diff --git a/CHANGES b/CHANGES
index 6b1d0484e..8341733d8 100644
--- a/CHANGES
+++ b/CHANGES
@@ -4,8 +4,8 @@ Pint Changelog
 0.24 (unreleased)
 -----------------
 
-- Nothing changed yet.
-
+- Fix converting to offset units of higher dimension e.g. gauge pressure (#1949).
+-
 
 0.23 (2023-12-08)
 -----------------
diff --git a/pint/facets/nonmultiplicative/registry.py b/pint/facets/nonmultiplicative/registry.py
index 67250ea48..e5e2791a6 100644
--- a/pint/facets/nonmultiplicative/registry.py
+++ b/pint/facets/nonmultiplicative/registry.py
@@ -193,7 +193,7 @@ def _add_ref_of_log_or_offset_unit(
         self, offset_unit: str, all_units: UnitsContainer
     ) -> UnitsContainer:
         slct_unit = self._units[offset_unit]
-        if slct_unit.is_logarithmic or (not slct_unit.is_multiplicative):
+        if slct_unit.is_logarithmic:
             # Extract reference unit
             slct_ref = slct_unit.reference
 
@@ -205,6 +205,11 @@ def _add_ref_of_log_or_offset_unit(
                 (u, e) = [(u, e) for u, e in slct_ref.items()].pop()
                 # Add it back to the unit list
                 return all_units.add(u, e)
+
+        if not slct_unit.is_multiplicative:  # is offset unit
+            # Extract reference unit
+            return slct_unit.reference
+
         # Otherwise, return the units unmodified
         return all_units