diff --git a/Doc/library/timeit.rst b/Doc/library/timeit.rst
index 8ca37034f79b7c..72a41987240c71 100644
--- a/Doc/library/timeit.rst
+++ b/Doc/library/timeit.rst
@@ -58,23 +58,29 @@ Python Interface
 The module defines three convenience functions and a public class:
 
 
-.. function:: timeit(stmt='pass', setup='pass', timer=<default timer>, number=1000000, globals=None)
+.. function:: timeit(stmt='pass', setup='pass', timer=<default timer>, number=1000000, globals=None, target_time=0.2)
 
    Create a :class:`Timer` instance with the given statement, *setup* code and
    *timer* function and run its :meth:`.timeit` method with *number* executions.
    The optional *globals* argument specifies a namespace in which to execute the
-   code.
+   code. If *number* is 0, :meth:`.autorange` method is executed, a convenience
+   function that calls :meth:`.timeit` repeatedly so that the total time >= *target_time* second.
 
    .. versionchanged:: 3.5
       The optional *globals* parameter was added.
 
+   .. versionchanged:: 3.8
+      The optional *target_time* parameter was added.
 
-.. function:: repeat(stmt='pass', setup='pass', timer=<default timer>, repeat=5, number=1000000, globals=None)
+
+.. function:: repeat(stmt='pass', setup='pass', timer=<default timer>, repeat=5, number=1000000, globals=None, target_time=0.2)
 
    Create a :class:`Timer` instance with the given statement, *setup* code and
    *timer* function and run its :meth:`.repeat` method with the given *repeat*
    count and *number* executions.  The optional *globals* argument specifies a
-   namespace in which to execute the code.
+   namespace in which to execute the code. If *number* is 0, :meth:`.autorange`
+   method is executed, a convenience function that calls :meth:`.timeit` repeatedly
+   so that the total time >= *target_time* second.
 
    .. versionchanged:: 3.5
       The optional *globals* parameter was added.
@@ -82,6 +88,9 @@ The module defines three convenience functions and a public class:
    .. versionchanged:: 3.7
       Default value of *repeat* changed from 3 to 5.
 
+   .. versionchanged:: 3.8
+      The optional *target_time* parameter was added.
+
 .. function:: default_timer()
 
    The default timer, which is always :func:`time.perf_counter`.
@@ -90,7 +99,7 @@ The module defines three convenience functions and a public class:
       :func:`time.perf_counter` is now the default timer.
 
 
-.. class:: Timer(stmt='pass', setup='pass', timer=<timer function>, globals=None)
+.. class:: Timer(stmt='pass', setup='pass', timer=<timer function>, globals=None, target_time=0.2)
 
    Class for timing execution speed of small code snippets.
 
@@ -116,6 +125,9 @@ The module defines three convenience functions and a public class:
    .. versionchanged:: 3.5
       The optional *globals* parameter was added.
 
+   .. versionchanged:: 3.8
+      The optional *target_time* parameter was added.
+
    .. method:: Timer.timeit(number=1000000)
 
       Time *number* executions of the main statement.  This executes the setup
@@ -137,15 +149,15 @@ The module defines three convenience functions and a public class:
             timeit.Timer('for i in range(10): oct(i)', 'gc.enable()').timeit()
 
 
-   .. method:: Timer.autorange(callback=None)
+   .. method:: Timer.autorange(callback=None, target_time=None)
 
       Automatically determine how many times to call :meth:`.timeit`.
 
       This is a convenience function that calls :meth:`.timeit` repeatedly
-      so that the total time >= 0.2 second, returning the eventual
+      so that the total time >= *Timer.target_time* seconds, returning the eventual
       (number of loops, time taken for that number of loops). It calls
       :meth:`.timeit` with increasing numbers from the sequence 1, 2, 5,
-      10, 20, 50, ... until the time taken is at least 0.2 second.
+      10, 20, 50, ... until the time taken is at least *target_time* seconds.
 
       If *callback* is given and is not ``None``, it will be called after
       each trial with two arguments: ``callback(number, time_taken)``.
@@ -233,6 +245,12 @@ Where the following options are understood:
 
    .. versionadded:: 3.5
 
+.. cmdoption:: -t, --target_time=T
+
+    calls :meth:`.timeit` repeatedly so that the total time >= *target_time* seconds
+
+   .. versionadded:: 3.8
+
 .. cmdoption:: -v, --verbose
 
    print raw timing results; repeat for more digits precision
diff --git a/Lib/test/test_timeit.py b/Lib/test/test_timeit.py
index e02d4a71a9ba7c..c86692c4fc7ef0 100644
--- a/Lib/test/test_timeit.py
+++ b/Lib/test/test_timeit.py
@@ -107,8 +107,8 @@ def timeit(self, stmt, setup, number=None, globals=None):
             kwargs['number'] = number
         delta_time = t.timeit(**kwargs)
         self.assertEqual(self.fake_timer.setup_calls, 1)
-        self.assertEqual(self.fake_timer.count, number)
-        self.assertEqual(delta_time, number)
+        self.assertEqual(self.fake_timer.count, number or 1)
+        self.assertEqual(delta_time, number or (1, 1.0))
 
