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Concept
Dimensionless quantity
Summary
A dimensionless quantity (also known as a bare quantity, pure quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned.
Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds).
The corresponding unit of measurement is one (symbol 1), which is not explicitly shown.
For any system of units, the number one is considered a base unit.
Dimensionless units are special names that serve as units of measurement for expressing other dimensionless quantities. For example, in the SI, radians (rad) and steradians (sr) are dimensionless units for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians.
Dimensional analysis#History
Quantities having dimension one, dimensionless quantities, regularly occur in sciences, and are formally treated within the field of dimensional analysis. In the nineteenth century, French mathematician Joseph Fourier and Scottish physicist James Clerk Maxwell led significant developments in the modern concepts of dimension and unit. Later work by British physicists Osborne Reynolds and Lord Rayleigh contributed to the understanding of dimensionless numbers in physics. Building on Rayleigh's method of dimensional analysis, Edgar Buckingham proved the pi theorem (independently of French mathematician Joseph Bertrand's previous work) to formalize the nature of these quantities.
Numerous dimensionless numbers, mostly ratios, were coined in the early 1900s, particularly in the areas of fluid mechanics and heat transfer. Measuring logarithm of ratios as levels in the (derived) unit decibel (dB) finds widespread use nowadays.
There have been periodic proposals to "patch" the SI system to reduce confusion regarding physical dimensions. For example, a 2017 op-ed in Nature argued for formalizing the radian as a physical unit.
Official source
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