diff --git a/test/vector.cpp b/test/vector.cpp
index 394e48d9..688bba0f 100644
--- a/test/vector.cpp
+++ b/test/vector.cpp
@@ -102,6 +102,56 @@ test_euler (util::TAP::logger &tap)
 }
 
 
+///////////////////////////////////////////////////////////////////////////////
+void
+test_spherical (util::TAP::logger &tap)
+{
+    static constexpr struct {
+        util::vector3f spherical;
+        util::vector3f cartesian;
+        const char *message;
+    } TESTS[] = {
+        { {  1,  0,  0 }, {  0,  0,  1 }, "+zero", },
+        { { -1,  0,  0 }, {  0,  0, -1 }, "-zero", },
+
+        { {  1,  1,  0 }, {  1,  0,  0 }, "90-theta", },
+        { {  1,  2,  0 }, {  0,  0, -1 }, "180-theta", },
+        { {  1,  3,  0 }, { -1,  0,  0 }, "270-theta", },
+
+        { {  1,  0,  1 }, {  0,  0,  1 }, "90-phi", },
+        { {  1,  0,  2 }, {  0,  0,  1 }, "180-phi", },
+        { {  1,  0,  3 }, {  0,  0,  1 }, "270-phi", },
+
+        { {  1,  1,  1 }, {  0,  1,  0 }, "90-theta,  90-phi" },
+        { {  1,  1,  2 }, { -1,  0,  0 }, "90-theta, 180-phi" },
+        { {  1,  1,  3 }, {  0, -1,  0 }, "90-theta, 270-phi" },
+    };
+
+    for (const auto t: TESTS) {
+        tap.expect_eq (
+            util::spherical_to_cartesian (t.spherical),
+            t.cartesian,
+            "%s, spherical-cartesian",
+            t.message
+        );
+
+        tap.expect_eq (
+            util::cartesian_to_spherical (t.cartesian),
+            t.spherical,
+            "%s, cartesian-spherical",
+            t.message
+        );
+    }
+
+
+    {
+        //util::vector3f s { 1, .5f, 2/3.f };
+        //util::vector3f c { 0.35f, 0.61f, 0.71f };
+        //tap.expect_eq
+    }
+};
+
+
 ///////////////////////////////////////////////////////////////////////////////
 int
 main ()
@@ -110,6 +160,7 @@ main ()
 
     test_polar (tap);
     test_euler (tap);
+    test_spherical (tap);
 
     tap.expect (!is_normalised (util::vector3f::zeros ()), "zeros isn't normalised");
     tap.expect (!is_normalised (util::vector3f::ones  ()), "ones isn't normalised");
diff --git a/vector.cpp b/vector.cpp
index da76eced..ea381a04 100644
--- a/vector.cpp
+++ b/vector.cpp
@@ -84,34 +84,6 @@ template util::vector2f util::to_euler (util::vector3f);
 template util::vector2d util::to_euler (util::vector3d);
 
 
-//-----------------------------------------------------------------------------
-template <typename T>
-vector<3,T>
-util::spherical_to_cartesian (vector<3,T> s)
-{
-    return vector<3,T> {
-        s.x * sin (s.y) * cos (s.z),
-        s.x * sin (s.y) * sin (s.z),
-        s.x * cos (s.y),
-    };
-}
-
-
-//-----------------------------------------------------------------------------
-template <typename T>
-vector<3,T>
-util::cartesian_to_spherical (vector<3,T> c)
-{
-    T mag = norm (c);
-
-    return vector<3,T> {
-        mag,
-        acos  (c.z / mag),
-        atan2 (c.y, c.x)
-    };
-}
-
-
 ///////////////////////////////////////////////////////////////////////////////
 template <size_t S, typename T>
 void
diff --git a/vector.hpp b/vector.hpp
index fcf5e9e4..5179e728 100644
--- a/vector.hpp
+++ b/vector.hpp
@@ -23,6 +23,7 @@
 #include "json/fwd.hpp"
 
 #include <cstddef>
+#include <cmath>
 
 
 ///////////////////////////////////////////////////////////////////////////////
@@ -56,8 +57,32 @@ namespace util {
     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> spherical_to_cartesian (vector<3,T>);
-    template <typename T> vector<3,T> cartesian_to_spherical (vector<3,T>);
+    // convert vector in spherical coordinates (r,theta,phi) with theta
+    // inclination and phi azimuth to cartesian coordinates (x,y,z)
+    template <typename T>
+    constexpr vector<3,T>
+    spherical_to_cartesian (const vector<3,T> s)
+    {
+        return {
+            s.x * std::sin (s.y) * std::cos (s.z),
+            s.x * std::sin (s.y) * std::sin (s.z),
+            s.x * std::cos (s.y)
+        };
+    }
+
+    // convert vector in cartesian coordinates (x,y,z) to spherical
+    // coordinates (r,theta,phi) with theta inclination and phi azimuth.
+    template <typename T>
+    constexpr vector<3,T>
+    cartesian_to_spherical (vector<3,T> c)
+    {
+        auto r = norm (c);
+        return {
+            r,
+            std::acos (c.z / r),
+            std::atan (c.y / c.z)
+        };
+    }
 
     template <typename T> vector<2,T> to_euler   (vector<3,T>);
     template <typename T> vector<3,T> from_euler (vector<2,T>);