     # Takes too long to run in debug build.
     #def test_timeit_default_iters(self):
@@ -139,7 +139,12 @@ def test_timeit_callable_stmt_and_setup(self):
     def test_timeit_function_zero_iters(self):
         delta_time = timeit.timeit(self.fake_stmt, self.fake_setup, number=0,
                 timer=FakeTimer())
-        self.assertEqual(delta_time, 0)
+        self.assertEqual(delta_time, (1, 1.0))
+
+    def test_timeit_function_max_time_taken(self):
+        delta_time = timeit.timeit(self.fake_stmt, self.fake_setup, number=0,
+                timer=FakeTimer(), target_time=1)
+        self.assertEqual(delta_time, (1, 1.0))
 
     def test_timeit_globals_args(self):
         global _global_timer
@@ -152,9 +157,9 @@ def test_timeit_globals_args(self):
         timeit.timeit(stmt='local_timer.inc()', timer=local_timer,
                       globals=locals(), number=3)
 
-    def repeat(self, stmt, setup, repeat=None, number=None):
+    def repeat(self, stmt, setup, repeat=None, number=None, target_time=0.5):
         self.fake_timer = FakeTimer()
-        t = timeit.Timer(stmt=stmt, setup=setup, timer=self.fake_timer)
+        t = timeit.Timer(stmt=stmt, setup=setup, timer=self.fake_timer, target_time=target_time)
         kwargs = {}
         if repeat is None:
             repeat = DEFAULT_REPEAT
@@ -166,8 +171,8 @@ def repeat(self, stmt, setup, repeat=None, number=None):
             kwargs['number'] = number
         delta_times = t.repeat(**kwargs)
         self.assertEqual(self.fake_timer.setup_calls, repeat)
-        self.assertEqual(self.fake_timer.count, repeat * number)
-        self.assertEqual(delta_times, repeat * [float(number)])
+        self.assertEqual(self.fake_timer.count, (repeat * number) if number else repeat)
+        self.assertEqual(delta_times, repeat * [float(number) or (1, 1.0)])
 
     # Takes too long to run in debug build.
     #def test_repeat_default(self):
@@ -186,6 +191,10 @@ def test_repeat_callable_stmt(self):
         self.repeat(self.fake_callable_stmt, self.fake_setup,
                 repeat=3, number=5)
 
+    def test_repeat_callable_max_time_taken(self):
+        self.repeat(self.fake_callable_stmt, self.fake_setup,
+                repeat=3, number=5, target_time=1)
+
     def test_repeat_callable_setup(self):
         self.repeat(self.fake_stmt, self.fake_callable_setup,
                 repeat=3, number=5)
@@ -208,7 +217,7 @@ def test_repeat_function_zero_reps(self):
     def test_repeat_function_zero_iters(self):
         delta_times = timeit.repeat(self.fake_stmt, self.fake_setup, number=0,
                 timer=FakeTimer())
-        self.assertEqual(delta_times, DEFAULT_REPEAT * [0.0])
+        self.assertEqual(delta_times, DEFAULT_REPEAT * [(1, 1.0)])
 
     def assert_exc_string(self, exc_string, expected_exc_name):
         exc_lines = exc_string.splitlines()
diff --git a/Lib/timeit.py b/Lib/timeit.py
index c0362bcc5f3e24..e02ca859a43b9a 100755
--- a/Lib/timeit.py
+++ b/Lib/timeit.py
@@ -19,6 +19,8 @@
   -p/--process: use time.process_time() (default is time.perf_counter())
   -v/--verbose: print raw timing results; repeat for more digits precision
   -u/--unit: set the output time unit (nsec, usec, msec, or sec)
+  -t/--target_time: if number is 0 the code will run until it
+                    takes *at least* ``target_time`` seconds
   -h/--help: print this usage message and exit
   --: separate options from statement, use when statement starts with -
   statement: statement to be timed (default 'pass')
@@ -59,6 +61,7 @@
 default_number = 1000000
 default_repeat = 5
 default_timer = time.perf_counter
+default_target_time = 0.2
 
 _globals = globals
 
@@ -75,10 +78,12 @@ def inner(_it, _timer{init}):
     return _t1 - _t0
 """
 
+
 def reindent(src, indent):
     """Helper to reindent a multi-line statement."""
     return src.replace("\n", "\n" + " "*indent)
 
+
 class Timer:
     """Class for timing execution speed of small code snippets.
 
