diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index 1b15bdafd..71e5ec81e 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -149,9 +149,9 @@ class binary_writer
                 break;
             }
 
-            case value_t::number_float: // Double-Precision Float
+            case value_t::number_float:
             {
-                oa->write_character(static_cast<CharType>(0xFB));
+                oa->write_character(get_cbor_float_prefix(j.m_value.number_float));
                 write_number(j.m_value.number_float);
                 break;
             }
@@ -409,9 +409,9 @@ class binary_writer
                 break;
             }
 
-            case value_t::number_float: // float 64
+            case value_t::number_float:
             {
-                oa->write_character(static_cast<CharType>(0xCB));
+                oa->write_character(get_msgpack_float_prefix(j.m_value.number_float));
                 write_number(j.m_value.number_float);
                 break;
             }
@@ -588,7 +588,7 @@ class binary_writer
                 if (use_type and not j.m_value.array->empty())
                 {
                     assert(use_count);
-                    const char first_prefix = ubjson_prefix(j.front());
+                    const CharType first_prefix = ubjson_prefix(j.front());
                     const bool same_prefix = std::all_of(j.begin() + 1, j.end(),
                                                          [this, first_prefix](const BasicJsonType & v)
                     {
@@ -599,7 +599,7 @@ class binary_writer
                     {
                         prefix_required = false;
                         oa->write_character(static_cast<CharType>('$'));
-                        oa->write_character(static_cast<CharType>(first_prefix));
+                        oa->write_character(first_prefix);
                     }
                 }
 
@@ -633,7 +633,7 @@ class binary_writer
                 if (use_type and not j.m_value.object->empty())
                 {
                     assert(use_count);
-                    const char first_prefix = ubjson_prefix(j.front());
+                    const CharType first_prefix = ubjson_prefix(j.front());
                     const bool same_prefix = std::all_of(j.begin(), j.end(),
                                                          [this, first_prefix](const BasicJsonType & v)
                     {
@@ -644,7 +644,7 @@ class binary_writer
                     {
                         prefix_required = false;
                         oa->write_character(static_cast<CharType>('$'));
-                        oa->write_character(static_cast<CharType>(first_prefix));
+                        oa->write_character(first_prefix);
                     }
                 }
 
@@ -712,7 +712,7 @@ class binary_writer
     {
         if (add_prefix)
         {
-            oa->write_character(static_cast<CharType>('D'));  // float64
+            oa->write_character(get_ubjson_float_prefix(n));
         }
         write_number(n);
     }
@@ -833,7 +833,7 @@ class binary_writer
           write_number_with_ubjson_prefix. Therefore, we return 'L' for any
           value that does not fit the previous limits.
     */
-    char ubjson_prefix(const BasicJsonType& j) const noexcept
+    CharType ubjson_prefix(const BasicJsonType& j) const noexcept
     {
         switch (j.type())
         {
@@ -892,7 +892,7 @@ class binary_writer
             }
 
             case value_t::number_float:
-                return 'D';
+                return get_ubjson_float_prefix(j.m_value.number_float);
 
             case value_t::string:
                 return 'S';
@@ -908,6 +908,36 @@ class binary_writer
         }
     }
 
+    static constexpr CharType get_cbor_float_prefix(float)
+    {
+        return static_cast<CharType>(0xFA);  // Single-Precision Float
+    }
+
+    static constexpr CharType get_cbor_float_prefix(double)
+    {
+        return static_cast<CharType>(0xFB);  // Double-Precision Float
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(float)
+    {
+        return static_cast<CharType>(0xCA);  // float 32
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(double)
+    {
+        return static_cast<CharType>(0xCB);  // float 64
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(float)
+    {
+        return 'd';  // float 32
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(double)
+    {
+        return 'D';  // float 64
+    }
+
   private:
     /// whether we can assume little endianess
     const bool is_little_endian = binary_reader<BasicJsonType>::little_endianess();
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 6b6655af8..b7558aa5a 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -6357,9 +6357,9 @@ class binary_writer
                 break;
             }
 
