This page is about Scalar Field in the context of Physics. For other uses, see Scalar Field.
Let $F$ be a field which acts on a region of space $S$.
Let the point-function giving rise to $F$ be a scalar quantity.
Then $F$ is a scalar field.
The distribution of temperature throughout a body is an example of a scalar field.
The density of a body is an example of a scalar field.
The electric potential within a region of space is an example of a scalar field.