# How should I typeset the physical dimensions of quantities?

As an example: The Newton's Law gives

F=ma      vs.      dim F=MLT^{-2}


My question is: Should I typeset the "MLT" in \mathit shape?

You can contrast

$\mathit{LT}\mathit{LT}\mathit{LT}\mathit{LT}$
$\mathit{L}\mathit{T}\mathit{L}\mathit{T}\mathit{L}\mathit{T}\mathit{L}\mathit{T}$


the latter is more close together. Is there some tricks on using \mathit shape?

Or I should choose the \mathrm family, or even just the default math font?

• If M, L and T are variables, treat them just like you would m and a; as-is. Jun 30 '13 at 6:23
• As far as I know, dimensional quantities (I don't know if this is the correct word in English) as M, L, T in physics have to be typeset in upright shape. So you'd better use \mathrm for them. Jun 30 '13 at 6:34
• And anyway \mathit is more or less the same font used by default in math mode. See this thread for more details: \mathit spacing with \mathnormal font Jun 30 '13 at 6:38
• "Quantity symbols are always written in an italic font, and symbols for dimensions in sans-serif roman capitals" ([page 105] (bipm.org/utils/common/pdf/si_brochure_8.pdf)). Sep 6 '13 at 11:25
• Use the siunitx package?
– user10274
Sep 9 '13 at 11:17

Both, the SI-Brochure nr. 8 (section 1.3, p. 105) and DIN EN ISO 80000-1:2012-10 (chapter 5, p. 19) use upright capital and sans-serif letters for this.

Quantity symbols are always written in an italic font, and symbols for dimensions in sans-serif roman capitals - SI-Brochure

Therefore you should write dimensions of quantities like this:

% arara: lualatex

\documentclass{article}
\usepackage{mathtools}
\usepackage[%
,math-style=ISO
,bold-style=ISO
,sans-style=italic
]{unicode-math}

\begin{document}
$\dim Q = \mathsfup{L}^\alpha \mathsfup{M}^\beta \mathsfup{T}^\gamma \mathsfup{I}^\delta \mathup{\Theta}^\varepsilon \mathsfup{N}^\zeta \mathsfup{J}^\eta$
\end{document}


This yields:

Unfortunately, there is no sans-serif font for medium-weight Greek letters in the range of uni-code characters. But if you normally use italic capital Greeks in your document (math-style=ISO), it will be distinguishable.

Three other remarks on your OP:

• Your two examples for $\mathit{LT}$ and $\mathit{L}\mathit{T}$ should (and do) look the same.
• The default math font normally yields the same as \mathit{...}.
• Before I edited your question, you wrote: "[F]=MLT^{-2}". Please note that [Q] means "the unit of Q". {Q} would signify "the value of Q" and for your case, it should be dim Q. $Q = \{Q\}\cdot[Q] \wedge \dim Q = \mathsfup{L}^\alpha \dots$.

• Shouldn't it be [X]=\mathsfup{L}? The operator \dim has a different meaning. Sep 9 '13 at 9:41
• You refer to the dimension of a vector space? I am not into that anymore, seems to be the same operator. But ISO and SI both use it in this place, too. [X] is the unit of X. Sep 9 '13 at 10:28
• @egreg any idea on how to get an \mathsfup{\Theta}? The more I look at it, the less I like the serifs here. Sep 9 '13 at 10:43
• For information on the different conventions for the symbol [X], see Square bracket notation for dimensions and units: usage and conventions at Physics.SE.
– E.P.
Sep 18 '13 at 10:07