diff --git a/regridding/_regrid/_tests/test_regrid.py b/regridding/_regrid/_tests/test_regrid.py
index 35ef7c9..97f2878 100644
--- a/regridding/_regrid/_tests/test_regrid.py
+++ b/regridding/_regrid/_tests/test_regrid.py
@@ -39,6 +39,15 @@
             None,
             np.square(np.linspace(-1, 1, num=11)),
         ),
+        (
+            (np.linspace(-1, 1, num=11) * u.mm,),
+            (np.linspace(-1, 1, num=11) * u.mm,),
+            np.square(np.linspace(-1, 1, num=11)),
+            None,
+            None,
+            None,
+            np.square(np.linspace(-1, 1, num=11)),
+        ),
         (
             (np.linspace(-1, 1, num=11),),
             (np.linspace(-1, 1, num=11),),
diff --git a/regridding/_util.py b/regridding/_util.py
index 3cf7004..8c1c62d 100644
--- a/regridding/_util.py
+++ b/regridding/_util.py
@@ -32,6 +32,15 @@ def _normalize_input_output_coordinates(
     if isinstance(coordinates_output, np.ndarray):
         coordinates_output = (coordinates_output,)
 
+    coordinates_input = list(coordinates_input)
+    for i in range(len(coordinates_input)):
+        coord_input = coordinates_input[i]
+        coord_output = coordinates_output[i]
+        if hasattr(coord_output, "unit"):
+            coord_input = coord_input << coord_output.unit
+        coordinates_input[i] = coord_input
+    coordinates_input = tuple(coordinates_input)
+
     shape_coordinates_input = np.broadcast(*coordinates_input).shape
     shape_coordinates_output = np.broadcast(*coordinates_output).shape