diff --git a/src/angst/test/test_points.py b/src/angst/test/test_points.py
index d106515..74b500e 100644
--- a/src/angst/test/test_points.py
+++ b/src/angst/test/test_points.py
@@ -67,3 +67,49 @@ def test_displace_abs(rng):
     cos_a = np.cos(th) * np.cos(th_) + np.cos(delt) * np.sin(th) * np.sin(th_)
 
     npt.assert_allclose(cos_a, np.cos(abs_alpha))
+
+
+def test_displacement(rng):
+    from textwrap import dedent
+    import angst
+
+    # unit changes for displacements
+    deg5 = np.radians(5.0)
+    north = np.exp(1j * 0.0)
+    east = np.exp(1j * (np.pi / 2))
+    south = np.exp(1j * np.pi)
+    west = np.exp(1j * (3 * np.pi / 2))
+
+    # test data: coordinates and expected displacement
+    data = [
+        # equator
+        (0.0, 0.0, 0.0, 5.0, deg5 * north),
+        (0.0, 0.0, -5.0, 0.0, deg5 * east),
+        (0.0, 0.0, 0.0, -5.0, deg5 * south),
+        (0.0, 0.0, 5.0, 0.0, deg5 * west),
+        # pole
+        (0.0, 90.0, 180.0, 85.0, deg5 * north),
+        (0.0, 90.0, -90.0, 85.0, deg5 * east),
+        (0.0, 90.0, 0.0, 85.0, deg5 * south),
+        (0.0, 90.0, 90.0, 85.0, deg5 * west),
+    ]
+
+    # test each displacement individually
+    for from_lon, from_lat, to_lon, to_lat, alpha in data:
+        alpha_ = angst.displacement(from_lon, from_lat, to_lon, to_lat)
+        assert np.allclose(alpha_, alpha), dedent(
+            f"""
+            displacement from ({from_lon}, {from_lat}) to ({to_lon}, {to_lat})
+            distance: expected {np.abs(alpha)}, got {np.abs(alpha_)}
+            direction: expected {np.angle(alpha)}, got {np.angle(alpha_)}
+            """
+        )
+
+    # test on an array
+    alpha = angst.displacement(
+        rng.uniform(-180.0, 180.0, size=(20, 1)),
+        rng.uniform(-90.0, 90.0, size=(20, 1)),
+        rng.uniform(-180.0, 180.0, size=5),
+        rng.uniform(-90.0, 90.0, size=5),
+    )
+    assert alpha.shape == (20, 5)