diff --git a/src/huggingface_hub/serialization/_base.py b/src/huggingface_hub/serialization/_base.py
index 23d82145cf..e16e4a8137 100644
--- a/src/huggingface_hub/serialization/_base.py
+++ b/src/huggingface_hub/serialization/_base.py
@@ -89,7 +89,8 @@ def split_state_dict_into_shards_factory(
     current_shard_size = 0
     total_size = 0
 
-    max_shard_size = convert_file_size_to_int(max_shard_size)
+    if isinstance(max_shard_size, str):
+        max_shard_size = parse_size_to_int(max_shard_size)
 
     for key, tensor in state_dict.items():
         # when bnb serialization is used the weights in the state dict can be strings
@@ -171,45 +172,42 @@ def split_state_dict_into_shards_factory(
     )
 
 
-def convert_file_size_to_int(size: Union[int, str]):
+SIZE_UNITS = {
+    "TB": 10**12,
+    "GB": 10**9,
+    "MB": 10**6,
+    "KB": 10**3,
+}
+
+
+def parse_size_to_int(size_as_str: str) -> int:
     """
-    Converts a size expressed as a string with digits an unit (like `"5MB"`) to an integer (in bytes).
+    Parse a size expressed as a string with digits and unit (like `"5MB"`) to an integer (in bytes).
+
+    Supported units are "TB", "GB", "MB", "KB".
 
     Args:
-        size (`int` or `str`): The size to convert. Will be directly returned if an `int`.
+        size_as_str (`str`): The size to convert. Will be directly returned if an `int`.
 
     Example:
 
     ```py
-    >>> convert_file_size_to_int("1MiB")
-    1048576
+    >>> parse_size_to_int("5MB")
+    5000000
     ```
     """
-    mem_size = -1
-    err_msg = (
-        f"`size` {size} is not in a valid format. Use an integer for bytes, or a string with an unit (like '5.0GB')."
-    )
+    size_as_str = size_as_str.strip()
+
+    # Parse unit
+    unit = size_as_str[-2:].upper()
+    if unit not in SIZE_UNITS:
+        raise ValueError(f"Unit '{unit}' not supported. Supported units are TB, GB, MB, KB. Got '{size_as_str}'.")
+    multiplier = SIZE_UNITS[unit]
+
+    # Parse value
     try:
-        if isinstance(size, int):
-            mem_size = size
-        elif size.upper().endswith("GIB"):
-            mem_size = int(float(size[:-3]) * (2**30))
-        elif size.upper().endswith("MIB"):
-            mem_size = int(float(size[:-3]) * (2**20))
-        elif size.upper().endswith("KIB"):
-            mem_size = int(float(size[:-3]) * (2**10))
-        elif size.upper().endswith("GB"):
-            int_size = int(float(size[:-2]) * (10**9))
-            mem_size = int_size // 8 if size.endswith("b") else int_size
-        elif size.upper().endswith("MB"):
-            int_size = int(float(size[:-2]) * (10**6))
-            mem_size = int_size // 8 if size.endswith("b") else int_size
-        elif size.upper().endswith("KB"):
-            int_size = int(float(size[:-2]) * (10**3))
-            mem_size = int_size // 8 if size.endswith("b") else int_size
-    except ValueError:
-        raise ValueError(err_msg)
-
-    if mem_size < 0:
-        raise ValueError(err_msg)
-    return mem_size
+        value = float(size_as_str[:-2].strip())
+    except ValueError as e:
+        raise ValueError(f"Could not parse the size value from '{size_as_str}': {e}") from e
+
+    return int(value * multiplier)
diff --git a/tests/test_serialization.py b/tests/test_serialization.py
index 4eecbe997d..47a78d5e2e 100644
--- a/tests/test_serialization.py
+++ b/tests/test_serialization.py
@@ -1,5 +1,7 @@
+import pytest
+
 from huggingface_hub.serialization import split_state_dict_into_shards_factory
-from huggingface_hub.serialization._base import convert_file_size_to_int
+from huggingface_hub.serialization._base import parse_size_to_int
 from huggingface_hub.serialization._numpy import get_tensor_size as get_tensor_size_numpy
 from huggingface_hub.serialization._tensorflow import get_tensor_size as get_tensor_size_tensorflow
 from huggingface_hub.serialization._torch import get_tensor_size as get_tensor_size_torch
@@ -126,11 +128,15 @@ def test_get_tensor_size_torch():
     assert get_tensor_size_torch(torch.tensor([1, 2, 3, 4, 5], dtype=torch.float16)) == 5 * 2
 
 
-def test_convert_file_size_to_int():
-    assert convert_file_size_to_int("1KiB") == 2**10
-    assert convert_file_size_to_int("1KB") == 10**3
-    assert convert_file_size_to_int("1MiB") == 2**20
-    assert convert_file_size_to_int("1MB") == 10**6
-    assert convert_file_size_to_int("1GiB") == 2**30
-    assert convert_file_size_to_int("1GB") == 10**9
-    assert convert_file_size_to_int("5GB") == 5 * 10**9
+def test_parse_size_to_int():
+    assert parse_size_to_int("1KB") == 1 * 10**3
+    assert parse_size_to_int("2MB") == 2 * 10**6
+    assert parse_size_to_int("3GB") == 3 * 10**9
+    assert parse_size_to_int(" 10 KB ") == 10 * 10**3  # ok with whitespace
+    assert parse_size_to_int("20mb") == 20 * 10**6  # ok with lowercase
+
+    with pytest.raises(ValueError, match="Unit 'IB' not supported"):
+        parse_size_to_int("1KiB")  # not a valid unit
+
+    with pytest.raises(ValueError, match="Could not parse the size value"):
+        parse_size_to_int("1ooKB")  # not a float