diff --git a/Makefile.am b/Makefile.am
index 0ec9976d..c93aef84 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -277,6 +277,7 @@ TEST_BIN = 			\
     test/signal			\
     test/stringid		\
     test/uri			\
+    test/vector			\
     test/version
 
 
diff --git a/test/vector.cpp b/test/vector.cpp
new file mode 100644
index 00000000..c6ec9c92
--- /dev/null
+++ b/test/vector.cpp
@@ -0,0 +1,67 @@
+#include "vector.hpp"
+
+#include "maths.hpp"
+
+using util::vector;
+using util::vector2f;
+
+
+void
+test_polar (void)
+{
+    static const struct {
+        util::vector2f polar;
+        util::vector2f cartesian;
+        const char *desc;
+    } TESTS[] {
+        {
+            { 0.f, 0.f },
+            { 0.f, 0.f },
+            "all zeroes"
+        },
+
+        {
+            { 1.f, 0.f },
+            { 1.f, 0.f },
+            "unit length, unrotated"
+        },
+
+        {
+            { 1.f, PI_f / 2.f },
+            { 0.f, 1.f },
+            "unit length, rotated"
+        },
+
+        {
+            { 1.f, 2 * PI_f },
+            { 1.f, 0.f },
+            "full rotation, unit length"
+        }
+    };
+
+    for (const auto &t: TESTS) {
+        // Compare the difference of cartesian representations. Don't use
+        // direct equality comparisons here as the numeric stability can be
+        // poor and we have nice whole numbers to start with.
+        auto in_cart = t.cartesian;
+        auto to_cart = util::polar_to_cartesian (t.polar);
+
+        CHECK_LT ((in_cart - to_cart).magnitude (), 0.00001f);
+
+        // Compare polar representations. Make sure to normalise them first.
+        auto in_polar = t.polar;
+        auto to_polar = util::cartesian_to_polar (t.cartesian);
+
+        in_polar[1] = std::fmod (in_polar[1], 2 * PI_f);
+        to_polar[1] = std::fmod (to_polar[1], 2 * PI_f);
+
+        CHECK_EQ (in_polar, to_polar);
+    }
+}
+
+
+int
+main ()
+{
+    test_polar ();
+}
diff --git a/vector.cpp b/vector.cpp
index 49fb231e..5ba8657e 100644
--- a/vector.cpp
+++ b/vector.cpp
@@ -98,10 +98,12 @@ util::vector<S,T>::normalised (void) const {
     return out;
 }
 
-//-----------------------------------------------------------------------------
+
+///////////////////////////////////////////////////////////////////////////////
 template <typename T>
 util::vector<2,T>
-util::polar_to_cartesian (util::vector<2,T> v) {
+util::polar_to_cartesian (util::vector<2,T> v)
+{
     return util::vector<2,T> {
         v[0] * std::cos (v[1]),
         v[0] * std::sin (v[1])
@@ -111,6 +113,18 @@ util::polar_to_cartesian (util::vector<2,T> v) {
 
 //-----------------------------------------------------------------------------
 template <typename T>
+util::vector<2,T>
+util::cartesian_to_polar (util::vector<2,T> v)
+{
+    return util::vector<2,T> {
+        std::hypot (v.x, v.y),
+        std::atan2 (v.y, v.x)
+    };
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
 util::vector<3,T>
 util::cross (const util::vector<3,T> &a,
              const util::vector<3,T> &b)
@@ -236,6 +250,7 @@ INSTANTIATE(double)
 //-----------------------------------------------------------------------------
 namespace util {
     template vector<2,float> polar_to_cartesian (util::vector<2,float>);
+    template vector<2,float> cartesian_to_polar (util::vector<2,float>);
 
     template <> vector<1,float> random (void) { util::vector<1,float> out; randomise (out.data); return out; }
     template <> vector<2,float> random (void) { util::vector<2,float> out; randomise (out.data); return out; }
diff --git a/vector.hpp b/vector.hpp
index ce36af7b..1fa01caa 100644
--- a/vector.hpp
+++ b/vector.hpp
@@ -57,6 +57,7 @@ namespace util {
 
     // free vector operators
     template <typename T> vector<2,T> polar_to_cartesian (vector<2,T>);
+    template <typename T> vector<2,T> cartesian_to_polar (vector<2,T>);
 
     template <typename T> vector<3,T> cross (const vector<3,T>&, const vector<3,T>&);
     template <typename T> vector<3,T> spherical_to_cartesian (const vector<3,T>&);