diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index c0ed198e200f1..a10d912b6aa79 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -730,16 +730,14 @@ def value_counts(
 
         # count, remove nulls (from the index), and but the bins
         result = ii.value_counts(dropna=dropna)
-        result = result[result.index.notna()]
-        result.index = result.index.astype("interval")
+        result.index = result.index.astype('interval')
         result = result.sort_index()
 
         # if we are dropna and we have NO values
         if dropna and (result.values == 0).all():
             result = result.iloc[0:0]
 
-        # normalizing is by len of all (regardless of dropna)
-        counts = np.array([len(ii)])
+        counts = np.array([result.sum()])
 
     else:
 
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index d81ee79418e9c..71f1280ff4d29 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1035,21 +1035,27 @@ def test_dropna(self):
             expected = Series([2, 1, 1], index=[5.0, 10.3, np.nan])
             tm.assert_series_equal(result, expected)
 
-    def test_value_counts_normalized(self):
+    @pytest.mark.parametrize('dropna, vals, index', [
+        (False, [0.6, 0.2, 0.2], [np.nan, 2.0, 1.0]),
+        (True, [0.5, 0.5], [2.0, 1.0])])
+    @pytest.mark.parametrize('dtype', [np.float64, np.object, 'M8[ns]'])
+    def test_value_counts_normalized(self, dropna, vals, index, dtype):
         # GH12558
         s = Series([1, 2, np.nan, np.nan, np.nan])
-        dtypes = (np.float64, np.object, "M8[ns]")
-        for t in dtypes:
-            s_typed = s.astype(t)
-            result = s_typed.value_counts(normalize=True, dropna=False)
-            expected = Series(
-                [0.6, 0.2, 0.2], index=Series([np.nan, 2.0, 1.0], dtype=t)
-            )
-            tm.assert_series_equal(result, expected)
+        s_typed = s.astype(dtype)
+        result = s_typed.value_counts(normalize=True, dropna=dropna)
+        expected = Series(vals, index=Series(index, dtype=dtype))
+        tm.assert_series_equal(result, expected)
 
-            result = s_typed.value_counts(normalize=True, dropna=True)
-            expected = Series([0.5, 0.5], index=Series([2.0, 1.0], dtype=t))
-            tm.assert_series_equal(result, expected)
+    @pytest.mark.parametrize('dropna, vals, tuples', [
+        (False, [0.5, 0.3, 0.2], [(-0.005, 2.0), (2.0, 4.0), np.nan]),
+        (True, [0.625, 0.375], [(-0.005, 2.0), (2.0, 4.0)])])
+    def test_value_counts_normalized_bins(self, dropna, vals, tuples):
+        # GH25970
+        s = Series([1, 1, 2, 0, 1, np.nan, 4, 4, np.nan, 3])
+        result = s.value_counts(normalize=True, bins=2, dropna=dropna)
+        expected = Series(vals, index=IntervalIndex.from_tuples(tuples))
+        tm.assert_series_equal(result, expected)
 
     def test_value_counts_uint64(self):
         arr = np.array([2 ** 63], dtype=np.uint64)