# Definition:Density (Physics)

## Contents

## 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

- 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.

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

- The SI units of
**area density**are $\mathrm {kg} \ \mathrm m^{-2}$ (kilograms per square metre).

- The CGS units of
**density**are $\mathrm g \ \mathrm{cm}^{-2}$ (grams per square centimetre).

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

- The CGS units of
**density**are $\mathrm g \ \mathrm{cm}^{-1}$ (grams per centimetre).

Thus:

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

## Also see

## Sources

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