diff --git a/pandas/io/formats/style.py b/pandas/io/formats/style.py
index 10cf8541effd6..4a8169c0609fd 100644
--- a/pandas/io/formats/style.py
+++ b/pandas/io/formats/style.py
@@ -1049,10 +1049,12 @@ def to_latex(
             clines=clines,
         )
 
-        encoding = encoding or get_option("styler.render.encoding")
-        return save_to_buffer(
-            latex, buf=buf, encoding=None if buf is None else encoding
+        encoding = (
+            (encoding or get_option("styler.render.encoding"))
+            if isinstance(buf, str)  # i.e. a filepath
+            else encoding
         )
+        return save_to_buffer(latex, buf=buf, encoding=encoding)
 
     def to_html(
         self,
@@ -1173,7 +1175,6 @@ def to_html(
         if caption is not None:
             obj.set_caption(caption)
 
-        encoding = encoding or get_option("styler.render.encoding")
         # Build HTML string..
         html = obj._render_html(
             sparse_index=sparse_index,
@@ -1181,7 +1182,7 @@ def to_html(
             max_rows=max_rows,
             max_cols=max_columns,
             exclude_styles=exclude_styles,
-            encoding=encoding,
+            encoding=encoding or get_option("styler.render.encoding"),
             doctype_html=doctype_html,
             **kwargs,
         )
diff --git a/pandas/tests/io/formats/style/test_style.py b/pandas/tests/io/formats/style/test_style.py
index fa054ff7ca6c0..1a056f8cb3363 100644
--- a/pandas/tests/io/formats/style/test_style.py
+++ b/pandas/tests/io/formats/style/test_style.py
@@ -1547,3 +1547,10 @@ def test_col_trimming_hide_columns():
         assert ctx["head"][0][c + 2]["is_visible"] == vals[1]
 
     assert len(ctx["body"][0]) == 6  # index + 2 hidden + 2 visible + trimming col
+
+
+@pytest.mark.parametrize("format", ["html", "latex"])
+def test_output_buffer(mi_styler, format):
+    # gh 47053
+    with open(f"delete_me.{format}", "w") as f:
+        getattr(mi_styler, f"to_{format}")(f)