diff --git a/doc/whats_new/v0.21.rst b/doc/whats_new/v0.21.rst
index 2fb76ebd2f33d..763334e7628dd 100644
--- a/doc/whats_new/v0.21.rst
+++ b/doc/whats_new/v0.21.rst
@@ -215,6 +215,10 @@ Support for Python 3.4 and below has been officially dropped.
   in the dense case. Also added a new parameter ``order`` which controls output
   order for further speed performances. :issue:`12251` by `Tom Dupre la Tour`_.
 
+- |Fix| Fixed the calculation overflow when using a float16 dtype with
+  :class:`preprocessing.StandardScaler`. :issue:`13007` by
+  :user:`Raffaello Baluyot <baluyotraf>`
+
 :mod:`sklearn.tree`
 ...................
 - |Feature| Decision Trees can now be plotted with matplotlib using
diff --git a/sklearn/preprocessing/tests/test_data.py b/sklearn/preprocessing/tests/test_data.py
index 1a5ad20d32ef4..b387379be2cee 100644
--- a/sklearn/preprocessing/tests/test_data.py
+++ b/sklearn/preprocessing/tests/test_data.py
@@ -450,6 +450,31 @@ def test_scaler_2d_arrays():
     assert X_scaled is not X
 
 
+def test_scaler_float16_overflow():
+    # Test if the scaler will not overflow on float16 numpy arrays
+    rng = np.random.RandomState(0)
+    # float16 has a maximum of 65500.0. On the worst case 5 * 200000 is 100000
+    # which is enough to overflow the data type
+    X = rng.uniform(5, 10, [200000, 1]).astype(np.float16)
+
+    with np.errstate(over='raise'):
+        scaler = StandardScaler().fit(X)
+        X_scaled = scaler.transform(X)
+
+    # Calculate the float64 equivalent to verify result
+    X_scaled_f64 = StandardScaler().fit_transform(X.astype(np.float64))
+
+    # Overflow calculations may cause -inf, inf, or nan. Since there is no nan
+    # input, all of the outputs should be finite. This may be redundant since a
+    # FloatingPointError exception will be thrown on overflow above.
+    assert np.all(np.isfinite(X_scaled))
+
+    # The normal distribution is very unlikely to go above 4. At 4.0-8.0 the
+    # float16 precision is 2^-8 which is around 0.004. Thus only 2 decimals are
+    # checked to account for precision differences.
+    assert_array_almost_equal(X_scaled, X_scaled_f64, decimal=2)
+
+
 def test_handle_zeros_in_scale():
     s1 = np.array([0, 1, 2, 3])
     s2 = _handle_zeros_in_scale(s1, copy=True)
diff --git a/sklearn/utils/extmath.py b/sklearn/utils/extmath.py
index fef2c7aff7971..44c6a392d9c6c 100644
--- a/sklearn/utils/extmath.py
+++ b/sklearn/utils/extmath.py
@@ -658,6 +658,38 @@ def make_nonnegative(X, min_value=0):
     return X
 
 
+# Use at least float64 for the accumulating functions to avoid precision issue
+# see https://github.com/numpy/numpy/issues/9393. The float64 is also retained
+# as it is in case the float overflows
+def _safe_accumulator_op(op, x, *args, **kwargs):
+    """
+    This function provides numpy accumulator functions with a float64 dtype
+    when used on a floating point input. This prevents accumulator overflow on
+    smaller floating point dtypes.
+
+    Parameters
+    ----------
+    op : function
+        A numpy accumulator function such as np.mean or np.sum
+    x : numpy array
+        A numpy array to apply the accumulator function
+    *args : positional arguments
+        Positional arguments passed to the accumulator function after the
+        input x
+    **kwargs : keyword arguments
+        Keyword arguments passed to the accumulator function
+
+    Returns
+    -------
+    result : The output of the accumulator function passed to this function
+    """
+    if np.issubdtype(x.dtype, np.floating) and x.dtype.itemsize < 8:
+        result = op(x, *args, **kwargs, dtype=np.float64)
+    else:
+        result = op(x, *args, **kwargs)
+    return result
+
+
 def _incremental_mean_and_var(X, last_mean, last_variance, last_sample_count):
     """Calculate mean update and a Youngs and Cramer variance update.
 
@@ -708,12 +740,7 @@ def _incremental_mean_and_var(X, last_mean, last_variance, last_sample_count):
     # new = the current increment
     # updated = the aggregated stats
     last_sum = last_mean * last_sample_count
-    if np.issubdtype(X.dtype, np.floating) and X.dtype.itemsize < 8:
-        # Use at least float64 for the accumulator to avoid precision issues;
-        # see https://github.com/numpy/numpy/issues/9393
-        new_sum = np.nansum(X, axis=0, dtype=np.float64).astype(X.dtype)
-    else:
-        new_sum = np.nansum(X, axis=0)
+    new_sum = _safe_accumulator_op(np.nansum, X, axis=0)
 
     new_sample_count = np.sum(~np.isnan(X), axis=0)
     updated_sample_count = last_sample_count + new_sample_count
@@ -723,7 +750,8 @@ def _incremental_mean_and_var(X, last_mean, last_variance, last_sample_count):
     if last_variance is None:
         updated_variance = None
     else:
-        new_unnormalized_variance = np.nanvar(X, axis=0) * new_sample_count
+        new_unnormalized_variance = (
+            _safe_accumulator_op(np.nanvar, X, axis=0) * new_sample_count)
         last_unnormalized_variance = last_variance * last_sample_count
 
         with np.errstate(divide='ignore', invalid='ignore'):
diff --git a/sklearn/utils/validation.py b/sklearn/utils/validation.py
index fc882e0719a8d..379aa738f7124 100644
--- a/sklearn/utils/validation.py
+++ b/sklearn/utils/validation.py
@@ -34,14 +34,18 @@
 
 def _assert_all_finite(X, allow_nan=False):
     """Like assert_all_finite, but only for ndarray."""
+    # validation is also imported in extmath
+    from .extmath import _safe_accumulator_op
+
     if _get_config()['assume_finite']:
         return
     X = np.asanyarray(X)
     # First try an O(n) time, O(1) space solution for the common case that
     # everything is finite; fall back to O(n) space np.isfinite to prevent
-    # false positives from overflow in sum method.
+    # false positives from overflow in sum method. The sum is also calculated
+    # safely to reduce dtype induced overflows.
     is_float = X.dtype.kind in 'fc'
-    if is_float and np.isfinite(X.sum()):
+    if is_float and (np.isfinite(_safe_accumulator_op(np.sum, X))):
         pass
     elif is_float:
         msg_err = "Input contains {} or a value too large for {!r}."