# Definition:Dimension (Measurement)

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## Definition

Every physical quantity has a **dimension** associated with it.

No attempt is made here to provide an abstract definition of this term. Instead, it will be defined by example.

## Fundamental Dimensions

The **fundamental dimensions** are:

- Mass, denoted $M$ or $\mathbf M$
- Length, denoted $L$ or $\mathbf L$
- Time, denoted $T$ or $\mathbf T$

It is convenient at elementary levels of physics to add:

- Temperature, denoted $\Theta$
- Electric charge, denoted $Q$ or $\mathbf Q$

However, it is possible to define these in terms of mass, length and time, so strictly speaking they are not **fundamental**, as such.

## Units

Compare with units of measurement.

This concept of **dimension** is more abstract than that of units, which are standard quantities of the particular dimension in question.

### Examples

- Displacement has dimension $L$.

- Velocity has dimension $L T^{-1}$ (change in displacement, that is length traveled, per unit of time).

- Acceleration has dimension $L T^{-2}$ (change in velocity per unit of time).

- Force has dimension $M L T^{-2}$ (mass times acceleration, from Newton's Second Law of Motion).

## Sources

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