@@ -98,9 +103,10 @@ class Timer:
     """
 
     def __init__(self, stmt="pass", setup="pass", timer=default_timer,
-                 globals=None):
+                 globals=None, target_time=default_target_time):
         """Constructor.  See class doc string."""
         self.timer = timer
+        self.target_time = target_time
         local_ns = {}
         global_ns = _globals() if globals is None else globals
         init = ''
@@ -169,6 +175,8 @@ def timeit(self, number=default_number):
         to one million.  The main statement, the setup statement and
         the timer function to be used are passed to the constructor.
         """
+        if not number:
+            return self.autorange()
         it = itertools.repeat(None, number)
         gcold = gc.isenabled()
         gc.disable()
@@ -205,16 +213,19 @@ def repeat(self, repeat=default_repeat, number=default_number):
             r.append(t)
         return r
 
-    def autorange(self, callback=None):
-        """Return the number of loops and time taken so that total time >= 0.2.
+    def autorange(self, callback=None, target_time=None):
+        """Return the number of loops and time taken so that
+        total time >= target_time (default is 0.2 seconds).
 
         Calls the timeit method with increasing numbers from the sequence
-        1, 2, 5, 10, 20, 50, ... until the time taken is at least 0.2
-        second.  Returns (number, time_taken).
+        1, 2, 5, 10, 20, 50, ... until the max_time_taken is reached.
+        Returns (number, time_taken).
 
         If *callback* is given and is not None, it will be called after
         each trial with two arguments: ``callback(number, time_taken)``.
         """
+        if target_time is None:
+            target_time = self.target_time
         i = 1
         while True:
             for j in 1, 2, 5:
@@ -222,19 +233,24 @@ def autorange(self, callback=None):
                 time_taken = self.timeit(number)
                 if callback:
                     callback(number, time_taken)
-                if time_taken >= 0.2:
+                if time_taken >= target_time:
                     return (number, time_taken)
             i *= 10
 
+
 def timeit(stmt="pass", setup="pass", timer=default_timer,
-           number=default_number, globals=None):
+           number=default_number, globals=None,
+           target_time=default_target_time):
     """Convenience function to create Timer object and call timeit method."""
-    return Timer(stmt, setup, timer, globals).timeit(number)
+    return Timer(stmt, setup, timer, globals, target_time).timeit(number)
+
 
 def repeat(stmt="pass", setup="pass", timer=default_timer,
-           repeat=default_repeat, number=default_number, globals=None):
+           repeat=default_repeat, number=default_number,
+           globals=None, target_time=default_target_time):
     """Convenience function to create Timer object and call repeat method."""
-    return Timer(stmt, setup, timer, globals).repeat(repeat, number)
+    return Timer(stmt, setup, timer, globals, target_time).repeat(repeat, number)
+
 
 def main(args=None, *, _wrap_timer=None):
     """Main program, used when run as a script.
@@ -259,7 +275,7 @@ def main(args=None, *, _wrap_timer=None):
     try:
         opts, args = getopt.getopt(args, "n:u:s:r:tcpvh",
                                    ["number=", "setup=", "repeat=",
-                                    "time", "clock", "process",
+                                    "time", "clock", "process", "max_time_taken="
                                     "verbose", "unit=", "help"])
     except getopt.error as err:
         print(err)
@@ -269,6 +285,7 @@ def main(args=None, *, _wrap_timer=None):
     timer = default_timer
     stmt = "\n".join(args) or "pass"
     number = 0 # auto-determine
+    target_time = default_target_time
     setup = []
     repeat = default_repeat
     verbose = 0
@@ -293,6 +310,8 @@ def main(args=None, *, _wrap_timer=None):
                 repeat = 1
         if o in ("-p", "--process"):
             timer = time.process_time
+        if o in ("-t", "--target_time"):
+            target_time = a
         if o in ("-v", "--verbose"):
             if verbose:
                 precision += 1
@@ -310,7 +329,7 @@ def main(args=None, *, _wrap_timer=None):
     if _wrap_timer is not None:
         timer = _wrap_timer(timer)
 
-    t = Timer(stmt, setup, timer)
+    t = Timer(stmt, setup, timer, target_time=target_time)
     if number == 0:
         # determine number so that 0.2 <= total time < 2.0
         callback = None
@@ -321,7 +340,7 @@ def callback(number, time_taken):
                 print(msg.format(num=number, s='s' if plural else '',
                                   secs=time_taken, prec=precision))
         try:
-            number, _ = t.autorange(callback)
+            number, _ = t.autorange(callback, target_time)
         except:
             t.print_exc()
             return 1
@@ -370,5 +389,6 @@ def format_time(dt):
                                UserWarning, '', 0)
     return None
 
+
 if __name__ == "__main__":
     sys.exit(main())
diff --git a/Misc/NEWS.d/next/Library/2019-04-25-21-11-37.bpo-36461.TO5YyP.rst b/Misc/NEWS.d/next/Library/2019-04-25-21-11-37.bpo-36461.TO5YyP.rst
new file mode 100644
index 00000000000000..41422d6e7fa315
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-04-25-21-11-37.bpo-36461.TO5YyP.rst
@@ -0,0 +1,4 @@
+In timeit module:
+- added a new parameter *target_time* to ``timeit.timeit()`` and ``timeit.replace()`` methods and ``timeit.Timer()`` class;
+- had `timeit` and `repeat` methods (and functions) fall back 
+  on `autorange` if the number is set to 0 or None.