diff --git a/lib/matplotlib/path.py b/lib/matplotlib/path.py
index e72eb1a9ca73..086a1207dbd1 100644
--- a/lib/matplotlib/path.py
+++ b/lib/matplotlib/path.py
@@ -943,13 +943,20 @@ def arc(cls, theta1, theta2, n=None, is_wedge=False):
            polylines, quadratic or cubic Bezier curves
            <https://web.archive.org/web/20190318044212/http://www.spaceroots.org/documents/ellipse/index.html>`_.
         """
+        # we want to get the same result when the input changes within [-tol, tol]
+        # this behavior is only for internal use to offset floating-point error
+        # so it should not be relied on by the user
+        tol = 1e-6
+
         halfpi = np.pi * 0.5
 
         eta1 = theta1
         eta2 = theta2 - 360 * np.floor((theta2 - theta1) / 360)
         # Ensure 2pi range is not flattened to 0 due to floating-point errors,
         # but don't try to expand existing 0 range.
-        if theta2 != theta1 and eta2 <= eta1:
+        # condition: theta1 != theta2 and eta2 <= eta1
+        # implementation note: use np.isclose() may break when theta1 = 0
+        if abs(theta1 - theta2) >= tol and (eta2 <= eta1 + tol):
             eta2 += 360
         eta1, eta2 = np.deg2rad([eta1, eta2])
 
diff --git a/lib/matplotlib/tests/test_path.py b/lib/matplotlib/tests/test_path.py
index 8c0c32dc133b..a475b10c7755 100644
--- a/lib/matplotlib/tests/test_path.py
+++ b/lib/matplotlib/tests/test_path.py
@@ -475,6 +475,22 @@ def test_full_arc(offset):
     np.testing.assert_allclose(maxs, 1)
 
 
+@pytest.mark.parametrize('offset', range(-720, 361, 45))
+def test_full_arc_rounding(offset):
+    # GH 26972 - edge case for floating point rounding
+    # we want get the same result when input of arc
+    # changes within [-tol, tol], where tol = 1e-6
+    tol = 1e-6
+    low = offset
+    high = 360 + offset + tol
+
+    path = Path.arc(low, high)
+    mins = np.min(path.vertices, axis=0)
+    maxs = np.max(path.vertices, axis=0)
+    np.testing.assert_allclose(mins, -1)
+    np.testing.assert_allclose(maxs, 1)
+
+
 def test_disjoint_zero_length_segment():
     this_path = Path(
         np.array([