diff --git a/doc/conversion.qbk b/doc/conversion.qbk
index 6cf1571..47d325d 100644
--- a/doc/conversion.qbk
+++ b/doc/conversion.qbk
@@ -173,17 +173,17 @@ This includes C++ built-in pointers, `std::shared_ptr`,
     // Throws: std::bad_cast if ( dynamic_cast<Derived>(x) == 0 )
     // Returns: dynamic_cast<Derived>(x)
     template <class Derived, class Base>
-    inline Derived polymorphic_cast(Base* x);
+    constexpr Derived polymorphic_cast(Base* x);
 
     // Effects: assert( dynamic_cast<Derived>(x) == x );
     // Returns: static_cast<Derived>(x)
     template <class Derived, class Base>
-    inline Derived polymorphic_downcast(Base* x);
+    constexpr Derived polymorphic_downcast(Base* x);
 
     // Effects: assert( dynamic_cast<Derived>(&x) == &x );
     // Returns: static_cast<Derived>(x)
     template <class Derived, class Base>
-    inline Derived polymorphic_downcast(Base& x);
+    constexpr Derived polymorphic_downcast(Base& x);
 
     // Throws: std::bad_cast if ( dynamic_pointer_cast<Derived>(x) == 0 )
     // Returns: dynamic_pointer_cast<Derived>(x)
diff --git a/include/boost/polymorphic_cast.hpp b/include/boost/polymorphic_cast.hpp
index ee0c6bb..f6162aa 100644
--- a/include/boost/polymorphic_cast.hpp
+++ b/include/boost/polymorphic_cast.hpp
@@ -62,6 +62,12 @@
 # include <typeinfo>
 # include <type_traits>
 
+#if defined(__cpp_constexpr) && __cpp_constexpr >= 201907L
+#define BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST constexpr
+#else
+#define BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST inline
+#endif
+
 namespace boost
 {
 //  See the documentation for descriptions of how to choose between
@@ -74,7 +80,7 @@ namespace boost
     //  section 15.8 exercise 1, page 425.
 
     template <class Target, class Source>
-    inline Target polymorphic_cast(Source* x)
+    BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST Target polymorphic_cast(Source* x)
     {
         Target tmp = dynamic_cast<Target>(x);
         if ( tmp == 0 ) boost::throw_exception( std::bad_cast() );
@@ -93,7 +99,7 @@ namespace boost
     //  Contributed by Dave Abrahams
 
     template <class Target, class Source>
-    inline Target polymorphic_downcast(Source* x)
+    BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST Target polymorphic_downcast(Source* x)
     {
         BOOST_ASSERT( dynamic_cast<Target>(x) == x );  // detect logic error
         return static_cast<Target>(x);
@@ -109,7 +115,7 @@ namespace boost
     //  Contributed by Julien Delacroix
 
     template <class Target, class Source>
-    inline typename std::enable_if<
+    BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST typename std::enable_if<
         std::is_reference<Target>::value, Target
     >::type polymorphic_downcast(Source& x)
     {
@@ -121,4 +127,6 @@ namespace boost
 
 } // namespace boost
 
+#undef BOOST_CONVERSION_IMPL_CONSTEXPR_DYN_CAST
+
 #endif  // BOOST_POLYMORPHIC_CAST_HPP
diff --git a/test/cast_test.cpp b/test/cast_test.cpp
index 8747397..5998bad 100644
--- a/test/cast_test.cpp
+++ b/test/cast_test.cpp
@@ -38,6 +38,48 @@ namespace
     };
 }
 
+constexpr bool compile_time_polymorphic_cast_check() {
+#if defined(__cpp_constexpr) && __cpp_constexpr >= 201907L
+    Derived derived;
+    Base* base = &derived;
+    return polymorphic_cast<Derived*>(base) != nullptr;
+#endif
+    return true;
+}
+
+static_assert(
+    compile_time_polymorphic_cast_check(),
+    "polymorphic_cast does not work at compile time"
+);
+
+constexpr bool compile_time_polymorphic_downcast_check() {
+#if defined(__cpp_constexpr) && __cpp_constexpr >= 201907L
+    Derived derived;
+    Base* base = &derived;
+    return polymorphic_downcast<Derived*>(base) != nullptr;
+#endif
+    return true;
+}
+
+static_assert(
+    compile_time_polymorphic_downcast_check(),
+    "polymorphic_downcast does not work at compile time"
+);
+
+constexpr bool compile_time_polymorphic_downcast2_check() {
+#if defined(__cpp_constexpr) && __cpp_constexpr >= 201907L
+    Derived derived;
+    Base& base = derived;
+    Derived& derived_again = polymorphic_downcast<Derived&>(base);
+    (void)derived_again;
+#endif
+    return true;
+}
+
+static_assert(
+    compile_time_polymorphic_downcast2_check(),
+    "polymorphic_downcast does not work at compile time"
+);
 
 int main( int argc, char * argv[] )
 {