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.
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 vectors. More formally, a scalar is a quantity that is invariant under coordinate rotations (or Lorentz transformations, for relativity).
Examples of (nonrelativistic) 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:
A related concept is a 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.)
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