# Definition:Scalar Quantity

*This page is about scalar quantity. For other uses, see Scalar.*

## Definition

A **scalar quantity** is a real-world concept that needs for its model a mathematical object which contains only one (usually numeric) component.

## Examples

### Mass

The **mass** of a body is a measure of how much matter it contains.

**Mass** is equivalent to inertia.

**Mass** also determines the degree to which a body creates or is affected by a gravitational field.

It is a scalar quantity.

### Volume

**Volume** is the measure of the extent of a body.

It has three dimensions and is specified in units of length cubed.

### Density

**Mass density** is a physical quantity.

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

### Speed

The **speed** of a body is a measure of the magnitude of its velocity, taking no account of its direction.

It is, therefore, a scalar quantity.

### Temperature

**Temperature** is a physical property of matter that quantifies how hot or cold a body is.

It is a scalar quantity which can be mapped directly to the real number line.

### Electric Potential

An **electric potential** is the amount of work needed to move a unit of electric charge from a given reference point to a specific point in an electric field without producing an acceleration.

The reference point is usually either Earth or a point at infinity, although any point can be used.

### Electric Charge

**Electric charge** is a physical quantity of matter which causes it to experience a force when near other electrically charged matter.

It is a scalar quantity.

It has been discovered by experiment that the corresponding force depends on the magnitudes of those **electric charges**, their displacements from each other, and their velocities.

### Entropy (Physics)

**Entropy** is a property of a thermodynamic system.

It quantifies the number $\Omega$ of microstates that are consistent with the macroscopic quantities that characterize the system.

The **entropy** of a system is equal to the expectation of the value:

- $k \ln P$

where:

- $k$ is a constant which relates the mean kinetic energy and absolute temperature of the system
- $P$ is the coefficient of probability of the system.

## Also see

- Results about
**scalar quantities**can be found**here**.

## 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.) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities - 1957: D.E. Rutherford:
*Vector Methods*(9th ed.) ... (next): Chapter $\text I$: Vector Algebra: $\S 1$. - 1960: M.B. Glauert:
*Principles of Dynamics*... (next): Chapter $1$: Vector Algebra: $1.1$ Definition of a Vector - 1966: Isaac Asimov:
*Understanding Physics*... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Forces and Vectors - 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 22$: Vectors and Scalars - 1970: George Arfken:
*Mathematical Methods for Physicists*(2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach - 1992: Frederick W. Byron, Jr. and Robert W. Fuller:
*Mathematics of Classical and Quantum Physics*... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.1$ Geometric and Algebraic Definitions of a Vector - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**scalar quantity** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**scalar quantity**