pgfplots: Setting the exact geometry of a graph paper

Question

For the following, I would like to get an exact measurement of 10mm for both the right and left margins of the graph paper instead of 20 mm.

% https://tex.stackexchange.com/a/356984/2288
\documentclass{article}

\usepackage{pgfplots}
\usepackage{siunitx}

\usepackage[
a4paper , right = 10mm , left = 10mm , includeheadfoot, 
]{geometry}

\begin{document}
\pagestyle{empty}
\centering

% http://tex.stackexchange.com/a/15002/100384
\newcommand*{\getlength}[2]{%
   % Convert to `cm` and round to two fractional digits:
   \pgfmathsetmacro#1{round(0.0351459804*#2)}%
}

\vspace*{\fill}

\rotatebox{0}{
    \begin{tikzpicture}
        % a factor for measures, since pfplots produces slightly bigger images than defined
        %   in width/height. This can be used to adjust that problem manually
        \pgfmathsetmacro{\factor}{0.9}% 0.9

        % we will need some length in `cm`, without units, and rounded
        \getlength{\yMax}{\factor*\textheight}
        \getlength{\xMax}{\factor*\textwidth}

        \begin{axis}[
            set layers,
            width=\factor\textwidth, height=\factor\textheight,
            x = 1cm, y = 1cm,
            xtick={0,1,...,\xMax},
            ytick={0,1,...,\yMax},
            minor xtick={0,0.1,0.2,...,\xMax},
            minor ytick={0,0.1,0.2,...,\yMax},
            tick style = {line width = 0.6pt, black!40!white},
            minor tick style = {draw = none},
            major tick style = {draw = none},
            ticklabel style = {draw = none},
            xticklabels=\empty, %xlabel = \empty,
            yticklabels=\empty, %ylabel = \empty,
            axis line style = {-latex},
            grid = both,
            minor grid style={line width=0.2pt, black!20!white},
            major grid style={line width=0.6pt, black!60!white},
            ymin=0, ymax=\yMax,
            xmin=0, xmax=\xMax,
            ]
            \begin{pgfonlayer}{axis grid}
            \draw[line width=0.40pt, step=0.5cm, black!40!white] (axis cs: 0, 0) grid (axis cs: \xMax, \yMax);
            \end{pgfonlayer}
        \end{axis}
    \end{tikzpicture}
}

\vspace*{\fill}

\end{document}

---

Update

When editing @JohnKormylo's answer to have

\usepackage[
a4paper , right = 10mm , left = 10mm , 
top = 5 mm, headheight = 0 mm, headsep = 0 mm, 
foot = 0 mm, bottom = 5 mm, showframe
]{geometry}

the output has two issues:

1- the drawing is on the second page, while the first page is empty

2- the bottom margin is less than the specified value of 5 mm.

Answer 1

Since your page already has 1cm margins, I assume you want the graph paper to fill the text area (rounded to the nearest cm).

There is an automatic \vskip\topskip at the start of every page to set the first baseline.

The showframe option is for debugging/alignment only.

\documentclass{article}

\usepackage{pgfplots}
\usepackage{siunitx}

\usepackage[
a4paper , right = 10mm , left = 10mm , includeheadfoot, showframe
]{geometry}


% http://tex.stackexchange.com/a/15002/100384
\newcommand*{\getlength}[2]{%
   % Convert to `cm` and round to two fractional digits:
   \pgfmathsetmacro#1{round(0.0351459804*#2)}%
}
\pagestyle{empty}

\begin{document}
\vspace*{\fill}\vskip-\topskip
\centering
\begin{tikzpicture}
        % a factor for measures, since pfplots produces slightly bigger images than defined
        %   in width/height. This can be used to adjust that problem manually
        \pgfmathsetmacro{\factor}{1.0}% 0.9

        % we will need some length in `cm`, without units, and rounded
        \getlength{\yMax}{\factor*\textheight}
        \getlength{\xMax}{\factor*\textwidth}

        \begin{axis}[
            set layers,
            width=\factor\textwidth, height=\factor\textheight,
            scale only axis, name=border,
            x = 1cm, y = 1cm,
            xtick={0,1,...,\xMax},
            ytick={0,1,...,\yMax},
            minor xtick={0,0.1,0.2,...,\xMax},
            minor ytick={0,0.1,0.2,...,\yMax},
            tick style = {line width = 0.6pt, black!40!white},
            minor tick style = {draw = none},
            major tick style = {draw = none},
            ticklabel style = {draw = none},
            xticklabels=\empty, %xlabel = \empty,
            yticklabels=\empty, %ylabel = \empty,
            axis line style = {-latex},
            grid = both,
            minor grid style={line width=0.2pt, black!20!white},
            major grid style={line width=0.6pt, black!60!white},
            ymin=0, ymax=\yMax,
            xmin=0, xmax=\xMax,
            ]
        %\begin{pgfonlayer}{axis grid}% redundant
        %\draw[line width=0.40pt, step=0.5cm, black!40!white] (axis cs: 0, 0) grid (axis cs: \xMax, \yMax);
        %\end{pgfonlayer}
        \end{axis}
    \pgfresetboundingbox
    \path (border.south west) (border.north east);
    \draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
\end{tikzpicture}\vspace*{\fill}
\end{document}

---

This version puts the grid into a savebox, then places it at (current page.center) using [remember picture, overlay]. Be sure to run it twice.

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\usepackage{siunitx}

% http://tex.stackexchange.com/a/15002/100384
\newcommand*{\getlength}[2]{%
   % Convert to `cm` and round to two fractional digits:
   \pgfmathsetmacro#1{round(0.0351459804*#2)}%
}
\newsavebox{\gridbox}
\savebox\gridbox{\begin{tikzpicture}
    \pgfmathsetmacro{\width}{\paperwidth-2cm}
    \pgfmathsetmacro{\height}{\paperheight-2cm}
        % we will need some length in `cm`, without units, and rounded
        \getlength{\yMax}{\height}
        \getlength{\xMax}{\width}

        \begin{axis}[
            set layers,
            width=\width, height=\height,
            scale only axis, name=border,
            x = 1cm, y = 1cm,
            xtick={0,1,...,\xMax},
            ytick={0,1,...,\yMax},
            minor xtick={0,0.1,0.2,...,\xMax},
            minor ytick={0,0.1,0.2,...,\yMax},
            tick style = {line width = 0.6pt, black!40!white},
            minor tick style = {draw = none},
            major tick style = {draw = none},
            ticklabel style = {draw = none},
            xticklabels=\empty, %xlabel = \empty,
            yticklabels=\empty, %ylabel = \empty,
            axis line style = {-latex},
            grid = both,
            minor grid style={line width=0.2pt, black!20!white},
            major grid style={line width=0.6pt, black!60!white},
            ymin=0, ymax=\yMax,
            xmin=0, xmax=\xMax,
            ]
        %\begin{pgfonlayer}{axis grid}% redundant
        %\draw[line width=0.40pt, step=0.5cm, black!40!white] (axis cs: 0, 0) grid (axis cs: \xMax, \yMax);
        %\end{pgfonlayer}
        \end{axis}
    \pgfresetboundingbox
    \path (border.south west) (border.north east);
\end{tikzpicture}}

\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[remember picture, overlay]
  \node at (current page.center) {\usebox\gridbox};
\end{tikzpicture}
\end{document}