diff -r a6548e230ed6 Lib/test/test_math.py
--- a/Lib/test/test_math.py	Thu Oct 27 19:33:22 2016 +0300
+++ b/Lib/test/test_math.py	Thu Oct 27 18:46:27 2016 +0100
@@ -475,6 +475,13 @@
         self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
         self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
         self.ftest('degrees(0)', math.degrees(0), 0)
+        self.assertEqual(math.degrees(INF), INF)
+        self.assertEqual(math.degrees(NINF), NINF)
+        self.assertTrue(math.isnan(math.degrees(NAN)))
+        with self.assertRaises(OverflowError):
+            math.degrees(FLOAT_MAX)
+        with self.assertRaises(OverflowError):
+            math.degrees(-FLOAT_MAX)
 
     def testExp(self):
         self.assertRaises(TypeError, math.exp)
@@ -999,6 +1006,9 @@
         self.ftest('radians(90)', math.radians(90), math.pi/2)
         self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
         self.ftest('radians(0)', math.radians(0), 0)
+        self.assertEqual(math.radians(INF), INF)
+        self.assertEqual(math.radians(NINF), NINF)
+        self.assertTrue(math.isnan(math.radians(NAN)))
 
     def testSin(self):
         self.assertRaises(TypeError, math.sin)
diff -r a6548e230ed6 Modules/mathmodule.c
--- a/Modules/mathmodule.c	Thu Oct 27 19:33:22 2016 +0300
+++ b/Modules/mathmodule.c	Thu Oct 27 18:46:27 2016 +0100
@@ -1927,10 +1927,24 @@
 static PyObject *
 math_degrees(PyObject *self, PyObject *arg)
 {
-    double x = PyFloat_AsDouble(arg);
+    double r, x;
+    x = PyFloat_AsDouble(arg);
     if (x == -1.0 && PyErr_Occurred())
         return NULL;
-    return PyFloat_FromDouble(x * radToDeg);
+
+    /* NaNs and infinities should be returned unchanged. */
+    if (!Py_IS_FINITE(x)) {
+        return PyFloat_FromDouble(x);
+    }
+
+    /* On overflow, raise OverflowError */
+    r = x * radToDeg;
+    if (!Py_IS_FINITE(r)) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "math range error");
+        return NULL;
+    }
+    return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_degrees_doc,