The concept of a **scalar** is used in mathematics and physics. The concept used in physics is a more concrete version of the same idea that goes by that name in mathematics.

In mathematics, the meaning of *scalar* depends on the context; it can refer to real numbers or complex numbers or rational numbers, or to members of some other specified field. Generally, when a vector space over the field *F* is studied, then *F* is called the *field of scalars*. A scalar is formally a tensor of rank zero.

In physics a *scalar* is a quantity that can be described by a single number (either dimensionless, or in terms of some physical quantity). Scalar quantities have magnitude, but not a direction and should thus be distinguished from vectorss. More formally, a scalar is a quantity that is invariant under coordinate rotations (or Lorentz transformations, for relativity).

Examples of (non-relativistic) scalar quantities include:

The word*scalar*is derived from

*scala*Latin for "ladder" and means "resembling a ladder". According to a citation in the

*Oxford English Dictionary*the first usage of the term (by W. R. Hamilton in 1846) described it as:

- "The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part."

**pseudoscalar**, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. One example is the scalar triple product (see vector). (Another example, if it existed, would be magnetic charge.)