diff --git a/CMakeLists.txt b/CMakeLists.txt
index 293cc6e..6c2faa7 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -419,9 +419,33 @@ endif()
 # pkg-config file.  Vulkan goes in Requires.private (consumer's
 # pkg-config call gets it via --static).  pthread + dl are needed
 # by the static archive's runtime helpers.
+#
+# `prefix` is derived from ${pcfiledir} so the .pc is relocatable:
+# pkg-config substitutes ${pcfiledir} with the directory holding the
+# .pc at lookup time, and the relative path from
+# <prefix>/<libdir>/pkgconfig back to <prefix> tells pkg-config the
+# install prefix without baking it in.  This is why
+# `cmake --install build --prefix /foo` produces a .pc that correctly
+# resolves `prefix=/foo` instead of baking whatever CMAKE_INSTALL_PREFIX
+# was at *configure* time (default /usr/local).  DESTDIR-staged
+# installs work too: at runtime pkg-config sees the .pc at its real
+# install path and computes the right prefix.
+#
+# Relative-path depth is computed from CMAKE_INSTALL_LIBDIR (and
+# whatever multiarch tuple GNUInstallDirs adds) so Debian-style
+# `lib/aarch64-linux-gnu/pkgconfig/...` resolves with the right number
+# of `..` components.  Layouts where libdir is *not* under prefix are
+# not supported by this scheme; if a packager overrides libdir to an
+# absolute path the relative-path machinery falls back to the absolute
+# value (CMake's file(RELATIVE_PATH) prepends `..` until they meet),
+# which is also relocatable but no longer prefix-agnostic.
+file(RELATIVE_PATH PKGCONFIG_PCDIR_TO_PREFIX
+    "${CMAKE_INSTALL_PREFIX}/${CMAKE_INSTALL_LIBDIR}/pkgconfig"
+    "${CMAKE_INSTALL_PREFIX}")
+
 set(PKGCONFIG_OUT ${CMAKE_CURRENT_BINARY_DIR}/daedalus-fourier.pc)
 file(WRITE ${PKGCONFIG_OUT}
-"prefix=${CMAKE_INSTALL_PREFIX}
+"prefix=\${pcfiledir}/${PKGCONFIG_PCDIR_TO_PREFIX}
 exec_prefix=\${prefix}
 libdir=\${prefix}/${CMAKE_INSTALL_LIBDIR}
 includedir=\${prefix}/${CMAKE_INSTALL_INCLUDEDIR}