diff --git a/lerp.cpp b/lerp.cpp
index d0fa7802..b1dfd8dd 100644
--- a/lerp.cpp
+++ b/lerp.cpp
@@ -42,7 +42,7 @@ lerp::linear (double a, double b, double weight) {
 double
 lerp::cosine (double a, double b, double weight) {
     CHECK (weight >= 0.0 && weight <= 1.0);
-    double t  = (1.0 - cos (weight * PI_d)) * 0.5;
+    double t  = (1.0 - cos (weight * PI<double>)) * 0.5;
 
     return a * (1.0 - t) + b * t;
 }
diff --git a/maths.hpp b/maths.hpp
index f2fa6f3c..07fd92f3 100644
--- a/maths.hpp
+++ b/maths.hpp
@@ -171,19 +171,17 @@ exactly_zero [[gnu::pure]] (T a)
 // angles, trig
 
 template <typename T>
-struct constants { };
+constexpr T PI = T(3.141592653589793238462643);
 
-constexpr double PI_d = 3.141592653589793238462643;
-constexpr float  PI_f = 3.141592653589793238462643f;
+template <typename T>
+constexpr T E = T(2.71828182845904523536028747135266250);
 
-constexpr float  E_f = 2.71828182845904523536028747135266250f;
-constexpr double E_d = 2.71828182845904523536028747135266250;
 
 template <typename T>
 constexpr T
 to_degrees [[gnu::pure]] (T radians)
 {
-    return radians * 180 / constants<T>::PI;
+    return radians * 180 / PI<T>;
 }
 
 
@@ -191,7 +189,7 @@ template <typename T>
 constexpr T
 to_radians [[gnu::pure]] (T degrees)
 {
-    return degrees / 180 * constants<T>::PI;
+    return degrees / 180 * PI<T>;
 }
 
 
@@ -200,7 +198,7 @@ template <typename T>
 constexpr T
 sincn [[gnu::pure]] (T x)
 {
-    return almost_zero (x) ? 1 : std::sin (constants<T>::PI * x) / (constants<T>::PI * x);
+    return almost_zero (x) ? 1 : std::sin (PI<T> * x) / (PI<T> * x);
 }
 
 
@@ -224,7 +222,7 @@ factorial [[gnu::pure]] (unsigned i)
 constexpr uintmax_t
 stirling [[gnu::pure]] (unsigned n)
 {
-    return static_cast<uintmax_t> (std::sqrt (2 * PI_f * n) * std::pow (n / E_f, n));
+    return static_cast<uintmax_t> (std::sqrt (2 * PI<float> * n) * std::pow (n / E<float>, n));
 }
 
 
diff --git a/maths.ipp b/maths.ipp
index 2f3e1dc6..72e328f3 100644
--- a/maths.ipp
+++ b/maths.ipp
@@ -66,20 +66,3 @@ sign (double v)
 {
     return std::signbit (v) ? -1. : 1.f;
 }
-
-
-//-----------------------------------------------------------------------------
-template <>
-struct constants<float>
-{
-    static constexpr float PI = PI_f;
-    static constexpr float E  = E_f;
-};
-
-
-template <>
-struct constants<double>
-{
-    static constexpr double PI = PI_d;
-    static constexpr double E  = E_d;
-};
diff --git a/polynomial.cpp b/polynomial.cpp
index c794e09c..0334f6b6 100644
--- a/polynomial.cpp
+++ b/polynomial.cpp
@@ -116,8 +116,8 @@ namespace util { namespace polynomial {
             const float t   = 2 * std::sqrt (-p);
 
             s[0] =  t * std::cos (phi);
-            s[1] = -t * std::cos (phi + PI_f / 3.f);
-            s[2] = -t * std::cos (phi - PI_f / 3.f);
+            s[1] = -t * std::cos (phi + PI<float> / 3.f);
+            s[2] = -t * std::cos (phi - PI<float> / 3.f);
         } else {
             float u = std::cbrt (std::sqrt (D) + abs (q));
             if (q > 0.f)
diff --git a/test/maths.cpp b/test/maths.cpp
index 8f44990f..dfc34c79 100644
--- a/test/maths.cpp
+++ b/test/maths.cpp
@@ -114,10 +114,10 @@ main (int, char **) {
     CHECK_EQ (sign ( numeric_limits<double>::infinity ()),  1);
     CHECK_EQ (sign (-numeric_limits<double>::infinity ()), -1);
 
-    CHECK_EQ (to_degrees (PI_d),  180.0);
-    CHECK_EQ (to_degrees (PI_f),  180.f);
-    CHECK_EQ (to_radians (180.f),  PI_f);
-    CHECK_EQ (to_radians (180.0),  PI_d);
+    CHECK_EQ (to_degrees (PI<double>),  180.0);
+    CHECK_EQ (to_degrees (PI<float>),  180.f);
+    CHECK_EQ (to_radians (180.f),  PI<float>);
+    CHECK_EQ (to_radians (180.0),  PI<double>);
 
     CHECK_EQ (log2 (8u), 3);
     CHECK_EQ (log2 (1u), 0);
diff --git a/test/vector.cpp b/test/vector.cpp
index ad160bf5..74610194 100644
--- a/test/vector.cpp
+++ b/test/vector.cpp
@@ -28,13 +28,13 @@ test_polar (void)
         },
 
         {
-            { 1.f, PI_f / 2.f },
+            { 1.f, PI<float> / 2.f },
             { 0.f, 1.f },
             "unit length, rotated"
         },
 
         {
-            { 1.f, 2 * PI_f },
+            { 1.f, 2 * PI<float> },
             { 1.f, 0.f },
             "full rotation, unit length"
         }
@@ -53,8 +53,8 @@ test_polar (void)
         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);
+        in_polar[1] = std::fmod (in_polar[1], 2 * PI<float>);
+        to_polar[1] = std::fmod (to_polar[1], 2 * PI<float>);
 
         CHECK_EQ (in_polar, to_polar);
     }