diff --git a/homeassistant/components/sensor/history_stats.py b/homeassistant/components/sensor/history_stats.py
index 7d9dfaaa48f..08546e3f0c8 100644
--- a/homeassistant/components/sensor/history_stats.py
+++ b/homeassistant/components/sensor/history_stats.py
@@ -44,8 +44,6 @@ UNITS = {
 }
 ICON = 'mdi:chart-line'
 
-ATTR_START = 'from'
-ATTR_END = 'to'
 ATTR_VALUE = 'value'
 
 
@@ -157,12 +155,9 @@ class HistoryStatsSensor(Entity):
     @property
     def device_state_attributes(self):
         """Return the state attributes of the sensor."""
-        start, end = self._period
         hsh = HistoryStatsHelper
         return {
             ATTR_VALUE: hsh.pretty_duration(self.value),
-            ATTR_START: start.strftime('%Y-%m-%d %H:%M:%S'),
-            ATTR_END: end.strftime('%Y-%m-%d %H:%M:%S'),
         }
 
     @property
@@ -172,13 +167,33 @@ class HistoryStatsSensor(Entity):
 
     def update(self):
         """Get the latest data and updates the states."""
+        # Get previous values of start and end
+        p_start, p_end = self._period
+
         # Parse templates
         self.update_period()
         start, end = self._period
 
-        # Convert to UTC
+        # Convert times to UTC
         start = dt_util.as_utc(start)
         end = dt_util.as_utc(end)
+        p_start = dt_util.as_utc(p_start)
+        p_end = dt_util.as_utc(p_end)
+        now = dt_util.as_utc(datetime.datetime.now())
+
+        # Compute integer timestamps
+        start_timestamp = math.floor(dt_util.as_timestamp(start))
+        end_timestamp = math.floor(dt_util.as_timestamp(end))
+        p_start_timestamp = math.floor(dt_util.as_timestamp(p_start))
+        p_end_timestamp = math.floor(dt_util.as_timestamp(p_end))
+        now_timestamp = math.floor(dt_util.as_timestamp(now))
+
+        # If period has not changed and current time after the period end...
+        if start_timestamp == p_start_timestamp and \
+            end_timestamp == p_end_timestamp and \
+                end_timestamp <= now_timestamp:
+            # Don't compute anything as the value cannot have changed
+            return
 
         # Get history between start and end
         history_list = history.state_changes_during_period(
@@ -191,7 +206,7 @@ class HistoryStatsSensor(Entity):
         last_state = history.get_state(self.hass, start, self._entity_id)
         last_state = (last_state is not None and
                       last_state == self._entity_state)
-        last_time = dt_util.as_timestamp(start)
+        last_time = start_timestamp
         elapsed = 0
         count = 0
 
@@ -210,8 +225,7 @@ class HistoryStatsSensor(Entity):
 
         # Count time elapsed between last history state and end of measure
         if last_state:
-            measure_end = min(dt_util.as_timestamp(end), dt_util.as_timestamp(
-                datetime.datetime.now()))
+            measure_end = min(end_timestamp, now_timestamp)
             elapsed += measure_end - last_time
 
         # Save value in hours
@@ -279,13 +293,11 @@ class HistoryStatsHelper:
         hours, seconds = divmod(seconds, 3600)
         minutes, seconds = divmod(seconds, 60)
         if days > 0:
-            return '%dd %dh %dm %ds' % (days, hours, minutes, seconds)
+            return '%dd %dh %dm' % (days, hours, minutes)
         elif hours > 0:
-            return '%dh %dm %ds' % (hours, minutes, seconds)
-        elif minutes > 0:
-            return '%dm %ds' % (minutes, seconds)
+            return '%dh %dm' % (hours, minutes)
         else:
-            return '%ds' % (seconds,)
+            return '%dm' % minutes
 
     @staticmethod
     def pretty_ratio(value, period):
diff --git a/tests/components/sensor/test_history_stats.py b/tests/components/sensor/test_history_stats.py
index 282991fba0b..7fdf732825b 100644
--- a/tests/components/sensor/test_history_stats.py
+++ b/tests/components/sensor/test_history_stats.py
@@ -58,16 +58,29 @@ class TestHistoryStatsSensor(unittest.TestCase):
             self.hass, 'test', 'on', None, today, duration, 'time', 'test')
 
         sensor1.update_period()
+        sensor1_start, sensor1_end = sensor1._period
         sensor2.update_period()
+        sensor2_start, sensor2_end = sensor2._period
 
-        self.assertEqual(
-            sensor1.device_state_attributes['from'][-8:], '00:00:00')
-        self.assertEqual(
-            sensor1.device_state_attributes['to'][-8:], '02:01:00')
-        self.assertEqual(
-            sensor2.device_state_attributes['from'][-8:], '21:59:00')
-        self.assertEqual(
-            sensor2.device_state_attributes['to'][-8:], '00:00:00')
+        # Start = 00:00:00
+        self.assertEqual(sensor1_start.hour, 0)
+        self.assertEqual(sensor1_start.minute, 0)
+        self.assertEqual(sensor1_start.second, 0)
+
+        # End = 02:01:00
+        self.assertEqual(sensor1_end.hour, 2)
+        self.assertEqual(sensor1_end.minute, 1)
+        self.assertEqual(sensor1_end.second, 0)
+
+        # Start = 21:59:00
+        self.assertEqual(sensor2_start.hour, 21)
+        self.assertEqual(sensor2_start.minute, 59)
+        self.assertEqual(sensor2_start.second, 0)
+
+        # End = 00:00:00
+        self.assertEqual(sensor2_end.hour, 0)
+        self.assertEqual(sensor2_end.minute, 0)
+        self.assertEqual(sensor2_end.second, 0)
 
     def test_measure(self):
         """Test the history statistics sensor measure."""