diff --git a/Lib/fontTools/misc/bezierTools.py b/Lib/fontTools/misc/bezierTools.py
index a1a707b09..5411ff99f 100644
--- a/Lib/fontTools/misc/bezierTools.py
+++ b/Lib/fontTools/misc/bezierTools.py
@@ -18,6 +18,9 @@ except (AttributeError, ImportError):
     COMPILED = False
 
 
+EPSILON = 1e-9
+
+
 Intersection = namedtuple("Intersection", ["pt", "t1", "t2"])
 
 
@@ -92,7 +95,7 @@ def _split_cubic_into_two(p0, p1, p2, p3):
 def _calcCubicArcLengthCRecurse(mult, p0, p1, p2, p3):
     arch = abs(p0 - p3)
     box = abs(p0 - p1) + abs(p1 - p2) + abs(p2 - p3)
-    if arch * mult >= box:
+    if arch * mult + EPSILON >= box:
         return (arch + box) * 0.5
     else:
         one, two = _split_cubic_into_two(p0, p1, p2, p3)
diff --git a/Tests/misc/bezierTools_test.py b/Tests/misc/bezierTools_test.py
index ce8a9e17e..4030f0704 100644
--- a/Tests/misc/bezierTools_test.py
+++ b/Tests/misc/bezierTools_test.py
@@ -3,6 +3,7 @@ from fontTools.misc.bezierTools import (
     calcQuadraticBounds,
     calcQuadraticArcLength,
     calcCubicBounds,
+    calcCubicArcLength,
     curveLineIntersections,
     curveCurveIntersections,
     segmentPointAtT,
@@ -192,6 +193,25 @@ def test_calcQuadraticArcLength():
     ) == pytest.approx(127.9225)
 
 
+@pytest.mark.parametrize(
+    "segment, expectedLength",
+    [
+        (
+            # https://github.com/fonttools/fonttools/issues/3502
+            ((377, 469), (377, 468), (377, 472), (377, 472)),  # off by one unit
+            3.32098765445,
+        ),
+        (
+            # https://github.com/fonttools/fonttools/issues/3502
+            ((242, 402), (242, 403), (242, 399), (242, 399)),  # off by one unit
+            3.32098765445,
+        ),
+    ],
+)
+def test_calcCubicArcLength(segment, expectedLength):
+    assert calcCubicArcLength(*segment) == pytest.approx(expectedLength)
+
+
 def test_intersections_linelike():
     seg1 = [(0.0, 0.0), (0.0, 0.25), (0.0, 0.75), (0.0, 1.0)]
     seg2 = [(0.0, 0.5), (0.25, 0.5), (0.75, 0.5), (1.0, 0.5)]