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:

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
• magnetic coupling coefficient
• demagnetising coefficient
• fringing flux factor
• quality factor Q
• phase angle in radians (radian is equivalent to a dimensionless number in the SI system)³⁾

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.

• SI units
• Relative permeability
• Number of turns