diff --git a/src/galdynamix/potential/_potential/param/core.py b/src/galdynamix/potential/_potential/param/core.py
index ba5f3397..194cf500 100644
--- a/src/galdynamix/potential/_potential/param/core.py
+++ b/src/galdynamix/potential/_potential/param/core.py
@@ -63,6 +63,7 @@ class ConstantParameter(AbstractParameter):
     # TODO: link this shape to the return shape from __call__
     value: FloatArrayAnyShape = eqx.field(converter=converter_float_array)
 
+    # This is a workaround since vectorized methods don't support kwargs.
     @partial_jit()
     @vectorize_method(signature="()->()")
     def _call_helper(self, _: FloatOrIntScalar) -> ArrayAnyShape:
@@ -93,6 +94,7 @@ def __call__(
 
 #####################################################################
 # User-defined Parameter
+# For passing a function as a parameter.
 
 
 @runtime_checkable
@@ -118,11 +120,19 @@ def __call__(self, t: FloatScalar, **kwargs: Any) -> ArrayAnyShape:
 
 
 class UserParameter(AbstractParameter):
-    """User-defined Parameter."""
+    """User-defined Parameter.
+
+    Parameters
+    ----------
+    func : Callable[[Array[float, ()] | float | int], Array[float, (*shape,)]]
+        The function to use to compute the parameter value.
+    unit : Unit, keyword-only
+        The output unit of the parameter.
+    """
 
     # TODO: unit handling
-    func: ParameterCallable
+    func: ParameterCallable = eqx.field(static=True)
 
     @partial_jit()
-    def __call__(self, t: FloatScalar, **kwargs: Any) -> ArrayAnyShape:
+    def __call__(self, t: FloatOrIntScalar, **kwargs: Any) -> FloatArrayAnyShape:
         return self.func(t, **kwargs)
diff --git a/src/galdynamix/potential/_potential/param/field.py b/src/galdynamix/potential/_potential/param/field.py
index 14348d97..cb390854 100644
--- a/src/galdynamix/potential/_potential/param/field.py
+++ b/src/galdynamix/potential/_potential/param/field.py
@@ -1,12 +1,13 @@
 __all__ = ["ParameterField"]
 
 from dataclasses import KW_ONLY, dataclass, field, is_dataclass
-from typing import Any, cast, overload
+from typing import Annotated, Any, cast, get_args, get_origin, get_type_hints, overload
 
 import astropy.units as u
 import jax.numpy as xp
 
 from galdynamix.potential._potential.core import AbstractPotential
+from galdynamix.typing import Unit
 
 from .core import AbstractParameter, ConstantParameter, ParameterCallable, UserParameter
 
@@ -27,7 +28,7 @@ class ParameterField:
 
     name: str = field(init=False)
     _: KW_ONLY
-    dimensions: u.PhysicalType  # TODO: add a converter_argument
+    dimensions: u.PhysicalType
     equivalencies: u.Equivalency | tuple[u.Equivalency, ...] | None = None
 
     def __post_init__(self) -> None:
@@ -76,6 +77,18 @@ def __get__(  # TODO: use `Self` when beartype is happy
 
     # -----------------------------
 
+    def _check_unit(self, potential: AbstractPotential, unit: Unit) -> None:
+        """Check that the given unit is compatible with the parameter's."""
+        if not unit.is_equivalent(
+            potential.units[self.dimensions],
+            equivalencies=self.equivalencies,
+        ):
+            msg = (
+                "Parameter function must return a value "
+                f"with units equivalent to {self.dimensions}"
+            )
+            raise ValueError(msg)
+
     def __set__(
         self,
         potential: AbstractPotential,
@@ -83,13 +96,15 @@ def __set__(
     ) -> None:
         # Convert
         if isinstance(value, AbstractParameter):
-            # TODO: use the dimensions & equivalencies info to check the parameters.
-            # TODO: use the units on the `potential` to convert the parameter value.
-            pass
+            # TODO: this doesn't handle the correct output unit, a. la.
+            # potential.units[self.dimensions]
+            self._check_unit(potential, value.unit)  # Check the unit is compatible
         elif callable(value):
-            # TODO: use the dimensions & equivalencies info to check the parameters.
-            # TODO: use the units on the `potential` to convert the parameter value.
-            value = UserParameter(func=value)
+            # TODO: this only gets the existing unit, it doesn't handle the
+            # correct output unit, a. la. potential.units[self.dimensions]
+            unit = _get_unit_from_return_annotation(value)
+            self._check_unit(potential, unit)  # Check the unit is compatible
+            value = UserParameter(func=value, unit=unit)
         else:
             # TODO: the issue here is that ``units`` hasn't necessarily been set
             #       on the potential yet. What is needed is to possibly bail out
@@ -100,8 +115,55 @@ def __set__(
             unit = potential.units[self.dimensions]
             if isinstance(value, u.Quantity):
                 value = value.to_value(unit, equivalencies=self.equivalencies)
-
             value = ConstantParameter(xp.asarray(value), unit=unit)
 
         # Set
         potential.__dict__[self.name] = value
+
+
+def _get_unit_from_return_annotation(func: ParameterCallable) -> Unit:
+    """Get the unit from the return annotation of a Parameter function.
+
+    Parameters
+    ----------
+    func : Callable[[Array[float, ()] | float | int], Array[float, (*shape,)]]
+        The function to use to compute the parameter value.
+
+    Returns
+    -------
+    Unit
+        The unit from the return annotation of the function.
+    """
+    # Get the return annotation
+    type_hints = get_type_hints(func, include_extras=True)
+    if "return" not in type_hints:
+        msg = "Parameter function must have a return annotation"
+        raise TypeError(msg)
+
+    # Check that the return annotation might contain a unit
+    return_annotation = type_hints["return"]
+    return_origin = get_origin(return_annotation)
+    if return_origin is not Annotated:
+        msg = "Parameter function return annotation must be annotated"
+        raise TypeError(msg)
+
+    # Get the unit from the return annotation
+    return_args = get_args(return_annotation)
+    has_unit = False
+    for arg in return_args[1:]:
+        # Try to convert the argument to a unit
+        try:
+            unit = u.Unit(arg)
+        except ValueError:
+            continue
+        # Only one unit annotation is allowed
+        if has_unit:
+            msg = "function has more than one unit annotation"
+            raise ValueError(msg)
+        has_unit = True
+
+    if not has_unit:
+        msg = "function did not have a valid unit annotation"
+        raise ValueError(msg)
+
+    return unit