diff --git a/finance/app/engine/pie.py b/finance/app/engine/pie.py
new file mode 100644
index 0000000..9d23832
--- /dev/null
+++ b/finance/app/engine/pie.py
@@ -0,0 +1,75 @@
+"""Tortendiagramm-Segmente (Ausbaustufe 13), rein.
+
+Beträge und Anteile bleiben Decimal; nur die Geometrie (Winkel, SVG-
+Koordinaten im Einheitskreis) rechnet mit float. Start 12 Uhr, im
+Uhrzeigersinn (SVG-y zeigt nach unten).
+"""
+import math
+from dataclasses import dataclass
+from decimal import ROUND_HALF_UP, Decimal
+
+UEBRIGE = "Übrige"
+MIN_SHARE = Decimal("0.03")
+MAX_NAMED = 8
+PCT = Decimal("0.1")
+
+
+@dataclass(frozen=True)
+class Slice:
+    label: str
+    value: Decimal
+    share: Decimal            # Prozent der Tortenbasis, eine Nachkommastelle
+    path: str | None          # SVG-d; None = Vollkreis (einziges Segment)
+    color: str                # "s1".."s8", "uebrige", "frei"
+    merged: bool
+    members: tuple[str, ...]
+    start: float              # Anteil 0..1
+    end: float
+
+
+def _point(fraction: float) -> tuple[float, float]:
+    angle = 2 * math.pi * fraction - math.pi / 2
+    return math.cos(angle), math.sin(angle)
+
+
+def _arc(start: float, end: float) -> str:
+    x0, y0 = _point(start)
+    x1, y1 = _point(end)
+    large = 1 if end - start > 0.5 else 0
+    return f"M 0 0 L {x0:.4f} {y0:.4f} A 1 1 0 {large} 1 {x1:.4f} {y1:.4f} Z"
+
+
+def pie_slices(values: list[tuple[str, Decimal]], rest: Decimal | None = None,
+               rest_label: str = "", min_share: Decimal = MIN_SHARE,
+               max_named: int = MAX_NAMED) -> list[Slice]:
+    items = sorted(((l, v) for l, v in values if v > 0), key=lambda lv: (-lv[1], lv[0]))
+    rest = rest if rest is not None and rest > 0 else None
+    total = sum((v for _, v in items), Decimal("0")) + (rest or Decimal("0"))
+    if total <= 0:
+        return []
+    named: list[tuple[str, Decimal]] = []
+    small: list[tuple[str, Decimal]] = []
+    for label, value in items:
+        if len(named) < max_named and value / total >= min_share:
+            named.append((label, value))
+        else:
+            small.append((label, value))
+    parts = [(l, v, f"s{i}", False, ()) for i, (l, v) in enumerate(named, 1)]
+    if len(small) == 1:
+        parts.append((small[0][0], small[0][1], "uebrige", False, ()))
+    elif small:
+        parts.append((UEBRIGE, sum((v for _, v in small), Decimal("0")), "uebrige",
+                      True, tuple(l for l, _ in small)))
+    if rest is not None:
+        parts.append((rest_label, rest, "frei", False, ()))
+    slices: list[Slice] = []
+    acc = Decimal("0")
+    for label, value, color, merged, members in parts:
+        start = float(acc / total)
+        acc += value
+        end = float(acc / total)
+        slices.append(Slice(label, value,
+                            (value * 100 / total).quantize(PCT, ROUND_HALF_UP),
+                            None if len(parts) == 1 else _arc(start, end),
+                            color, merged, members, start, end))
+    return slices
diff --git a/finance/tests/test_pie.py b/finance/tests/test_pie.py
new file mode 100644
index 0000000..7657d1f
--- /dev/null
+++ b/finance/tests/test_pie.py
@@ -0,0 +1,76 @@
+from decimal import Decimal
+
+import pytest
+
+from app.engine.pie import UEBRIGE, pie_slices
+
+D = Decimal
+
+
+def test_leer_und_nullwerte():
+    assert pie_slices([]) == []
+    assert pie_slices([("A", D("0")), ("B", D("-5"))]) == []
+
+
+def test_segmente_lueckenlos_und_anteile():
+    sl = pie_slices([("C", D("20")), ("A", D("50")), ("B", D("30"))])
+    assert [s.label for s in sl] == ["A", "B", "C"]
+    assert [s.color for s in sl] == ["s1", "s2", "s3"]
+    assert [s.share for s in sl] == [D("50.0"), D("30.0"), D("20.0")]
+    assert sl[0].start == 0.0 and sl[-1].end == pytest.approx(1.0)
+    for a, b in zip(sl, sl[1:]):
+        assert a.end == pytest.approx(b.start)
+    assert sl[0].path.startswith("M 0 0 L 0.0000 -1.0000 A 1 1 0 0 1 ")
+
+
+def test_large_arc_flag():
+    a, b = pie_slices([("A", D("70")), ("B", D("30"))])
+    assert " A 1 1 0 1 1 " in a.path
+    assert " A 1 1 0 0 1 " in b.path
+
+
+def test_einzelsegment_ist_vollkreis():
+    (s,) = pie_slices([("A", D("12.34"))])
+    assert s.path is None and s.share == D("100.0") and s.color == "s1"
+
+
+def test_kleine_werte_zu_uebrige():
+    sl = pie_slices([("A", D("95")), ("B", D("2")), ("C", D("2")), ("D", D("1"))])
+    assert [s.label for s in sl] == ["A", UEBRIGE]
+    u = sl[1]
+    assert (u.value, u.color, u.merged, u.members) == (D("5"), "uebrige", True, ("B", "C", "D"))
+
+
+def test_einzelner_kleiner_wert_behaelt_namen():
+    sl = pie_slices([("A", D("98")), ("B", D("2"))])
+    assert [(s.label, s.color, s.merged) for s in sl] == [("A", "s1", False), ("B", "uebrige", False)]
+
+
+def test_hoechstens_acht_benannte_segmente():
+    sl = pie_slices([(f"K{i}", D("10")) for i in range(10)], rest=D("5"),
+                    rest_label="Frei verfügbar")
+    assert [s.color for s in sl] == ["s1", "s2", "s3", "s4", "s5", "s6", "s7", "s8",
+                                     "uebrige", "frei"]
+    assert sl[-2].merged and sl[-2].members == ("K8", "K9")
+
+
+def test_acht_kategorien_ohne_uebrige():
+    sl = pie_slices([(f"K{i}", D("10")) for i in range(8)])
+    assert [s.color for s in sl] == [f"s{i}" for i in range(1, 9)]
+    assert not any(s.merged for s in sl)
+
+
+def test_rest_wird_nie_zusammengefasst():
+    sl = pie_slices([("A", D("99.5"))], rest=D("0.5"), rest_label="Frei verfügbar")
+    assert [(s.label, s.color, s.merged) for s in sl] == [("A", "s1", False), ("Frei verfügbar", "frei", False)]
+    assert sl[1].share == D("0.5")
+
+
+def test_nur_rest_ist_vollkreis():
+    (s,) = pie_slices([], rest=D("100"), rest_label="Frei verfügbar")
+    assert (s.label, s.color, s.path) == ("Frei verfügbar", "frei", None)
+
+
+def test_rest_none_oder_null_ignoriert():
+    assert len(pie_slices([("A", D("1"))], rest=None)) == 1
+    assert len(pie_slices([("A", D("1"))], rest=D("0"), rest_label="X")) == 1