diff --git a/src/pyrecest/tracking/ellipse_geometry.py b/src/pyrecest/tracking/ellipse_geometry.py
index 163e55f63..489ca7230 100644
--- a/src/pyrecest/tracking/ellipse_geometry.py
+++ b/src/pyrecest/tracking/ellipse_geometry.py
@@ -37,7 +37,7 @@ def symmetrize(matrix):
     """Return the symmetric part of ``matrix``."""
 
     matrix = asarray(matrix)
-    return 0.5 * (matrix + matrix.T)
+    return 0.5 * matrix + 0.5 * matrix.T
 
 
 def project_symmetric_covariance(covariance, minimum_eigenvalue=0.0):
diff --git a/tests/tracking/test_ellipse_geometry_integer_overflow.py b/tests/tracking/test_ellipse_geometry_integer_overflow.py
new file mode 100644
index 000000000..9d5a9cdcb
--- /dev/null
+++ b/tests/tracking/test_ellipse_geometry_integer_overflow.py
@@ -0,0 +1,28 @@
+from __future__ import annotations
+
+import numpy as np
+import numpy.testing as npt
+from pyrecest.tracking import project_symmetric_covariance
+
+
+def test_covariance_projection_avoids_integer_overflow() -> None:
+    covariance = np.array(
+        [
+            [120, 100],
+            [80, 110],
+        ],
+        dtype=np.int8,
+    )
+
+    projected = np.asarray(project_symmetric_covariance(covariance))
+
+    npt.assert_allclose(
+        projected,
+        np.array(
+            [
+                [120.0, 90.0],
+                [90.0, 110.0],
+            ]
+        ),
+    )
+    assert np.issubdtype(projected.dtype, np.floating)