diff --git a/sklearn/preprocessing/tests/test_data.py b/sklearn/preprocessing/tests/test_data.py
index 2ff9dfd776a03..1d45b035333c5 100644
--- a/sklearn/preprocessing/tests/test_data.py
+++ b/sklearn/preprocessing/tests/test_data.py
@@ -873,6 +873,30 @@ def test_scaler_without_copy():
     assert_array_equal(X_csc.toarray(), X_csc_copy.toarray())
 
 
+def test_scaler_partial_fit_overflow():
+    # Test StandardScaler does not overflow in partial_fit #5602
+    rng = np.random.RandomState(0)
+
+    def gen_1d_uniform_batch(min_, max_, n):
+        return rng.uniform(min_, max_, size=(n, 1))
+
+    max_f = np.finfo(np.float64).max / 1e5
+    min_f = max_f / 1e2
+    stream_dim = 100
+    batch_dim = 500000
+
+    X = gen_1d_uniform_batch(min_=min_f, max_=min_f, n=batch_dim)
+
+    scaler = StandardScaler(with_std=False).fit(X)
+
+    iscaler = StandardScaler(with_std=False)
+    batch = gen_1d_uniform_batch(min_=min_f, max_=min_f, n=batch_dim)
+    for _ in range(stream_dim):
+        iscaler = iscaler.partial_fit(batch)
+
+    assert_allclose(iscaler.mean_, scaler.mean_)
+
+
 def test_scale_sparse_with_mean_raise_exception():
     rng = np.random.RandomState(42)
     X = rng.randn(4, 5)
diff --git a/sklearn/utils/extmath.py b/sklearn/utils/extmath.py
index 218733145a0de..4d731fe676a31 100644
--- a/sklearn/utils/extmath.py
+++ b/sklearn/utils/extmath.py
@@ -696,13 +696,16 @@ def _incremental_mean_and_var(X, last_mean, last_variance, last_sample_count):
     # old = stats until now
     # new = the current increment
     # updated = the aggregated stats
-    last_sum = last_mean * last_sample_count
     new_sum = np.nansum(X, axis=0)
 
     new_sample_count = np.sum(~np.isnan(X), axis=0)
     updated_sample_count = last_sample_count + new_sample_count
 
-    updated_mean = (last_sum + new_sum) / updated_sample_count
+    new_mean = new_sum / new_sample_count
+    delta = new_mean - last_mean
+    updated_mean = \
+        last_mean + (delta * new_sample_count) / updated_sample_count  # fixes test
+        # (last_mean * last_sample_count + new_sum) / updated_sample_count  # breaks stability test
 
     if last_variance is None:
         updated_variance = None
@@ -710,6 +713,7 @@ def _incremental_mean_and_var(X, last_mean, last_variance, last_sample_count):
         new_unnormalized_variance = np.nanvar(X, axis=0) * new_sample_count
         last_unnormalized_variance = last_variance * last_sample_count
 
+        last_sum = last_mean * last_sample_count
         with np.errstate(divide='ignore', invalid='ignore'):
             last_over_new_count = last_sample_count / new_sample_count
             updated_unnormalized_variance = (
diff --git a/sklearn/utils/tests/test_extmath.py b/sklearn/utils/tests/test_extmath.py
index ee08e016abe68..5373f5072a171 100644
--- a/sklearn/utils/tests/test_extmath.py
+++ b/sklearn/utils/tests/test_extmath.py
@@ -609,7 +609,7 @@ def naive_mean_variance_update(x, last_mean, last_variance,
             _incremental_mean_and_var(A1[i, :].reshape((1, A1.shape[1])),
                                       mean, var, n)
     assert_array_equal(n, A.shape[0])
-    assert_array_almost_equal(A.mean(axis=0), mean)
+    assert_allclose(A.mean(axis=0), mean, rtol=1e-12)
     assert_greater(tol, np.abs(stable_var(A) - var).max())