diff --git a/pint/delegates/formatter/_format_helpers.py b/pint/delegates/formatter/_format_helpers.py
index 2ed4ba985..868663b99 100644
--- a/pint/delegates/formatter/_format_helpers.py
+++ b/pint/delegates/formatter/_format_helpers.py
@@ -268,6 +268,61 @@ def format_compound_unit(
     return out
 
 
+def dim_sort(items: Iterable[tuple[str, Number]], registry: UnitRegistry):
+    """Sort a list of units by dimensional order (from `registry.formatter.dim_order`).
+
+    Parameters
+    ----------
+    items : tuple
+        a list of tuples containing (unit names, exponent values).
+    registry : UnitRegistry
+        the registry to use for looking up the dimensions of each unit.
+
+    Returns
+    -------
+    list
+        the list of units sorted by most significant dimension first.
+
+    Raises
+    ------
+    KeyError
+        If unit cannot be found in the registry.
+    """
+    
+    if registry is None:
+        return items
+    ret_dict = dict()
+    dim_order = registry.formatter.dim_order
+    for unit_name, unit_exponent in items:
+        cname = registry.get_name(unit_name)
+        if not cname:
+            continue
+        cname_dims = registry.get_dimensionality(cname)
+        if len(cname_dims) == 0:
+            cname_dims = {"[]": None}
+        dim_types = iter(dim_order)
+        while True:
+            try:
+                dim = next(dim_types)
+                if dim in cname_dims:
+                    if dim not in ret_dict:
+                        ret_dict[dim] = list()
+                    ret_dict[dim].append(
+                        (
+                            unit_name,
+                            unit_exponent,
+                        )
+                    )
+                    break
+            except StopIteration:
+                raise KeyError(
+                    f"Unit {unit_name} (aka {cname}) has no recognized dimensions"
+                )
+
+    ret = sum([ret_dict[dim] for dim in dim_order if dim in ret_dict], [])
+    return ret
+
+
 def formatter(
     items: Iterable[tuple[str, Number]],
     as_ratio: bool = True,
@@ -309,6 +364,8 @@ def formatter(
          (Default value = lambda x: f"{x:n}")
     sort : bool, optional
         True to sort the formatted units alphabetically (Default value = True)
+    sort_func : callable
+        If not None, `sort_func` returns its sorting of the formatted units
 
     Returns
     -------
@@ -320,14 +377,14 @@ def formatter(
     if sort is False:
         warn(
             "The boolean `sort` argument is deprecated. "
-            "Use `sort_fun` to specify the sorting function (default=sorted) "
+            "Use `sort_func` to specify the sorting function (default=sorted) "
             "or None to keep units in the original order."
         )
         sort_func = None
     elif sort is True:
         warn(
             "The boolean `sort` argument is deprecated. "
-            "Use `sort_fun` to specify the sorting function (default=sorted) "
+            "Use `sort_func` to specify the sorting function (default=sorted) "
             "or None to keep units in the original order."
         )
         sort_func = sorted
diff --git a/pint/delegates/formatter/full.py b/pint/delegates/formatter/full.py
index fae26d524..a8dc1ec56 100644
--- a/pint/delegates/formatter/full.py
+++ b/pint/delegates/formatter/full.py
@@ -11,9 +11,9 @@
 
 from __future__ import annotations
 
-from typing import TYPE_CHECKING, Literal, Optional, Any
+from typing import TYPE_CHECKING, Callable, Literal, Optional, Any
 import locale
-from ...compat import babel_parse, Unpack
+from ...compat import babel_parse, Number, Unpack
 from ...util import iterable
 
 from ..._typing import Magnitude
@@ -38,6 +38,18 @@ class FullFormatter:
     _formatters: dict[str, Any] = {}
 
     default_format: str = ""
+    # TODO: This can be over-riden by the registry definitions file
+    dim_order = (
+        "[substance]",
+        "[mass]",
+        "[current]",
+        "[luminosity]",
+        "[length]",
+        "[]",
+        "[time]",
+        "[temperature]",
+    )
+    default_sort_func: Optional[Callable[Iterable[tuple[str, Number]]], Iterable[tuple[str, Number]]] = None
 
