diff --git a/dvc/utils/stream.py b/dvc/utils/stream.py
index 27fafc806..fc71de920 100644
--- a/dvc/utils/stream.py
+++ b/dvc/utils/stream.py
@@ -70,6 +70,7 @@ class HashedStreamReader(io.IOBase):
     def __init__(self, fobj):
         self.fobj = fobj
         self.md5 = hashlib.md5()
+        self.total_read = 0
         self.is_text_file = None
         super().__init__()
 
@@ -95,9 +96,12 @@ class HashedStreamReader(io.IOBase):
         else:
             data = chunk
         self.md5.update(data)
+        self.total_read += len(data)
 
         return chunk
 
     @property
     def hash_info(self):
-        return HashInfo(self.PARAM_CHECKSUM, self.md5.hexdigest(), nfiles=1)
+        return HashInfo(
+            self.PARAM_CHECKSUM, self.md5.hexdigest(), size=self.total_read
+        )
diff --git a/tests/func/test_add.py b/tests/func/test_add.py
index ece3cc33b..b5559ddc3 100644
--- a/tests/func/test_add.py
+++ b/tests/func/test_add.py
@@ -1024,6 +1024,7 @@ def test_add_to_remote(tmp_dir, dvc, local_cloud, local_remote):
 
     hash_info = stage.outs[0].hash_info
     assert local_remote.hash_to_path_info(hash_info.value).read_text() == "foo"
+    assert hash_info.size == len("foo")
 
 
 def test_add_to_remote_absolute(tmp_dir, make_tmp_dir, dvc, local_remote):
@@ -1067,6 +1068,8 @@ def test_add_to_cache_dir(tmp_dir, dvc, local_cloud):
     (stage,) = dvc.add(str(local_cloud / "data"), out="data")
     assert len(stage.deps) == 0
     assert len(stage.outs) == 1
+    assert stage.outs[0].hash_info.size == len("foo") + len("bar")
+    assert stage.outs[0].hash_info.nfiles == 2
 
     data = tmp_dir / "data"
     assert data.read_text() == {"foo": "foo", "bar": "bar"}
diff --git a/tests/func/test_import_url.py b/tests/func/test_import_url.py
index 42a3ebb4e..b222ae18f 100644
--- a/tests/func/test_import_url.py
+++ b/tests/func/test_import_url.py
@@ -282,6 +282,7 @@ def test_import_url_to_remote_single_file(
 
     hash_info = stage.outs[0].hash_info
     assert local_remote.hash_to_path_info(hash_info.value).read_text() == "foo"
+    assert hash_info.size == len("foo")
 
 
 @pytest.mark.parametrize(