diff --git a/src/highdicom/spatial.py b/src/highdicom/spatial.py
index 043f6eb0..97d01d37 100644
--- a/src/highdicom/spatial.py
+++ b/src/highdicom/spatial.py
@@ -3859,19 +3859,24 @@ def get_volume_positions(
             (origin_distances - origin_distances.min()) / spacing
         )
 
-        is_regular = np.allclose(
-            origin_distance_multiples,
-            origin_distance_multiples.round(),
-            rtol=rtol,
-            atol=atol,
+        # Deviations are measured in mm, against the position each slice would
+        # occupy if it sat exactly on its integer multiple of the spacing.
+        # Comparing the multiples themselves would make the tolerances mean
+        # "fractions of a slice" here but "mm" in the branch below, so the same
+        # 'atol' would accept a larger physical error the wider the spacing.
+        expected_distances = (
+            origin_distance_multiples.round() * spacing +
+            origin_distances.min()
         )
+        deviations = np.abs(origin_distances - expected_distances)
+
+        # 'rtol' is relative to the slice spacing, matching its meaning in the
+        # regularly-spaced branch below, where each spacing is compared with
+        # the nominal spacing.
+        tolerance = atol + rtol * abs(spacing)
+        is_regular = bool((deviations <= tolerance).all())
         if not is_regular:
-            max_deviation = float(
-                np.abs(
-                    origin_distance_multiples -
-                    origin_distance_multiples.round()
-                ).max()
-            )
+            max_deviation = float(deviations.max())
             logger.info("Frame positions are not regularly spaced.")
             logger.debug(
                 f"Maximum spacing deviation from regular: {max_deviation:.2e} "
diff --git a/tests/test_spatial.py b/tests/test_spatial.py
index 8b46b411..72c95696 100644
--- a/tests/test_spatial.py
+++ b/tests/test_spatial.py
@@ -1047,6 +1047,46 @@ def test_get_volume_positions_missing():
     assert volume_positions is None
 
 
+def test_get_volume_positions_missing_tolerance_units():
+    # 'atol' is documented in mm and must mean the same thing whatever the
+    # slice spacing is, including when missing slices are allowed. Previously
+    # the deviation was measured in multiples of the spacing, so the same
+    # physical error was accepted at wide spacings and rejected at narrow ones.
+    orientation = [1.0, 0.0, 0.0, 0.0, 1.0, 0.0]
+    error = 0.5  # mm, out of place by more than atol below
+
+    for spacing in [1.0, 5.0, 10.0, 20.0]:
+        positions = [
+            [0.0, 0.0, 0.0],
+            [0.0, 0.0, spacing],
+            [0.0, 0.0, 2 * spacing + error],
+        ]
+        out_spacing, volume_positions = get_volume_positions(
+            positions,
+            orientation,
+            allow_missing_positions=True,
+            atol=0.1,
+        )
+        assert out_spacing is None
+        assert volume_positions is None
+
+    # A deviation smaller than 'atol' remains acceptable at every spacing
+    for spacing in [1.0, 5.0, 10.0, 20.0]:
+        positions = [
+            [0.0, 0.0, 0.0],
+            [0.0, 0.0, spacing],
+            [0.0, 0.0, 2 * spacing + 0.05],
+        ]
+        out_spacing, volume_positions = get_volume_positions(
+            positions,
+            orientation,
+            allow_missing_positions=True,
+            atol=0.1,
+        )
+        assert out_spacing is not None
+        assert volume_positions is not None
+
+
 def test_get_volume_positions_missing_duplicates():
     # Test ability to determine spacing and volume positions with missing
     # slices and duplicate positions