     locale: Optional[Locale] = None
     babel_length: Literal["short", "long", "narrow"] = "long"
diff --git a/pint/delegates/formatter/html.py b/pint/delegates/formatter/html.py
index 3dc14330c..ea88fb13b 100644
--- a/pint/delegates/formatter/html.py
+++ b/pint/delegates/formatter/html.py
@@ -87,6 +87,7 @@ def format_unit(
             division_fmt=r"{}/{}",
             power_fmt=r"{}<sup>{}</sup>",
             parentheses_fmt=r"({})",
+            sort_func=lambda x: unit._REGISTRY.formatter.default_sort_func(x, unit._REGISTRY),
         )
 
     def format_quantity(
diff --git a/pint/delegates/formatter/latex.py b/pint/delegates/formatter/latex.py
index aacf8cdf5..cf2b57848 100644
--- a/pint/delegates/formatter/latex.py
+++ b/pint/delegates/formatter/latex.py
@@ -173,6 +173,9 @@ def format_unit(
         self, unit: PlainUnit, uspec: str = "", **babel_kwds: Unpack[BabelKwds]
     ) -> str:
         units = format_compound_unit(unit, uspec, **babel_kwds)
+        if unit._REGISTRY.formatter.default_sort_func:
+            # Lift the sorting by dimensions b/c the preprocessed units are unrecognizeable
+            units = unit._REGISTRY.formatter.default_sort_func(units, unit._REGISTRY)
 
         preprocessed = {rf"\mathrm{{{latex_escape(u)}}}": p for u, p in units}
         formatted = formatter(
@@ -183,6 +186,7 @@ def format_unit(
             division_fmt=r"\frac[{}][{}]",
             power_fmt="{}^[{}]",
             parentheses_fmt=r"\left({}\right)",
+            sort_func=None,
         )
         return formatted.replace("[", "{").replace("]", "}")
 
diff --git a/pint/delegates/formatter/plain.py b/pint/delegates/formatter/plain.py
index 4b9616631..01c352bf9 100644
--- a/pint/delegates/formatter/plain.py
+++ b/pint/delegates/formatter/plain.py
@@ -269,6 +269,7 @@ def format_unit(
             power_fmt="{}{}",
             parentheses_fmt="({})",
             exp_call=pretty_fmt_exponent,
+            sort_func=lambda x: unit._REGISTRY.formatter.default_sort_func(x, unit._REGISTRY),
         )
 
     def format_quantity(
diff --git a/pint/testsuite/test_issues.py b/pint/testsuite/test_issues.py
index 3db01fb4e..167d6bb4d 100644
--- a/pint/testsuite/test_issues.py
+++ b/pint/testsuite/test_issues.py
@@ -1155,3 +1155,52 @@ def test_issues_1505():
     assert isinstance(
         ur.Quantity("m/s").magnitude, decimal.Decimal
     )  # unexpected fail (magnitude should be a decimal)
+
+
+def test_issues_1841(subtests):
+    import pint
+    from pint.delegates.formatter._format_helpers import dim_sort
+
+    ur = UnitRegistry()
+    ur.formatter.default_sort_func = dim_sort
+
+    for x, spec, result in (
+            (ur.Unit(UnitsContainer(hour=1,watt=1)), "P~", "W·h"),
+            (ur.Unit(UnitsContainer(ampere=1,volt=1)), "P~", "V·A"),
+            (ur.Unit(UnitsContainer(meter=1,newton=1)), "P~", "N·m"),
+    ):
+        with subtests.test(spec):
+            ur.default_format = spec
+            breakpoint()
+            assert f"{x}" == result, f"Failed for {spec}, {result}"
+
+
+@pytest.mark.xfail
+def test_issues_1841_xfail():
+    import pint
+    from pint import formatting as fmt
+    import pint.delegates.formatter._format_helpers
+    from pint.delegates.formatter._format_helpers import dim_sort
+
+    # sets compact display mode by default
+    ur = UnitRegistry()
+    ur.default_format = "~P"
+    ur.formatter.default_sort_func = dim_sort
+
+    q = ur.Quantity("2*pi radian * hour")
+
+    # Note that `radian` (and `bit` and `count`) are treated as dimensionless.
+    # And note that dimensionless quantities are stripped by this process,
+    # leading to errorneous output.  Suggestions?
+    breakpoint()
+    assert (
+        fmt.format_unit(q.u._units, spec="", registry=ur, sort_dims=True)
+        == "radian * hour"
+    )
+    assert (
+        fmt.format_unit(q.u._units, spec="", registry=ur, sort_dims=False)
+        == "hour * radian"
+    )
+
+    # this prints "2*pi hour * radian", not "2*pi radian * hour" unless sort_dims is True
+    # print(q)