### Table of Contents

# Unitless

Stan Zurek, Unitless, Encyclopedia Magnetica, https://e-magnetica.pl/doku.php/unitless |

**Unitless** or **dimensionless** - a word denoting the lack of physical unit of a given quantity.^{1)}

Many quantities in physics and engineering are expressed in such a way that they require physical units such as “metre”, “kilogram” or “second”. However, there are some quantities, which are calculated as a ratio of the same two units, and therefore become “**unitless**”.

For example, magnetic permeability can be expressed as absolute permeability $μ$ (H/m) or as relative permeability $μ_r$ (unitless), being a ratio of two other absolute values, so that:

$$μ_r = \frac{μ}{μ_0}$$ | (H/m) / (H/m) ≡ (unitless) |

where: $μ_r$ - relative permeability (unitless), $μ$ - absolute permeability of material (H/m), $μ_0$ - absolute permeability of vacuum (H/m) |

Examples of other unitless or dimensionless quantities related to magnetism:^{2)}

- number of turns (of a coil)
- change of length due to magnetostriction, known as relative strain

In the SI system of units the dimensionless numbers can be treated as having the unit or dimension of “1” (“one”).^{4)}
However, there is no need to explicitly write such “dimension”, and therefore is simply omitted.

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