diff --git a/src/Magnum/Math/Constants.h b/src/Magnum/Math/Constants.h
index ec86fc1de..c51f7a2e6 100644
--- a/src/Magnum/Math/Constants.h
+++ b/src/Magnum/Math/Constants.h
@@ -150,14 +150,17 @@ template<class> struct Constants;
 template<> struct Constants<Double> {
     Constants() = delete;
 
-    static constexpr Double pi()        { return 3.141592653589793; }
-    static constexpr Double piHalf()    { return 1.570796326794897; }
-    static constexpr Double piQuarter() { return 0.785398163397448; }
-    static constexpr Double tau()       { return 6.283185307179586; }
-    static constexpr Double e()         { return 2.718281828459045; }
-    static constexpr Double sqrt2()     { return 1.414213562373095; }
-    static constexpr Double sqrt3()     { return 1.732050807568877; }
-    static constexpr Double sqrtHalf()  { return 0.707106781186547; }
+    /* 17-digit string representation gives back the same value on rountrip.
+       https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+       Values taken using Wolfram Alpha.         1.2345678901234567 */
+    static constexpr Double pi()        { return 3.1415926535897932; }
+    static constexpr Double piHalf()    { return 1.5707963267948966; }
+    static constexpr Double piQuarter() { return 0.7853981633974483; }
+    static constexpr Double tau()       { return 6.2831853071795864; }
+    static constexpr Double e()         { return 2.7182818284590452; }
+    static constexpr Double sqrt2()     { return 1.4142135623730950; }
+    static constexpr Double sqrt3()     { return 1.7320508075688773; }
+    static constexpr Double sqrtHalf()  { return 0.7071067811865475; }
 
     static constexpr Double nan()   { return Double(NAN); }
     static constexpr Double inf()   { return HUGE_VAL; }
@@ -165,6 +168,9 @@ template<> struct Constants<Double> {
 template<> struct Constants<Float> {
     Constants() = delete;
 
+    /* 9-digit string representation gives back the same value on rountrip.
+       https://en.wikipedia.org/wiki/Single-precision_floating-point_format
+       Values rounded from the above.            1.23456789 */
     static constexpr Float pi()         { return 3.141592654f; }
     static constexpr Float piHalf()     { return 1.570796327f; }
     static constexpr Float piQuarter()  { return 0.785398163f; }