diff --git a/docs/cli.rst b/docs/cli.rst
index dc0c072..572b0e5 100644
--- a/docs/cli.rst
+++ b/docs/cli.rst
@@ -1342,6 +1342,8 @@ You can include named parameters in your where clause and populate them using on
 
 The ``--dry-run`` option will output a preview of the conversion against the first ten rows, without modifying the database.
 
+By default any rows with a falsey value for the column - such as ``0`` or ``null`` - will be skipped. Use the ``--no-skip-false`` option to disable this behaviour.
+
 .. _cli_convert_import:
 
 Importing additional modules
diff --git a/docs/python-api.rst b/docs/python-api.rst
index 206e5e6..4d883db 100644
--- a/docs/python-api.rst
+++ b/docs/python-api.rst
@@ -916,6 +916,8 @@ This will add the new column, if it does not already exist. You can pass ``outpu
 
 If you want to drop the original column after saving the results in a separate output column, pass ``drop=True``.
 
+By default any rows with a falsey value for the column - such as ``0`` or ``None`` - will be skipped. Pass ``skip_false=False`` to disable this behaviour.
+
 You can create multiple new columns from a single input column by passing ``multi=True`` and a conversion function that returns a Python dictionary. This example creates new ``upper`` and ``lower`` columns populated from the single ``title`` column:
 
 .. code-block:: python
diff --git a/sqlite_utils/cli.py b/sqlite_utils/cli.py
index c3c55e2..ce354e0 100644
--- a/sqlite_utils/cli.py
+++ b/sqlite_utils/cli.py
@@ -2811,6 +2811,7 @@ def _generate_convert_help():
     type=click.Choice(["integer", "float", "blob", "text"]),
 )
 @click.option("--drop", is_flag=True, help="Drop original column afterwards")
+@click.option("--no-skip-false", is_flag=True, help="Don't skip falsey values")
 @click.option("-s", "--silent", is_flag=True, help="Don't show a progress bar")
 def convert(
     db_path,
@@ -2825,6 +2826,7 @@ def convert(
     output,
     output_type,
     drop,
+    no_skip_false,
     silent,
 ):
     sqlite3.enable_callback_tracebacks(True)
@@ -2882,6 +2884,7 @@ def convert(
                 output=output,
                 output_type=output_type,
                 drop=drop,
+                skip_false=not no_skip_false,
                 multi=multi,
                 show_progress=not silent,
             )
diff --git a/tests/test_cli_convert.py b/tests/test_cli_convert.py
index d26ab8c..97988b9 100644
--- a/tests/test_cli_convert.py
+++ b/tests/test_cli_convert.py
@@ -626,3 +626,30 @@ def test_convert_initialization_pattern(fresh_db_and_path):
     assert list(db["names"].rows) == [
         {"id": 1, "name": "17"},
     ]
+
+
+@pytest.mark.parametrize(
+    "no_skip_false,expected",
+    (
+        (True, 1),
+        (False, 0),
+    ),
+)
+def test_convert_no_skip_false(fresh_db_and_path, no_skip_false, expected):
+    db, db_path = fresh_db_and_path
+    args = [
+        "convert",
+        db_path,
+        "t",
+        "x",
+        "-",
+    ]
+    if no_skip_false:
+        args.append("--no-skip-false")
+    db["t"].insert_all([{"x": 0}, {"x": 1}])
+    assert db["t"].get(1)["x"] == 0
+    assert db["t"].get(2)["x"] == 1
+    result = CliRunner().invoke(cli.cli, args, input="value + 1")
+    assert 0 == result.exit_code, result.output
+    assert db["t"].get(1)["x"] == expected
+    assert db["t"].get(2)["x"] == 2