A physical dimension is a quality that we attach with physical quantities in order to classify or differentiate them. Physical dimensions include mass, length, and force. Primitive dimensions can be used to define composite physical dimensions. A dimension is the product of any two dimensions. For example, volume = length x width x height.
Physical dimensions can be classified into three categories based on their use in mathematics: measurement, basis, and limit. In measurement, we express an attribute of a single object by using two or more dimensions. For example, the weight of an object can be measured by using length and mass as dimensions. The coefficient of thermal expansion describes the change in length of a piece of material when it changes temperature; it is a property of some materials used in thermometers and other measuring devices. The term "dimension" is also used for other attributes that can be measured along with one or more others. For example, the density of water is the mass per unit volume. When we say that water is "dense", we mean that it has a high mass per unit volume. Molecules have many different dimensions: they have size, shape, charge, and so on. But we usually ignore these atomic-level details in our daily lives because they are not relevant at the scale at which we live.
In mathematics, physical dimensions are used to express relationships between variables.
Describing dimensions aids in understanding the link between physical quantities and their dependency on basic or fundamental variables, i.e., how dimensions of a body are dependent on mass, time, length, temperature, and so on. Dimensions are useful in dimension analysis because they may be used to convert and exchange units. For example, if you want to convert miles per hour to centimeters per second, you first need to know that one mile equals 3.6 million feet, so 33,000 ft/mile x 60 min/hr = 1,922.4 cm/s.
In physics, dimensions are properties of physical quantities that describe their magnitude and how they relate to other physical quantities. In mathematics, dimensions are numbers that can be used to express the size of objects or groups of objects. In science, dimensions are characteristics that can be measured to test hypotheses or theories about the behavior of matter under certain conditions.
In chemistry, the term "dimension" refers to the number of atoms in a molecule. The term "dimers" refers to molecules composed of two identical atoms or molecules joined together. The term "trimers" refers to molecules composed of three identical atoms or molecules joined together. Based on this definition, carbon dioxide has a dimer structure with two oxygen atoms attached to each carbon atom, and water has a trimer structure with three hydrogen atoms attached to each oxygen atom.
A physical quantity's dimension is the power to which the fundamental units must be elevated in order to express it. The fundamental quantities are mass, length, time, temperature, electric current, luminous intensity, and amount of material. A unit of measurement for each of these quantities has been defined by the International System of Units (SI). There are three main categories of dimension: numerical value, physical magnitude, and logical relation.
Numerical values are numbers that describe how much of something there is. The dimensions of most physical quantities are expressed in units that have been assigned special names for convenience. For example, the dimension of mass is given by the word "grams", while the dimension of velocity is given by the word "meters per second". Dimensions are usually expressed with two numbers after the word "dimension": one number for the actual quantity being measured and another number for its corresponding unit. For example, the dimension of temperature is "degrees Kelvin", while the dimension of pressure is "pascals (Pa)".
Physical magnitudes are quantities that cannot be reduced any further into smaller components. Mass, length, and time are examples of physical magnitudes. Temperature, electric current, and luminous intensity are examples of quantitative values.
Logical relations are ways in which different quantities can be compared.
Dimensions do not exist for physical amounts. In the defining equations, these are applied to algebraic equations. You can freely add and delete base units. For example, you could define "meter" as 1/10 meter or 10 meters. There is no difference between these two definitions.
Physical quantities include mass, length, time, electric charge, and magnetic flux. A dimensionless quantity is one that does not depend on the scale of measurement. For example, the speed of light in a vacuum is always c = 3 × 108 m/s. Masses appear with dimensions of kg (kilograms) in most systems. Electric charge appears with the dimension of an ampère. Magnetic flux appears with the dimension of webers. These are all physical quantities with well-defined values that do not change unless something else changes. They are all dimensionless numbers.
In physics, dimensions are used to describe how much each quantity weighs, measures along its own axis, or whatever other property is being described. For example, the weight of a book is measured in kilograms, while its width is measured in meters. The amount of material it contains is said to have volume, which has the same dimension as length when talking about three-dimensional objects.