diff --git a/doc/source/whatsnew/v3.1.0.rst b/doc/source/whatsnew/v3.1.0.rst
index ba68d142e1eda..d46933f459b3b 100644
--- a/doc/source/whatsnew/v3.1.0.rst
+++ b/doc/source/whatsnew/v3.1.0.rst
@@ -303,6 +303,7 @@ Indexing
 - Bug in :meth:`Index.take` where ``fill_value`` was silently ignored and integer-dtype indexes raised ``ValueError`` instead of filling with the provided value. Passing ``fill_value=None`` now fills ``-1`` entries with the Index's NA value (matching the :class:`~pandas.api.extensions.ExtensionArray` convention); omit ``fill_value`` to retain the previous behavior where negative indices wrap (:issue:`65210`)
 - Bug in :meth:`Index.where` and :meth:`Index.putmask` preserving ``numpy.datetime64`` / ``numpy.timedelta64`` ``NaT`` scalars in the object-dtype result for mismatched-dtype inputs, instead of normalizing to :attr:`pandas.NaT` as :meth:`Series.where` does (:issue:`55174`)
 - Bug in :meth:`MultiIndex.get_loc` returning a slice instead of an integer for a unique key when the :class:`MultiIndex` contained duplicates elsewhere, causing ``.loc`` to return a :class:`Series` instead of a scalar (:issue:`42102`)
+- Bug in :meth:`RangeIndex.memory_usage` and :attr:`RangeIndex.nbytes` raising ``TypeError`` on PyPy (:issue:`46176`)
 - Bug in :meth:`Series.where` and :meth:`Series.mask` raising ``ValueError`` when ``other`` is a tuple on object-dtype :class:`Series` (:issue:`37681`)
 - Fixed bug in :meth:`DataFrame.loc` where assigning with duplicate column names and new columns corrupted unrelated columns (:issue:`58317`)
 - Fixed segfault in :meth:`DataFrame.loc` when repeatedly adding new rows to an object-dtype-indexed :class:`DataFrame` (:issue:`21968`)
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 0a67d80aa6611..c0a479de4f6cb 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -417,8 +417,12 @@ def nbytes(self) -> int:
         Return the number of bytes in the underlying data.
         """
         rng = self._range
-        return getsizeof(rng) + sum(
-            getsizeof(getattr(rng, attr_name))
+        # passing a default to getsizeof avoids a TypeError on PyPy, where
+        # sys.getsizeof always raises TypeError unless a default is provided
+        # (GH#46176)
+        objsize = 24
+        return getsizeof(rng, objsize) + sum(
+            getsizeof(getattr(rng, attr_name), objsize)
             for attr_name in ["start", "stop", "step"]
         )
 
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index 325393a320c2a..91a3d5cdc0986 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -9,6 +9,7 @@
     RangeIndex,
 )
 import pandas._testing as tm
+import pandas.core.indexes.range as range_module
 from pandas.core.indexes.range import min_fitting_element
 
 
@@ -371,6 +372,19 @@ def test_nbytes(self):
         i2 = RangeIndex(0, 10)
         assert idx.nbytes == i2.nbytes
 
+    def test_nbytes_pypy_compat(self, monkeypatch):
+        # GH#46176 sys.getsizeof always raises TypeError on PyPy unless
+        # a default is provided; nbytes must keep working there.
+        def pypy_getsizeof(obj, default=None):
+            if default is None:
+                raise TypeError("PyPy")
+            return default
+
+        monkeypatch.setattr(range_module, "getsizeof", pypy_getsizeof)
+        idx = RangeIndex(0, 1000)
+        assert isinstance(idx.nbytes, int)
+        assert idx.memory_usage() == idx.nbytes
+
     @pytest.mark.parametrize(
         "start,stop,step",
         [