# What is a dimensionless indicator?

What is a dimensionless indicator? I assume it refers to the fact that it is consistent in the way that it doesn't vary disproportionately at the variation of its factors.

I'm an engineering guy, so my first thought was "dimensionless number" but I wanted to be sure. I looked around and found your term here, and here that support a variation on it.

A dimensionless number or dimensionless variable is something used extensively in physics and engineering because they sometimes can be amazingly informative.

Here are some dimensionless numbers (ref):

• Archimedes Number: $Ar = \frac {g \rho L^3}{\mu^2}$ (ratio of gravitational force to viscous force)
• Biot Number: $Bi = \frac {h L} {k}$ (ratio of internal thermal resistance to boundary thermal resistance)
• Cauchy Number: $\frac {\rho {\nu}^2} {E}$ (ratio of inertial force to modulus)

... et cetera.

Not every dimensional number is applicable to every model or situation.

The Buckingham Pi theorem is a way to make candidate dimensionless numbers given your phenomena. It doesn't say which is useful, but it gives a finite set.

Here are some relevant links on the subject:

EDIT

Some "sneakier" indicators:

• Signal to noise ratio: $SNR = \frac {\mu} {\sigma}$ where $\mu$ is expected signal and $\sigma$ is standard deviation in signal.
• Reynolds number: $Re = \frac {\nu L \rho} {\mu}$ ratio of inertial and viscous forces.
Dimensions of statistics. Journal of the Royal Statistical Society. Series C (Applied Statistics), 26: 285-289. (Finney 1917$$-$$2018)