[Tex/LaTex] Get partly filled circle symbol scale linearly with parameter

Question

I want to create a \rating command that draws a partly filled circle, according to a numeric parameter between 0 and 100:

Question: How can I modify the expression for determining the angles in arc, so that the filling rises more steadily over the whole value range? Right now, ratings from 0 to 20 look empty, 80 to 100 look completely filled and only in between there is a steady rise.

Clarification: Rather than a mathematically rigoros expression, I am looking for the simplest expression that looks right, i.e. that \rating{25}, \rating{50} and \rating{75} visually look like 1/4, 2/4 and 3/4.

\documentclass{minimal}
\usepackage{tikz}

\newcommand{\rating}[1]{
\begin{tikzpicture}
\fill[lightgray] ({270-1.8*#1}:1ex) arc ({270-1.8*#1}:{270+1.8*#1}:1ex) -- cycle;
\draw[black, thin, radius=1ex] (0,0) circle;
\end{tikzpicture}}

\begin{document}
This really should scale\dots
\rating{0} \rating{10} \rating{20} \rating{30} \rating{40} \rating{50}
\rating{50} \rating{60} \rating{70} \rating{80} \rating{90} \rating{100}
\dots linearly.
\end{document}

Answer 1

As an aside, please see Why should the minimal class be avoided?

Here is a solution using a clipped path in TikZ. Note that the clip path cannot have extra options added, so I've drawn the circle with your specifications separately, outside the scope of the \clip path.

\documentclass{article}
\usepackage{tikz}

\newcommand{\rating}[1]{%
  \begin{tikzpicture}[x=1ex,y=1ex]
    \begin{scope}
      \clip (0,1) circle (1);
      \fill[lightgray] (-1,0) rectangle (1,#1/50);
    \end{scope}
    \draw[black, thin, radius=1] (0,1) circle;
  \end{tikzpicture}%
}

\begin{document}
This really should scale\dots
\foreach \h in {0,5,...,100} {\rating{\h}}
\dots linearly.
\end{document}