Linear density

For other meanings of density, see Density (disambiguation).

Linear density, linear mass density or linear mass is a measure of mass per unit of length, and it is a characteristic of strings or other one-dimensional objects. The SI unit of linear density is the kilogram per metre (kg/m). The linear density, $\mu$ (sometimes denoted by λ), of an object is defined as:

$\mu = \frac{\partial m}{\partial x}$

where m is the mass, and x is a coordinate along the (one dimensional) object.

For the common case of a homogeneous substance of length L and total mass m, this simplifies to:

$\mu = \frac{m}{L}$

In drawing or printing, the term linear density also refers to how densely or heavily a line is drawn.

Units

See also: Units of textile measurement

Common units include:

• kilogram per meter
• ounce (mass) per foot
• ounce (mass) per inch
• pound (mass) per yard: used in the North American railway industry for the linear density of rails
• pound (mass) per foot
• pound (mass) per inch
• denier, a unit of measure for the linear density of fibers, defined as the mass in grams per 9,000 meters.
• decitex (dtex), the SI unit for the linear density of fibers, defined as the mass in grams per 10,000 meters