diff --git a/spatialmath/geom3d.py b/spatialmath/geom3d.py
index c1efbbb2..a1921abf 100644
--- a/spatialmath/geom3d.py
+++ b/spatialmath/geom3d.py
@@ -638,14 +638,16 @@ def contains(
         the Line3 object self.
 
         If ``X`` is an array with 3 rows, the test is performed on every column and
-        an array of booleans is returned.
+        an array of booleans is returned. The tolerance applies to perpendicular
+        distance, independent of the scale of the Plucker coordinates.
         """
+        direction = self.w / np.linalg.norm(self.w)
         if base.isvector(x, 3):
             x = cast(R3, base.getvector(x))
-            return bool(np.linalg.norm(np.cross(x - self.pp, self.w)) < tol * _eps)
+            return bool(np.linalg.norm(np.cross(x - self.pp, direction)) < tol * _eps)
         elif base.ismatrix(x, (3, None)):
             return [
-                bool(np.linalg.norm(np.cross(p - self.pp, self.w)) < tol * _eps)
+                bool(np.linalg.norm(np.cross(p - self.pp, direction)) < tol * _eps)
                 for p in x.T
             ]
         else:
diff --git a/tests/test_line_contains_scale.py b/tests/test_line_contains_scale.py
new file mode 100644
index 00000000..5effdb62
--- /dev/null
+++ b/tests/test_line_contains_scale.py
@@ -0,0 +1,38 @@
+"""Point containment must not depend on homogeneous Plucker scale."""
+
+import numpy as np
+import numpy.testing as nt
+import pytest
+from spatialmath import Line3
+
+
+@pytest.mark.parametrize("direction", [[1, 0, 0], [0, 1, 0], [1, 2, -1]])
+@pytest.mark.parametrize("scale", [1.0, -1.0, 1e-8, -1e-8, 1e8])
+def test_contains_scalar_and_batch_are_scale_invariant(direction, scale):
+    direction = np.asarray(direction, dtype=float)
+    normal = np.cross(direction, [0, 0, 1])
+    normal /= np.linalg.norm(normal)
+    origin = np.array([1.0, 2.0, 3.0])
+    line = Line3.PointDir(origin, scale * direction)
+    direction /= np.linalg.norm(direction)
+    # Far outside tolerance even for the translated/oblique lines.
+    on_line = origin + 2 * direction
+    off_line = on_line + 1e-8 * normal
+    assert line.contains(on_line, tol=100)
+    assert not line.contains(off_line, tol=100)
+    nt.assert_array_equal(
+        line.contains(np.column_stack([on_line, off_line]), tol=100), [True, False]
+    )
+
+
+@pytest.mark.parametrize("scale", [1.0, -1.0, 1e-8, 1e8])
+def test_contains_tolerance_is_a_geometric_distance(scale):
+    line = Line3.PointDir([0, 0, 0], [scale, 0, 0])
+    eps = np.finfo(float).eps
+    assert line.contains([1, 10 * eps, 0], tol=20)
+    assert not line.contains([1, 30 * eps, 0], tol=20)
+    assert line.contains([1, 30 * eps, 0], tol=40)
+    nt.assert_array_equal(
+        line.contains(np.array([[1, 1], [10 * eps, 30 * eps], [0, 0]]), tol=20),
+        [True, False],
+    )