diff --git a/ibis_ml/steps/_standardize.py b/ibis_ml/steps/_standardize.py
index 2ccefa1..7df080f 100644
--- a/ibis_ml/steps/_standardize.py
+++ b/ibis_ml/steps/_standardize.py
@@ -11,6 +11,8 @@
     from collections.abc import Iterable
 
 _DOCS_PAGE_NAME = "standardization"
+# a small epsilon value to handle near-constant columns during normalization
+_APPROX_EPS = 10e-7
 
 
 class ScaleMinMax(Step):
@@ -68,7 +70,11 @@ def fit_table(self, table: ir.Table, metadata: Metadata) -> None:
     def transform_table(self, table: ir.Table) -> ir.Table:
         return table.mutate(
             [
-                ((table[c] - min) / (max - min)).name(c)  # type: ignore
+                # for near-constant column, set the scale to 1.0
+                (
+                    (table[c] - min)
+                    / (1.0 if abs(max - min) < _APPROX_EPS else max - min)
+                ).name(c)
                 for c, (max, min) in self.stats_.items()
             ]
         )
@@ -128,7 +134,10 @@ def fit_table(self, table: ir.Table, metadata: Metadata) -> None:
     def transform_table(self, table: ir.Table) -> ir.Table:
         return table.mutate(
             [
-                ((table[c] - center) / scale).name(c)  # type: ignore
+                # for near-constant column, set the scale to 1.0
+                (
+                    (table[c] - center) / (1.0 if abs(scale) < _APPROX_EPS else scale)
+                ).name(c)
                 for c, (center, scale) in self.stats_.items()
             ]
         )
diff --git a/tests/test_standardize.py b/tests/test_standardize.py
new file mode 100644
index 0000000..ad35217
--- /dev/null
+++ b/tests/test_standardize.py
@@ -0,0 +1,42 @@
+import ibis
+import numpy as np
+import pandas as pd
+import pandas.testing as tm
+import pytest
+
+import ibis_ml as ml
+
+
+def test_scalestandard():
+    cols = np.arange(0, 100)
+    mean = np.mean(cols)
+    std = np.std(cols)
+    table = ibis.memtable({"col": cols})
+    step = ml.ScaleStandard("col")
+    step.fit_table(table, ml.core.Metadata())
+    result = step.transform_table(table)
+    expected = pd.DataFrame({"col": (cols - mean) / std})
+    tm.assert_frame_equal(result.execute(), expected, check_exact=False)
+
+
+def test_scaleminmax():
+    cols = np.arange(0, 100)
+    min_val = np.min(cols)
+    max_val = np.max(cols)
+    table = ibis.memtable({"col": cols})
+    step = ml.ScaleMinMax("col")
+    step.fit_table(table, ml.core.Metadata())
+    result = step.transform_table(table)
+    expected = pd.DataFrame({"col": (cols - min_val) / (max_val - min_val)})
+    tm.assert_frame_equal(result.execute(), expected, check_exact=False)
+
+
+@pytest.mark.parametrize("scaler", ["ScaleStandard", "ScaleMinMax"])
+def test_constant_columns(scaler):
+    table = ibis.memtable({"int_col": [100], "float_col": [100.0]})
+    scaler_class = getattr(ml, scaler)
+    scale_step = scaler_class(ml.numeric())
+    scale_step.fit_table(table, ml.core.Metadata())
+    result = scale_step.transform_table(table)
+    expected = pd.DataFrame({"int_col": [0.0], "float_col": [0.0]})
+    tm.assert_frame_equal(result.execute(), expected)