diff --git a/README.md b/README.md
index 29cd5f1e..d1522d3f 100644
--- a/README.md
+++ b/README.md
@@ -87,6 +87,14 @@ Multiply a `Vector2` by another `Vector2` to get the dot product.
     >>> Vector2(45, 60).length
     75.0
 
+### Cross-product
+
+Take the cross-product between two (2D) vectors.
+The result is expressed as a scalar, as it is known to lie on the z-axis.
+
+    >>> Vector(1, 0) ^ Vector(0, 1)
+    1
+
 ### Access Values
 
 Convenient access to `Vector2` members via dot notation, indexes, or keys.
@@ -122,6 +130,16 @@ Rotate a vector in relation to its own origin and return a new `Vector2`.
 
 Positive rotation is counter/anti-clockwise.
 
+#### angle(vector)
+
+Compute the angle between two vectors, expressed as a scalar in degrees.
+
+    >>> Vector(1, 0).angle(Vector(0, 1))
+    90
+
+As with `rotate()`, angles are signed, and refer to a direct coordinate system
+(i.e. positive rotations are counter-clockwise).
+
 #### normalize()
 
 Return the normalized `Vector2` for the given `Vector2`.
diff --git a/ppb_vector/vector2.py b/ppb_vector/vector2.py
index e13eda4d..04ea9d75 100644
--- a/ppb_vector/vector2.py
+++ b/ppb_vector/vector2.py
@@ -1,4 +1,4 @@
-from math import cos, hypot, radians, sin
+from math import acos, cos, degrees, hypot, radians, sin
 from numbers import Number
 from collections.abc import Sequence
 
@@ -46,6 +46,9 @@ def __rmul__(self, other):
         if isinstance(other, Number):
             return Vector2(self.x * other, self.y * other)
 
+    def __xor__(self, other):
+        return self.x * other.y - self.y * other.x
+
     def __getitem__(self, item):
         if hasattr(item, '__index__'):
             item = item.__index__()
@@ -88,6 +91,9 @@ def __iter__(self):
     def __neg__(self):
         return self * -1
 
+    def angle(self, other):
+        return degrees(acos(self.normalize() * other.normalize()))
+
     def rotate(self, degrees):
         r = radians(degrees)
         r_cos = cos(r)
diff --git a/tests/test_vector2_rotate.py b/tests/test_vector2_rotate.py
index 4fe3d4d8..30142840 100644
--- a/tests/test_vector2_rotate.py
+++ b/tests/test_vector2_rotate.py
@@ -11,9 +11,14 @@
     (Vector2(math.pi, math.e), 67, Vector2(-1.27467, 3.95397))
 ]
 
+def isclose(x, y, epsilon = 6.5e-5):
+    d = (x - y) % 360
+    return (d < epsilon) or (d > 360 - epsilon)
+
 @pytest.mark.parametrize('input, degrees, expected', data)
 def test_multiple_rotations(input, degrees, expected):
     assert input.rotate(degrees) == expected
+    assert isclose(input.angle(expected), degrees)
 
 def test_for_exception():
     with pytest.raises(TypeError):