# Units - Definition and Use

Edition Date: June 2018
Part Number: 370858P-01
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This section contains information about how physical quantities, units, dimensions, and symbols, are defined.

## Definitions and Contexts

A physical quantity is a property of a physical object, which can be specified as a quantity. Physical quantities can either be measured directly, such as surfaces, or can be calculated from other measurement values. Physical quantities that you can add or subtract have the same quantity. Quantities often result from multiplying or dividing two physical quantities. There are a number of basic quantities that are not interrelated. These basic quantities and all the quantities that can be derived from them, constitute a quantity system. The number of basic quantities determines the degree of the quantity system. To describe all natural phenomena, you require a seventh degree quantity system that consists of the following basic quantities: length, mass, time, current, thermodynamic temperature, amount of substance, and luminous intensity.

## Exponents, Dimension, and Category

Each quantity is the product of the basic quantities with an integer exponent of the basic quantity. The value of each exponent specifies the physical dimension. For example, the surface has the dimension (2,0,0,0,0,0,0). This means that the surface consists of the length with the exponent 2 and the mass, time, current, thermodynamic temperature, amount of substance, and luminous intensity, with the exponent 0. The dimension describes the mapping of a quantity onto the basic quantities of a quantity system.

Several quantities can have the same dimension. For example, the physical quantities radioactivity and angular velocity both have the same dimension, (0,0,-1,0,0,0,0), which is the time to the power -1. Whether or not you can execute mathematical functions on a set of physical quantities depends on the quantity type, not on the dimension. Radioactivity and angular velocity describe different physical quantities. Therefore, you cannot include them in one mathematical function. In this case you can use the category as an extension of the dimension. DIAdem does not use quantities from different categories when the program calculates result units in ANALYSIS. This is why when a rotation angle is divided by time, the result is angular velocity, not radioactivity.

## Units

You specify physical quantities with a numeric value, called the multiplier, and a comparison quantity. The comparison quantity is called the unit. The unit is identified with a unit symbol. The numeric value in front of the symbol identifies the multiplier of the comparison quantity.

A unit system is defined by the number of base units and all the units that are derived from the base units. The base units of a unit system usually belong to the basic quantities of the quantity system described above. In science, the most widely used system of units is the international system of units (SI), with the base units length (m), mass (kg), time (s), current (A), thermodynamic temperature (K), amount of substance (mol), and luminous intensity (cd).