Dimensionless quantities

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is applicable. It is also known as a bare number or a quantity of dimension one and the corresponding unit of measurement in the SI is one (or 1) unit and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, engineering, and economics. By contrast, examples of quantities with dimensions are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second.

Quantities having dimension 1, habitually called 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 π theorem (independent of French mathematician Joseph Bertrand's previous work) to formalize the nature of these quantities. Numerous other dimensionless numbers, mostly ratios, were coined in the early 1900s, particularly in the areas of fluid mechanics and heat transfer. Measuring ratios in the (derived) unit dB (decibel) finds widespread use nowadays. In the early 2000s, the International Committee for Weights and Measures discussed naming the unit of 1 as the 'uno', but the idea of just introducing a new SI-name for 1 was dropped.

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