diff --git a/src/Magnum/Math/Random.h b/src/Magnum/Math/Random.h
index 6cd1a2c5a..e0d335153 100644
--- a/src/Magnum/Math/Random.h
+++ b/src/Magnum/Math/Random.h
@@ -11,6 +11,7 @@
 #include "Magnum/Math/Vector3.h"
 #include "Magnum/Math/Quaternion.h"
 #include "Magnum/Math/Functions.h"
+#include <iostream>
 
 namespace Magnum
 {
@@ -70,7 +71,7 @@ T randomSignedScalar() // range [-1, 1]
 }
 
 template <class T = Float>
-Vector3<T> randomUnitVector2()
+Vector2<T> randomUnitVector2()
 {
     auto a = Implementation::RandomGenerator::generate(0.0f, 2 * Math::Constants<T>::pi());
     return {std::cos(a), std::sin(a)};
@@ -100,17 +101,23 @@ Vector2<T> randomPointInACircle() // always length < 1
 template <class T = Float>
 Vector3<T> randomPointInASphere() // always length < 1
 {
-    auto x = randomSignedScalar();
-    auto y = randomSignedScalar();
+
     while (true)
     {
-        auto p = Vector3<T>(x, y, randomSignedScalar());
+        auto p = Vector3<T>(randomSignedScalar(),
+                            randomSignedScalar(),
+                            randomSignedScalar());
         if (p.length() >= 1)
             continue;
         return p;
     }
 }
 
+bool randomBool()
+{
+    return static_cast<bool>(randomUnsignedScalar<Int>());
+}
+
 template <class T = Float>
 Quaternion<T> randomRotation()
 {
diff --git a/src/Magnum/Math/Test/CMakeLists.txt b/src/Magnum/Math/Test/CMakeLists.txt
index de48dbe70..873a0e95c 100644
--- a/src/Magnum/Math/Test/CMakeLists.txt
+++ b/src/Magnum/Math/Test/CMakeLists.txt
@@ -70,6 +70,8 @@ corrade_add_test(MathStrictWeakOrderingTest StrictWeakOrderingTest.cpp LIBRARIES
 
 corrade_add_test(MathMatrixBenchmark MatrixBenchmark.cpp LIBRARIES MagnumMathTestLib)
 
+corrade_add_test(MathRandomTest RandomTest.cpp LIBRARIES MagnumMathTestLib)
+
 set_property(TARGET
     MathVectorTest
     MathMatrixTest
@@ -85,6 +87,8 @@ set_property(TARGET
 
     MathDistanceTest
     MathIntersectionTest
+
+    MathRandomTest
     APPEND PROPERTY COMPILE_DEFINITIONS "CORRADE_GRACEFUL_ASSERT")
 
 set_target_properties(
@@ -130,4 +134,6 @@ set_target_properties(
 
     MathConfigurationValueTest
     MathStrictWeakOrderingTest
+
+    MathRandomTest
     PROPERTIES FOLDER "Magnum/Math/Test")
diff --git a/src/Magnum/Math/Test/RandomTest.cpp b/src/Magnum/Math/Test/RandomTest.cpp
new file mode 100644
index 000000000..6265c80ac
--- /dev/null
+++ b/src/Magnum/Math/Test/RandomTest.cpp
@@ -0,0 +1,112 @@
+#include <Corrade/TestSuite/Tester.h>
+#include <Corrade/Utility/DebugStl.h>
+
+#include "Magnum/Math/Random.h"
+
+namespace Magnum
+{
+namespace Math
+{
+
+namespace Test
+{
+namespace
+{
+
+struct RandomTest : Corrade::TestSuite::Tester
+{
+    explicit RandomTest();
+
+    void unsignedScalar();
+    void signedScalar();
+    void unitVector2();
+    void unitVector3();
+    void pointInACircle();
+    void pointInASphere();
+    void randomRotation();
+};
+
+typedef Vector<2, Float> Vector2;
+typedef Vector<3, Float> Vector3;
+typedef Math::Constants<Float> Constants;
+
+RandomTest::RandomTest()
+{
+    addTests({&RandomTest::unsignedScalar,
+              &RandomTest::signedScalar,
+              &RandomTest::unitVector2,
+              &RandomTest::unitVector3,
+              &RandomTest::pointInACircle,
+              &RandomTest::pointInASphere,
+              &RandomTest::randomRotation});
+}
+
+// void RandomTest::construct() {
+//     constexpr Matrix4x4 a = {Vector4(3.0f,  5.0f, 8.0f, -3.0f),
+//                              Vector4(4.5f,  4.0f, 7.0f,  2.0f),
+//                              Vector4(1.0f,  2.0f, 3.0f, -1.0f),
+//                              Vector4(7.9f, -1.0f, 8.0f, -1.5f)};
+//     CORRADE_COMPARE(a, Matrix4x4(Vector4(3.0f,  5.0f, 8.0f, -3.0f),
+//                                  Vector4(4.5f,  4.0f, 7.0f,  2.0f),
+//                                  Vector4(1.0f,  2.0f, 3.0f, -1.0f),
+//                                  Vector4(7.9f, -1.0f, 8.0f, -1.5f)));
+
+//     CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4x4, Vector4, Vector4, Vector4, Vector4>::value));
+// }
+void RandomTest::unsignedScalar()
+{
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_VERIFY(Math::Random::randomUnsignedScalar<Float>() < 1.000000001);
+        CORRADE_VERIFY(Math::Random::randomUnsignedScalar<Float>() > -.000000001);
+    }
+}
+
+void RandomTest::signedScalar()
+{
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_VERIFY(Math::Random::randomUnsignedScalar<Float>() < 1.000000001);
+        CORRADE_VERIFY(Math::Random::randomUnsignedScalar<Float>() > -1.000000001);
+    }
+}
+
+void RandomTest::unitVector2()
+{
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_COMPARE((Math::Random::randomUnitVector2()).length(),1.0f);
+    }
+}
+void RandomTest::unitVector3()
+{
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_COMPARE((Math::Random::randomUnitVector3()).length(),1.0f);
+    }
+}
+
+void RandomTest::pointInACircle(){
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_VERIFY((Math::Random::randomPointInACircle()).length()<1.0f);
+    }
+}
+void RandomTest::pointInASphere(){
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_VERIFY((Math::Random::randomPointInASphere()).length()<1.0f);
+    }
+}
+void RandomTest::randomRotation(){
+    for (std::size_t i = 0; i < 10; i++)
+    {
+        CORRADE_COMPARE(Math::Random::randomRotation().length(), 1.0f);
+    }
+}
+} // namespace
+} // namespace Test
+} // namespace Math
+} // namespace Magnum
+
+CORRADE_TEST_MAIN(Magnum::Math::Test::RandomTest)