Scalär

Scalär is the term used in some languages (for example Swedish) to denote a scalar quantity. In mathematics and physics, a scalar is a physical quantity described by a single real number and a unit, representing only magnitude without any directional component. This is in contrast to vector quantities, which have both magnitude and direction, and to tensors, which require several components to describe more complex directional dependencies.

Common examples of scalar quantities include mass, temperature, time, energy, distance, and volume. Not all “magnitude-only” products are scalar in every context, but these quantities are typically invariant under changes of coordinate system. In other words, their numerical value does not depend on the orientation or the chosen reference frame (though the units may be converted).

Scalar quantities can be added, subtracted, and multiplied just like ordinary numbers. When two scalars are combined, the result is another scalar. They can also be used to form scalar fields, which assign a scalar value to every point in a space or space-time. Examples include a temperature field in a room or a gravitational potential field in a region of space.

In physics, scalars are contrasted with vectors, which require direction in addition to magnitude (for example, velocity or force). Scalars play a fundamental role as the simplest class of quantities and are foundational in measurements, equations, and dimensional analysis.