Define the height of text in cm

Question

I know the question I am going to ask is similar to others posted here. However, I still can not find the right answer. I have checked:

How to export a math formula with a beautiful, high resolution font for a tattoo?

What measure in the text is it that is the font size?

What is the local height of a capital letter?

\settoheight is slightly shorter than actual height

Down to business, I want to get a tattoo with Eulers' identity. So I want to be sure of the height of the text.

And basically that is my question, how to set the height of the text to a specific height (in this case probably fron the baseline to the ascender) in cm, say 1 cm.

Here is what I have done so far:

\documentclass{standalone}
\usepackage{xcolor}
\usepackage{tikz}
\usepackage{adjustbox}

\begin{document}
\begin{tikzpicture}
 \draw[red,line width = 1mm] (0,0)--node[color=black,left](T) { \adjustbox{scale=3}{
$\displaystyle e^{i \pi} + 1 = 0$
}} (0,1cm);
\draw[red] (0,0)--(-6cm,0);
\draw[red] (0,1)--++(-6cm,0);
\end{tikzpicture}
\end{document}

Here I am getting approx. the height I want, but basically I am just working around the problem for the solution, instead of doing it right. I draw a vertical line of height 1 cm, and two other horizontal lines, on the base and upper part. Then, after tweaking around with the value of the scale in the adjust box, I get something similar to what I am looking for.

But once again, Is there any other way (direct, efficient, or simple better) to get the desire result?

Thanks in advance for your contribution!

Editing 1:
I have one additional question: In either my solution as with the @pascal974 s, the plus sign is lower than the baseline.
Is there a way to move up the + such that it stays above the baseline?

I tried by wrapping the + sign in scriptstyle:

$e^{i \pi}\, {\scriptstyle + } \,1 = 0$

But this command just makes the sign smaller, placing it a the same "ground".

Cheers!

Answer 1

With {adjustbox}{totalheight=..} 3cm in my example.

    \documentclass{article}
    \usepackage{tikz}
    \usepackage{adjustbox}

    \begin{document}
    \newcommand{\h}{3cm}
    \begin{tikzpicture}
    \node [draw,inner sep =0pt] at (0,0){%
    \begin{adjustbox}{totalheight=\h}
            $e^{i \pi} + 1 = 0$
    \end{adjustbox}};
    \end{tikzpicture}\rule{1mm}{\h}
    \end{document}