A physical-quantity is a measure of some quantifiable aspect of the modeled world, such as 'the earth's diameter' (a constant length) and 'the stress in a loaded deformable solid' (a measure of stress, which is a function of three spatial coordinates). The first type is called constant-quantity and the second type is called function-quantity. All physical quantities are either constant-quantities or function-quantities. Although the name and definition of this concept is inspired from physics, physical quantities need not be material. For example, amounts of money are physical quantities. In fact, all real numbers and numeric-valued tensors are special cases of physical quantities. In engineering textbooks, quantities are often called variables.
Physical quantities are distinguished from purely numeric entities like a real numbers by their physical dimensions. A physical-dimension is a property that distinguishes types of quantities. Every physical-quantity has exactly one associated physical-dimension. In physics, we talk about dimensions such as length, time, and velocity; again, nonphysical dimensions such as currency are also possible. The dimension of purely numeric entities is the identity-dimension.
The 'value' of a physical-quantity depends on its type. The value of a constant-quantity is dependent on a unit-of-measure. Physical quantities of the identity-dimension (dimensionless quantities) are just numbers or tensors to start with. Physical quantities of the type function-quantity are functions that map quantities to other quantities (e.g., time-dependent quantities are function-quantities). See the definitions of these other classes and functions for detail.