# Definition:Density (Physics)

## Definition

Density is a physical quantity.

The density of a body is its mass per unit volume.

For a homogeneous body it is found by finding its total mass and dividing it by its total volume.

However, if the substance of the body varies throughout, then its density may be a function of position within the body.

The usual symbol used to denote density is $\rho$ (Greek letter rho).

### Dimension of Density

The dimension of density is $M L^{-3}$: mass per unit volume.

### Units of Density

Thus:

$1 \ \mathrm g \ \mathrm {cm}^{-3} = 1000 \ \mathrm {kg} \ \mathrm m^{-3}$

## Area Density

The area density of a two-dimensional body is its mass per unit area.

The usual symbol used to denote area density is $\rho_A$, although some sources simply use $\rho$ if the context makes it clear that it refers to area density rather than volume density.

Occasionally, $\sigma$ (Greek letter sigma) is also used, but this is more commonly used for surface charge density.

### Dimension of Area Density

The dimension of area density is $M L^{-2}$: mass per unit area.

### Units of Area Density

Thus:

$1 \ \mathrm g \ \mathrm{cm}^{-2} = 10 \ \mathrm{kg} \ \mathrm m^{-2}$

## Linear Density

The linear density of a one-dimensional body is its mass per unit length.

The usual symbol used to denote linear density is $\mu$ (Greek letter mu).

Sometimes $\lambda$ (Greek letter lambda) is also used.

### Dimension of Linear Density

The dimension of linear density is $M L^{-1}$: mass per unit length.

### Units of Linear Density

Thus:

$1 \ \mathrm{kg} \ \mathrm m^{-1} = 10 \ \mathrm g \ \mathrm{cm}^{-1}$