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:

$\rho = \dfrac m V$

where:

$m$ is the body's mass

$V$ is the body's volume

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

Symbol

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

Some sources use $d$, but that has so many other uses that it may become confused with other things.

Dimension

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

Units

• The SI units of density are $\mathrm {kg} \, \mathrm m^{-3}$ (kilograms per cubic metre).

• The CGS units of density are $\mathrm g \, \mathrm{cm}^{-3}$ or, less formally: $\mathrm g / \mathrm {cc}$ (grams per cubic centimetre).

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.

Linear Density

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

Also see

• Definition:Dirichlet Density

Sources

• 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $1$. Scalar and vector quantities
• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: density