diff --git a/Modules/audioop.c b/Modules/audioop.c
index 6ca7d72ca6e..07b41d49d0a 100644
--- a/Modules/audioop.c
+++ b/Modules/audioop.c
@@ -1160,25 +1160,16 @@ audioop_ratecv(PyObject *self, PyObject *args)
            ceiling(len*outrate/inrate) output frames, and each frame
            requires bytes_per_frame bytes.  Computing this
            without spurious overflow is the challenge; we can
-           settle for a reasonable upper bound, though. */
-        int ceiling;   /* the number of output frames */
-        int nbytes;    /* the number of output bytes needed */
-        int q = len / inrate;
-        /* Now len = q * inrate + r exactly (with r = len % inrate),
-           and this is less than q * inrate + inrate = (q+1)*inrate.
-           So a reasonable upper bound on len*outrate/inrate is
-           ((q+1)*inrate)*outrate/inrate =
-           (q+1)*outrate.
-        */
-        ceiling = (q+1) * outrate;
-        nbytes = ceiling * bytes_per_frame;
-        /* See whether anything overflowed; if not, get the space. */
-        if (q+1 < 0 ||
-            ceiling / outrate != q+1 ||
-            nbytes / bytes_per_frame != ceiling)
+           settle for a reasonable upper bound, though, in this
+           case ceiling(len/inrate) * outrate. */
+
+        /* compute ceiling(len/inrate) without overflow */
+        int q = len > 0 ? 1 + (len - 1) / inrate : 0;
+        if (outrate > INT_MAX / q / bytes_per_frame)
             str = NULL;
         else
-            str = PyBytes_FromStringAndSize(NULL, nbytes);
+            str = PyBytes_FromStringAndSize(NULL,
+                                            q * outrate * bytes_per_frame);
 
         if (str == NULL) {
             PyErr_SetString(PyExc_MemoryError,