇T.