diff --git a/make.py b/make.py
index 146a525ea..409ca0d3b 100755
--- a/make.py
+++ b/make.py
@@ -14,6 +14,7 @@
 
 import os
 import subprocess
+import sys
 from contextlib import contextmanager
 from pathlib import Path
 from shutil import rmtree, which
@@ -216,6 +217,8 @@ def docs_full():
     run_doc([SPHINX_BUILD, DOC_DIR, "build", "-W"])
     print()
     print("Build finished")
+    # Sphinx doesn't check plain links, such as a figure's :target:
+    run_doc([sys.executable, "util/check_internal_links.py", "build"])
 
 
 @app.command(rich_help_panel="Docs")
diff --git a/util/check_internal_links.py b/util/check_internal_links.py
new file mode 100644
index 000000000..5ef2cbebc
--- /dev/null
+++ b/util/check_internal_links.py
@@ -0,0 +1,88 @@
+"""
+Check a built copy of the docs for links to pages, files or anchors that
+don't exist.
+
+Sphinx's nitpicky mode catches broken cross-references such as ``:ref:``
+and ``:py:class:``, but not plain links, such as a figure's ``:target:``
+or a named link written without its trailing underscore. This checks the
+HTML Sphinx wrote instead. It doesn't check links to other sites.
+
+Usage::
+
+    python util/check_internal_links.py build
+
+Exits with status 1 if it finds broken links.
+"""
+
+import os
+import re
+import sys
+from collections import defaultdict
+from pathlib import Path
+from urllib.parse import unquote, urldefrag
+
+LINK_RE = re.compile(r'(?:href|src)="([^"]+)"')
+ID_RE = re.compile(r'id="([^"]+)"')
+EXTERNAL_PREFIXES = ("http:", "https:", "mailto:", "data:", "javascript:", "//")
+# Generated by Sphinx, and full of links to every page
+SKIPPED = ("_modules/", "_static/", "_sources/", "genindex.html", "search.html")
+
+
+def find_broken_links(root: Path) -> dict[str, list[str]]:
+    """Return {link: [pages it's on]} for links that go nowhere."""
+    # Every page repeats the sidebar, so the same link from the same folder
+    # comes up hundreds of times. Check each one once.
+    link_ok: dict[tuple[str, str], bool] = {}
+    ids: dict[str, set[str]] = {}
+    broken: dict[str, list[str]] = defaultdict(list)
+
+    def is_ok(page: str, folder: str, link: str) -> bool:
+        url, anchor = urldefrag(unquote(link))
+        url = url.split("?")[0]  # Cache-busting such as ?v=1234
+        # normpath, not Path.resolve(), which can hang on Windows
+        target = os.path.normpath(os.path.join(folder, url)) if url else page
+        if not os.path.exists(target):
+            return False
+        if anchor and target.endswith(".html"):
+            if target not in ids:
+                with open(target, encoding="utf-8", errors="replace") as file:
+                    ids[target] = set(ID_RE.findall(file.read()))
+            return anchor in ids[target]
+        return True
+
+    for path in sorted(root.rglob("*.html")):
+        name = path.relative_to(root).as_posix()
+        if name.startswith(SKIPPED):
+            continue
+        page = str(path)
+        folder = os.path.dirname(page)
+        links = set(LINK_RE.findall(path.read_text(encoding="utf-8", errors="replace")))
+        for link in links:
+            if link.startswith(EXTERNAL_PREFIXES):
+                continue
+            # An anchor-only link depends on the page, not just the folder
+            key = (page if link.startswith("#") else folder, link)
+            if key not in link_ok:
+                link_ok[key] = is_ok(page, folder, link)
+            if not link_ok[key]:
+                broken[link].append(name)
+    return broken
+
+
+def main() -> int:
+    root = Path(sys.argv[1] if len(sys.argv) > 1 else "build")
+    if not root.is_dir():
+        print(f"No built docs at {root}")
+        return 1
+    broken = find_broken_links(root)
+    if not broken:
+        print("No broken internal links")
+        return 0
+    print(f"{len(broken)} broken internal links:")
+    for link, pages in sorted(broken.items()):
+        print(f"  {link}  (in {', '.join(pages[:3])}{', ...' if len(pages) > 3 else ''})")
+    return 1
+
+
+if __name__ == "__main__":
+    sys.exit(main())