LaTeX template for a single formula.

formula.tex

\documentclass[10pt]{article}
\pagestyle{empty}
\setlength{\topskip}{0pt}
\setlength{\parindent}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}

\usepackage[T1]{fontenc}

\usepackage{geometry}
\usepackage{xstring}

\usepackage{amsmath}

\newsavebox{\snippetbox}
\newlength{\snippetwidth}
\newlength{\snippetheight}
\newlength{\snippetdepth}
\newlength{\pagewidth}
\newlength{\pageheight}
\newlength{\pagelmargin}
\newlength{\pagetmargin}
\newlength{\pagermargin}
\newlength{\pagebmargin}

\begin{lrbox}{\snippetbox}
$\displaystyle F_n=\frac{\left(1+\sqrt{5}\right)^n-\left(1-\sqrt{5}\right)^n}{2^n\sqrt{5}}$
\end{lrbox}

\settowidth{\snippetwidth}{\usebox{\snippetbox}}
\settoheight{\snippetheight}{\usebox{\snippetbox}}
\settodepth{\snippetdepth}{\usebox{\snippetbox}}

\setlength\pagelmargin{4pt}
\setlength\pagetmargin{4pt}
\setlength\pagermargin{4pt}
\setlength\pagebmargin{4pt}

\setlength\pagewidth\snippetwidth
\addtolength\pagewidth\pagelmargin
\addtolength\pagewidth\pagermargin

\setlength\pageheight\snippetheight
\addtolength{\pageheight}{\snippetdepth}
\addtolength\pageheight\pagetmargin
\addtolength\pageheight\pagebmargin

\newwrite\foo
\immediate\openout\foo=\jobname.json
% https://latex.org/forum/viewtopic.php?t=5180
\begingroup 
   \catcode`\[ = 1\relax
   \catcode`\] = 2\relax
   \catcode`\{ = 12\relax
   \catcode`\} = 12 \relax 
   \gdef\OpenBrace[{]
   \gdef\CloseBrace[}]
\endgroup
  \immediate\write\foo{\OpenBrace}
  \immediate\write\foo{  "snippetdepth": "\the\snippetdepth",}
  \immediate\write\foo{  "snippetheight": "\the\snippetheight",}
  \immediate\write\foo{  "snippetwidth": "\the\snippetwidth",}
  \immediate\write\foo{  "pagewidth": "\the\pagewidth",}
  \immediate\write\foo{  "pageheight": "\the\pageheight",}
  \immediate\write\foo{  "pagelmargin": "\the\pagelmargin",}
  \immediate\write\foo{  "pagermargin": "\the\pagermargin",}
  \immediate\write\foo{  "pagetmargin": "\the\pagetmargin",}
  \immediate\write\foo{  "pagebmargin": "\the\pagebmargin"}
  \immediate\write\foo{\CloseBrace}
\closeout\foo

\geometry{paperwidth=\pagewidth,paperheight=\pageheight,lmargin=\pagelmargin,tmargin=\pagetmargin,rmargin=\pagermargin,bmargin=\pagebmargin}

\begin{document}
\usebox{\snippetbox}
\end{document}