a physical quantity that is completely described by its magnitude; examples of scalars are volume, density, speed, energy, mass, and time. Other quantities, such as force and velocity, have both magnitude and direction and are called vectors (vector).

Scalars are described by real numbers (real number) that are usually but not necessarily positive. The work done on a particle by a force, for example, is a negative number when the particle moves in a direction opposite to that in which the force acts. Scalars can be manipulated by the ordinary laws of algebra.