diff --git a/doc/source/whatsnew/v0.20.1.txt b/doc/source/whatsnew/v0.20.1.txt
index 504f8004bc8a6..ce843d56c5ae2 100644
--- a/doc/source/whatsnew/v0.20.1.txt
+++ b/doc/source/whatsnew/v0.20.1.txt
@@ -78,7 +78,7 @@ Reshaping
 Numeric
 ^^^^^^^
 
-
+- Bug in ``.rolling.quantile()`` which incorrectly used different defaults than Series.quantile() and DataFrame.quantile()
 
 
 Other
diff --git a/pandas/_libs/window.pyx b/pandas/_libs/window.pyx
index 3bb8abe26c781..275ff26a7eb35 100644
--- a/pandas/_libs/window.pyx
+++ b/pandas/_libs/window.pyx
@@ -1348,6 +1348,7 @@ def roll_quantile(ndarray[float64_t, cast=True] input, int64_t win,
         bint is_variable
         ndarray[int64_t] start, end
         ndarray[double_t] output
+        double qlow, qhigh, vlow, vhigh
 
     if quantile < 0.0 or quantile > 1.0:
         raise ValueError("quantile value {0} not in [0, 1]".format(quantile))
@@ -1391,7 +1392,19 @@ def roll_quantile(ndarray[float64_t, cast=True] input, int64_t win,
 
         if nobs >= minp:
             idx = int(quantile * <double>(nobs - 1))
-            output[i] = skiplist.get(idx)
+
+            # Exactly last point
+            if idx == nobs - 1:
+                output[i] = skiplist.get(idx)
+
+            # Interpolated quantile
+            else:
+                qlow = (<double> idx) / (<double>(nobs - 1))
+                qhigh = (<double> (idx + 1)) / (<double>(nobs - 1))
+                vlow = skiplist.get(idx)
+                vhigh = skiplist.get(idx + 1)
+                output[i] = vlow + (vhigh - vlow) * \
+                    (quantile - qlow) / (qhigh - qlow)
         else:
             output[i] = NaN
 
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index 634cd5fe2586b..33f0ecd001436 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -1078,8 +1078,19 @@ def test_rolling_quantile(self):
         def scoreatpercentile(a, per):
             values = np.sort(a, axis=0)
 
-            idx = per / 1. * (values.shape[0] - 1)
-            return values[int(idx)]
+            idx = int(per / 1. * (values.shape[0] - 1))
+
+            if idx == values.shape[0] - 1:
+                retval = values[-1]
+
+            else:
+                qlow = float(idx) / float(values.shape[0] - 1)
+                qhig = float(idx + 1) / float(values.shape[0] - 1)
+                vlow = values[idx]
+                vhig = values[idx + 1]
+                retval = vlow + (vhig - vlow) * (per - qlow) / (qhig - qlow)
+
+            return retval
 
         for q in qs:
 
@@ -1094,6 +1105,28 @@ def alt(x):
 
             self._check_moment_func(f, alt, name='quantile', quantile=q)
 
+    def test_rolling_quantile_np_percentile(self):
+        # #9413
+        row = 10
+        col = 5
+        idx = pd.date_range(20100101, periods=row, freq='B')
+        df = pd.DataFrame(np.random.rand(row * col).reshape((row, -1)),
+                          index=idx)
+
+        df_quantile = df.quantile([0.25, 0.5, 0.75], axis=0)
+        np_percentile = np.percentile(df, [25, 50, 75], axis=0)
+
+        tm.assert_almost_equal(df_quantile.values, np.array(np_percentile))
+
+    def test_rolling_quantile_series(self):
+        # #16211
+        arr = np.arange(100)
+        s = pd.Series(arr)
+        q1 = s.quantile(0.1)
+        q2 = s.rolling(100).quantile(0.1).iloc[-1]
+
+        tm.assert_almost_equal(q1, q2)
+
     def test_rolling_quantile_param(self):
         ser = Series([0.0, .1, .5, .9, 1.0])
 
@@ -3514,7 +3547,7 @@ def test_ragged_quantile(self):
 
         result = df.rolling(window='2s', min_periods=1).quantile(0.5)
         expected = df.copy()
-        expected['B'] = [0.0, 1, 1.0, 3.0, 3.0]
+        expected['B'] = [0.0, 1, 1.5, 3.0, 3.5]
         tm.assert_frame_equal(result, expected)
 
     def test_ragged_std(self):