diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index 554abe8d6677..ce0ddbfe4216 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -2075,3 +2075,26 @@ def _check_and_log_subprocess(command, logger, **kwargs):
             .format(command, exc.output.decode('utf-8')))
     logger.debug(report)
     return report
+
+
+def _print_unit(st, dpi=None):
+    """
+    Convert from a string with a number and units into inches
+    """
+    print_units = {'cm': 2.54, 'pt': 72.0, 'mm': 25.4, 'in': 1.0}
+    if len(st) > 2:
+        num = float(st[:-2])
+    else:
+        num = 1
+    unit = st[-2:]
+    # special case "px"
+    if unit == 'px':
+        if dpi is not None:
+            return num / dpi
+        else:
+            raise ValueError('px units need dpi to be set')
+    elif unit in print_units:
+        return num / print_units[unit]
+    else:
+        # let the parent handle the errors
+        return st
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index 819525482cb7..9a0212f46722 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -344,14 +344,17 @@ def __init__(self,
         if frameon is None:
             frameon = rcParams['figure.frameon']
 
-        if not np.isfinite(figsize).all():
-            raise ValueError('figure size must be finite not '
-                             '{}'.format(figsize))
-        self.bbox_inches = Bbox.from_bounds(0, 0, *figsize)
-
+        self.canvas = None
+        self._suptitle = None
         self.dpi_scale_trans = Affine2D().scale(dpi, dpi)
         # do not use property as it will trigger
         self._dpi = dpi
+
+        # init the bbox to dummy values:
+        self.bbox_inches = Bbox.from_bounds(0, 0, 1, 1)
+        # set properly.
+        self.set_size(figsize)
+
         self.bbox = TransformedBbox(self.bbox_inches, self.dpi_scale_trans)
 
         self.frameon = frameon
@@ -364,9 +367,6 @@ def __init__(self,
         self._set_artist_props(self.patch)
         self.patch.set_antialiased(False)
 
-        self.canvas = None
-        self._suptitle = None
-
         if subplotpars is None:
             subplotpars = SubplotParams()
 
@@ -391,6 +391,14 @@ def __init__(self,
         # list of child gridspecs for this figure
         self._gridspecs = []
 
+    def _parse_figsize(self, figsize):
+        if len(figsize) == 3:
+            unit = figsize[-1]
+            figsize = figsize[:2]
+            conv = cbook._print_unit(unit, dpi=self._dpi)
+            figsize = [f * conv for f in figsize]
+        return figsize
+
     # TODO: I'd like to dynamically add the _repr_html_ method
     # to the figure in the right context, but then IPython doesn't
     # use it, for some reason.
@@ -862,19 +870,85 @@ def figimage(self, X, xo=0, yo=0, alpha=None, norm=None, cmap=None,
         self.stale = True
         return im
 
+    def set_size(self, w, h=None, units=None, forward=True):
+        """
+        Set the figure size
+
+        Parameters
+        ----------
+
+        w: float, string, or two-tuple of either.
+
+            If a two-tuple, (width, height) of the figure.
+
+            If a float, width of figure in inches.
+
+            If a string, its a float followed by a 2-character suffix
+            of either 'in', 'cm', 'mm', 'pt' (inches, centimeters,
+            millimeters, or points).  i.e. ``w='4.6cm'``.
+
+        h: float or string
+            As above, if a float it is the hieght of the figure in inches,
+            or a string decoded as above.
+
+        units : string
+            If specified, will be applied to floats in (w, h).  If
+            either (w, h) are strings, the units they specify are used
+            for that dimension.  Allows ``fig.set_size(12, 15, units='cm')``
+
+        forward : bool, default True
+            Forward to the window so the canvas size is updated;
+            e.g., you can resize the figure window from the shell
+
+        See Also
+        --------
+        matplotlib.Figure.set_size_inches
+
+        """
+        if h is None:
+            figsize = self._parse_figsize(w)
+            w, h = figsize
+
+        conv = 1  # default units are inches.
+        if isinstance(units, str):
+            conv = cbook._print_unit(units, dpi=self._dpi)
+            if isinstance(conv, str):
+                raise ValueError('Could not convert units str {} to '
+                                 'inches'.format(conv))
+
+        if isinstance(w, str):
+            w = cbook._print_unit(w, dpi=self._dpi)
+            if isinstance(w, str):
+                raise ValueError('Could not convert str {} to '
+                                 'inches'.format(w))
+        else:
+            # convert using units arg
+            w = w * conv
+
+        if isinstance(h, str):
+            h = cbook._print_unit(h, dpi=self._dpi)
+            if isinstance(h, str):
+                raise ValueError('Could not convert str {} to '
+                                 'inches'.format(h))
+        else:
+            # convert using units arg
+            h = h * conv
+        # all done:  set...
+        self.set_size_inches(w, h, forward=forward)
+
     def set_size_inches(self, w, h=None, forward=True):
-        """Set the figure size in inches.
+        """Set the figure size.
 
         Call signatures::
 
              fig.set_size_inches(w, h)  # OR
              fig.set_size_inches((w, h))
 
-        optional kwarg *forward=True* will cause the canvas size to be
+        Optional kwarg *forward=True* will cause the canvas size to be
         automatically updated; e.g., you can resize the figure window
         from the shell
 
-        ACCEPTS: a (w, h) tuple with w, h in inches
+        ACCEPTS: a (w, h) tuple with w, h in inches.
 
         See Also
         --------
@@ -883,8 +957,10 @@ def set_size_inches(self, w, h=None, forward=True):
 
         # the width and height have been passed in as a tuple to the first
         # argument, so unpack them
+
         if h is None:
             w, h = w
+
         if not all(np.isfinite(_) for _ in (w, h)):
             raise ValueError('figure size must be finite not '
                              '({}, {})'.format(w, h))