# How to create fractional SI units (\SI{...}{\sqrt{s}})?

I want to express a variable that has "square root units", i.e. 0.8e-3 m/sec^1.5.

I have tried to use the SI package:

\SI{0.8e-3}{\radian\per\second\sqrt{\second}}


However, this does not work. It only works in cases like this:

\SI{42}{\second}


Is there a good way of expressing "square root units" or similar? Or is it necessary to use a workaround like:

\num{0.87e-5}\,$\mathrm{m}/\mathrm{s}\sqrt{\mathrm{s}}$


Arbitrary powers can be given using \tothe:

\documentclass{article}
\usepackage{siunitx}
\begin{document}

\SI[per-mode = symbol]{0.87e-5}{\metre\per\second\tothe{1.5}}

\end{document}


• I took a liberty and add image produced by your code (+1). Commented Sep 21, 2019 at 8:10

I've had to deal with noise figure calculations in the past, where things are often expressed in volts per square-root-hertz. Because this was the only fractional power unit I ever used, I just declared:

\DeclareSIUnit{\sqrthertz}{\sqrt{\unit{\hertz}}}


which I would use as:

\SI[per-mode=symbol]{20}{\volt\per\sqrthertz}


In your case you could write:

\SI[per-mode=symbol]{0.87e-5}{{\metre\per\second}\sqrthertz}


assuming that the unit Hertz makes sense in your case. You could define $\sqrtsecond$ instead.

I admit it's not a generic solution. But since fractional units are not that common, maybe you don't need one.