Difference between units and dimensions

The difference is quite subtle and of little practical importance if done accordingly.

The difference is that a unit incorporates a property of scale while dimension doesn't. For example in the case of length it could be measured in meters, decimeters or kilometers, but nevertheless the dimension is length.

If you use unit-analysis instead of dimensional analysis you would have to take into account that different units of length only differs by a (dimensionless) constant.


You would say speed has dimensions of distance / time. Checking that a formula has the right dimensions is always a good check on a calculation. Units are the choice which has been made to quantify a dimension, e.g. distance in cubits or mega-parsecs.


I think there is no difference between dimension and unit in your case. They can be used interchangeably. However, the same word "dimension" is also used in another context, namely, describing the amount of numbers needed to describe a point in your space uniquely. These two use cases should not be confused. They are very different.

For example, the space we live in is 3-dimensional. This means we describe a point inside by giving three values of the dimension (= unit) [M].

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Unit Of Measure

Dimensional Analysis

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