diff --git a/src/graphomotor/features/trails/drawing_metrics.py b/src/graphomotor/features/trails/drawing_metrics.py
index 752287c..98a2a80 100644
--- a/src/graphomotor/features/trails/drawing_metrics.py
+++ b/src/graphomotor/features/trails/drawing_metrics.py
@@ -1,5 +1,8 @@
 """Feature extraction module for drawing error-based metrics in trails drawing data."""
 
+import numpy as np
+import pandas as pd
+
 from graphomotor.core import models
 
 
@@ -35,9 +38,54 @@ def percent_accurate_paths(drawing: models.Drawing) -> dict[str, float]:
         raise ValueError(
             "DataFrame must contain 'correct_path' and 'actual_path' columns."
         )
-
     return {
         "percent_accurate_paths": (
             (drawing.data["correct_path"] == drawing.data["actual_path"]).mean() * 100
         )
     }
+
+
+def calculate_smoothness(points: pd.DataFrame) -> float:
+    """Calculate path smoothness based on Root Mean Square (RMS) curvature.
+
+    Represents the curvature per unit arc length.
+    Lower values indicate smoother drawings. Penalizes sharp corners (e.g., 90° turns)
+    and noisy corrections. Normalized by arc length to reduce sampling-rate dependence.
+
+    Args:
+        points: DataFrame representing drawing points.
+
+    Returns:
+        Smoothness metric as a float.
+    """
+    if len(points) < 3:
+        return 0.0
+
+    xy = points[["x", "y"]].to_numpy()
+
+    forward_vector = xy[1:-1] - xy[:-2]
+    backward_vector = xy[2:] - xy[1:-1]
+
+    forward_norm = np.linalg.norm(forward_vector, axis=1)
+    backward_norm = np.linalg.norm(backward_vector, axis=1)
+
+    valid = (forward_norm > 0) & (backward_norm > 0)
+    if not np.any(valid):
+        return 0.0
+
+    valid_forward_vector = forward_vector[valid]
+    valid_backward_vector = backward_vector[valid]
+    valid_forward_norm = forward_norm[valid]
+    valid_backward_norm = backward_norm[valid]
+
+    cos_angle = (valid_forward_vector * valid_backward_vector).sum(axis=1) / (
+        valid_forward_norm * valid_backward_norm
+    )
+    cos_angle = np.clip(cos_angle, -1.0, 1.0)
+
+    angles = np.arccos(cos_angle)
+
+    avg_segment_length = (valid_forward_norm + valid_backward_norm) / 2.0
+    curvatures = angles / avg_segment_length
+
+    return float(np.sqrt(np.mean(curvatures**2)))
diff --git a/tests/unit/test_trails_drawing_metrics.py b/tests/unit/test_trails_drawing_metrics.py
index cd87758..19e13ad 100644
--- a/tests/unit/test_trails_drawing_metrics.py
+++ b/tests/unit/test_trails_drawing_metrics.py
@@ -1,5 +1,6 @@
 """Test cases for drawing_metrics.py functions."""
 
+import numpy as np
 import pandas as pd
 import pytest
 
@@ -52,3 +53,64 @@ def test_percent_accurate_paths_sample_data() -> None:
 
     result = drawing_metrics.percent_accurate_paths(drawing)
     assert result == {"percent_accurate_paths": 100.0}
+
+
+def test_smoothness_less_than_three_points() -> None:
+    """Less than 3 points cannot define curvature."""
+    points = pd.DataFrame({"x": [0, 1], "y": [0, 1]})
+    assert drawing_metrics.calculate_smoothness(points) == 0.0
+
+
+def test_smoothness_straight_line() -> None:
+    """Collinear points have zero curvature."""
+    points = pd.DataFrame({"x": [0, 1, 2, 3], "y": [0, 0, 0, 0]})
+    assert drawing_metrics.calculate_smoothness(points) == 0.0
+
+
+def test_smoothness_single_right_angle() -> None:
+    """A single 90-degree corner should produce a large smoothness value.
+
+    (non-zero), since sharp turns are penalized.
+    """
+    points = pd.DataFrame({"x": [0, 1, 1], "y": [0, 0, 1]})
+    expected = np.pi / 2
+    smoothness = drawing_metrics.calculate_smoothness(points)
+    assert np.isclose(smoothness, expected)
+
+
+def test_smoothness_varied_angles() -> None:
+    """Multiple angles should produce RMS curvature.
+
+    Path has a 90° turn followed by a 45° turn.
+    """
+    points = pd.DataFrame({"x": [0, 1, 1, 2], "y": [0, 0, 1, 2]})
+    c1 = np.pi / 2
+    c2 = (np.pi / 4) / ((1 + np.sqrt(2)) / 2)
+    expected = np.sqrt((c1**2 + c2**2) / 2)
+
+    smoothness = drawing_metrics.calculate_smoothness(points)
+
+    assert np.isclose(smoothness, expected)
+
+
+def test_smoothness_zero_length_segments() -> None:
+    """Zero-length segments should be skipped; no angles → smoothness 0."""
+    points = pd.DataFrame({"x": [0, 1, 1, 2], "y": [0, 0, 0, 0]})
+    smoothness = drawing_metrics.calculate_smoothness(points)
+    assert smoothness == 0.0
+
+
+def test_smoothness_single_180_degree_turn() -> None:
+    """A single 180-degree turn should produce a very large smoothness value.
+
+    Since it represents maximal curvature.
+    """
+    points = pd.DataFrame(
+        {
+            "x": [0, 1, 0],
+            "y": [0, 0, 0],
+        }
+    )
+    expected = np.pi
+    smoothness = drawing_metrics.calculate_smoothness(points)
+    assert np.isclose(smoothness, expected)