diff --git a/skimage/transform/_geometric.py b/skimage/transform/_geometric.py
index 1179811d..96ea4687 100644
--- a/skimage/transform/_geometric.py
+++ b/skimage/transform/_geometric.py
@@ -604,7 +604,7 @@ class PolynomialTransform(GeometricTransform):
             raise ValueError("invalid shape of transformation parameters")
         self._params = params
 
-    def estimate(self, src, dst, order):
+    def estimate(self, src, dst, order=2):
         """Set the transformation matrix with the explicit transformation
         parameters.
 
@@ -645,7 +645,7 @@ class PolynomialTransform(GeometricTransform):
             Source coordinates.
         dst : (N, 2) array
             Destination coordinates.
-        order : int
+        order : int, optional
             Polynomial order (number of coefficients is order + 1).
 
         """
@@ -750,7 +750,8 @@ def estimate_transform(ttype, src, dst, **kwargs):
             'affine'            `src, `dst`
             'piecewise-affine'  `src, `dst`
             'projective'        `src, `dst`
-            'polynomial'        `src, `dst`, `order` (polynomial order)
+            'polynomial'        `src, `dst`, `order` (polynomial order,
+                                                      default order is 2)
 
         Also see examples below.
 
diff --git a/skimage/transform/tests/test_geometric.py b/skimage/transform/tests/test_geometric.py
index d3a75f7b..c7f9f832 100644
--- a/skimage/transform/tests/test_geometric.py
+++ b/skimage/transform/tests/test_geometric.py
@@ -159,6 +159,12 @@ def test_polynomial_init():
     assert_array_almost_equal(tform2._params, tform._params)
 
 
+def test_polynomial_default_order():
+    tform = estimate_transform('polynomial', SRC, DST)
+    tform2 = estimate_transform('polynomial', SRC, DST, order=2)
+    assert_array_almost_equal(tform2._params, tform._params)
+
+
 def test_union():
     tform1 = SimilarityTransform(scale=0.1, rotation=0.3)
     tform2 = SimilarityTransform(scale=0.1, rotation=0.9)