# Definition:Density (Physics)

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## 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:

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

## 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

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