As the TeX Book says (p. 63)
From TeX's viewpoint, a single character from a font is a box [...]
The character shape need not fit inside the boundaries of its box.
Here we have such a situation: the \leftarrow is larger than the box, as the following snippet shows
\documentclass{article}
\begin{document}
\mathsurround0pt % for safety
\fboxsep-.1pt
\fboxrule.1pt
\fbox{$\leftarrow$}
\end{document}

However, standalone doesn't know that, so we must force it to consider a somewhat larger box. One easy way is to insert some vertical phantom, like \vphantom{A} or even a simple \strut. Alternatively, the standalone class accepts an optional argument border with syntax
border=〈length (all sides)〉
border={〈length (left/right)〉 〈length (bottom/top)〉}
border={〈length (left)〉 〈length (right)〉 〈length (bottom)〉 〈length (top)〉}
So in this case one might use
\documentclass[border=2pt]{standalone}
or
\documentclass[border={0pt 0pt 0pt 2pt}]{standalone}
if you want the border only above.
\vphantomwill do the work... ortotalheightoffromcalcpackage... – koleygr Aug 31 '17 at 12:47\vphantomwould work too;\strutis even simpler. But sometimes you have glyphs that protrude horizontally out of the box, so an overall border is in my opinion the easiest way to cover all cases. – campa Aug 31 '17 at 12:53border={0pt 0pt 0pt 2pt}(left right bottom top) to only add those 2pt at the top. – Torbjørn T. Aug 31 '17 at 14:02