diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 06a3925dd35a..4658385ffc56 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1526,8 +1526,11 @@ def convert_units(self, x):
 
         if self.converter is None:
             return x
-
-        ret = self.converter.convert(x, self.units, self)
+        try:
+            ret = self.converter.convert(x, self.units, self)
+        except Exception as e:
+            raise munits.ConversionError('Failed to convert value(s) to axis '
+                                         f'units: {x!r}') from e
         return ret
 
     def set_units(self, u):
diff --git a/lib/matplotlib/category.py b/lib/matplotlib/category.py
index bdc05301e5ad..74ed8137a493 100644
--- a/lib/matplotlib/category.py
+++ b/lib/matplotlib/category.py
@@ -23,24 +23,30 @@
 class StrCategoryConverter(units.ConversionInterface):
     @staticmethod
     def convert(value, unit, axis):
-        """Converts strings in value to floats using
+        """Convert strings in value to floats using
         mapping information store in the unit object.
 
         Parameters
         ----------
         value : string or iterable
-            value or list of values to be converted
-        unit : :class:`.UnitData`
-           object string unit information for value
-        axis : :class:`~matplotlib.Axis.axis`
-            axis on which the converted value is plotted
+            Value or list of values to be converted.
+        unit : `.UnitData`
+            An object mapping strings to integers.
+        axis : `~matplotlib.axis.Axis`
+            axis on which the converted value is plotted.
+
+            .. note:: *axis* is unused.
 
         Returns
         -------
-        mapped_ value : float or ndarray[float]
-
-        .. note:: axis is not used in this function
+        mapped_value : float or ndarray[float]
         """
+        if unit is None:
+            raise ValueError(
+                'Missing category information for StrCategoryConverter; '
+                'this might be caused by unintendedly mixing categorical and '
+                'numeric data')
+
         # dtype = object preserves numerical pass throughs
         values = np.atleast_1d(np.array(value, dtype=object))
 
@@ -190,7 +196,7 @@ def update(self, data):
                 self._mapping[val] = next(self._counter)
 
 
-# Connects the convertor to matplotlib
+# Register the converter with Matplotlib's unit framework
 units.registry[str] = StrCategoryConverter()
 units.registry[np.str_] = StrCategoryConverter()
 units.registry[bytes] = StrCategoryConverter()
diff --git a/lib/matplotlib/units.py b/lib/matplotlib/units.py
index c23d791b092a..1798f59db7dc 100644
--- a/lib/matplotlib/units.py
+++ b/lib/matplotlib/units.py
@@ -49,6 +49,10 @@ def default_units(x, axis):
 from matplotlib.cbook import iterable, safe_first_element
 
 
+class ConversionError(TypeError):
+    pass
+
+
 class AxisInfo(object):
     """
     Information to support default axis labeling, tick labeling, and