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I use the following document class

\documentclass[11pt,a4paper,twoside]{scrbook}

with default header and footer (chapter/section in header and the page number in the footer)

My problem is, that the ratio between the margin of the header and the footer is not 1:2 when considering the header but not considering the footer. It is always 1:2 considering header and footer. I already tested the commands headinclude and footexclude, but it did not solve the problem.

Does somebody have an idea how to solve this issue?

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I can't reproduce your "issue". Compare the following examples (the second one features the headinclude class option):

\documentclass[11pt,a4paper,twoside]{scrbook}

\usepackage{showframe}% just for the example

\usepackage{lipsum}

\begin{document}

\chapter{foo}

\section{foobar}

\lipsum[1-12]

\end{document}

\documentclass[11pt,a4paper,twoside,headinclude]{scrbook}

\usepackage{showframe}% just for the example

\usepackage{lipsum}

\begin{document}

\chapter{foo}

\section{foobar}

\lipsum[1-12]

\end{document}

Output (page 2) of both examples:

enter image description here

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