-            case value_t::number_float: // Double-Precision Float
+            case value_t::number_float:
             {
-                oa->write_character(static_cast<CharType>(0xFB));
+                oa->write_character(get_cbor_float_prefix(j.m_value.number_float));
                 write_number(j.m_value.number_float);
                 break;
             }
@@ -6617,9 +6617,9 @@ class binary_writer
                 break;
             }
 
-            case value_t::number_float: // float 64
+            case value_t::number_float:
             {
-                oa->write_character(static_cast<CharType>(0xCB));
+                oa->write_character(get_msgpack_float_prefix(j.m_value.number_float));
                 write_number(j.m_value.number_float);
                 break;
             }
@@ -6796,7 +6796,7 @@ class binary_writer
                 if (use_type and not j.m_value.array->empty())
                 {
                     assert(use_count);
-                    const char first_prefix = ubjson_prefix(j.front());
+                    const CharType first_prefix = ubjson_prefix(j.front());
                     const bool same_prefix = std::all_of(j.begin() + 1, j.end(),
                                                          [this, first_prefix](const BasicJsonType & v)
                     {
@@ -6807,7 +6807,7 @@ class binary_writer
                     {
                         prefix_required = false;
                         oa->write_character(static_cast<CharType>('$'));
-                        oa->write_character(static_cast<CharType>(first_prefix));
+                        oa->write_character(first_prefix);
                     }
                 }
 
@@ -6841,7 +6841,7 @@ class binary_writer
                 if (use_type and not j.m_value.object->empty())
                 {
                     assert(use_count);
-                    const char first_prefix = ubjson_prefix(j.front());
+                    const CharType first_prefix = ubjson_prefix(j.front());
                     const bool same_prefix = std::all_of(j.begin(), j.end(),
                                                          [this, first_prefix](const BasicJsonType & v)
                     {
@@ -6852,7 +6852,7 @@ class binary_writer
                     {
                         prefix_required = false;
                         oa->write_character(static_cast<CharType>('$'));
-                        oa->write_character(static_cast<CharType>(first_prefix));
+                        oa->write_character(first_prefix);
                     }
                 }
 
@@ -6920,7 +6920,7 @@ class binary_writer
     {
         if (add_prefix)
         {
-            oa->write_character(static_cast<CharType>('D'));  // float64
+            oa->write_character(get_ubjson_float_prefix(n));
         }
         write_number(n);
     }
@@ -7041,7 +7041,7 @@ class binary_writer
           write_number_with_ubjson_prefix. Therefore, we return 'L' for any
           value that does not fit the previous limits.
     */
-    char ubjson_prefix(const BasicJsonType& j) const noexcept
+    CharType ubjson_prefix(const BasicJsonType& j) const noexcept
     {
         switch (j.type())
         {
@@ -7100,7 +7100,7 @@ class binary_writer
             }
 
             case value_t::number_float:
-                return 'D';
+                return get_ubjson_float_prefix(j.m_value.number_float);
 
             case value_t::string:
                 return 'S';
@@ -7116,6 +7116,36 @@ class binary_writer
         }
     }
 
+    static constexpr CharType get_cbor_float_prefix(float)
+    {
+        return static_cast<CharType>(0xFA);  // Single-Precision Float
+    }
+
+    static constexpr CharType get_cbor_float_prefix(double)
+    {
+        return static_cast<CharType>(0xFB);  // Double-Precision Float
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(float)
+    {
+        return static_cast<CharType>(0xCA);  // float 32
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(double)
+    {
+        return static_cast<CharType>(0xCB);  // float 64
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(float)
+    {
+        return 'd';  // float 32
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(double)
+    {
+        return 'D';  // float 64
+    }
+
   private:
     /// whether we can assume little endianess
     const bool is_little_endian = binary_reader<BasicJsonType>::little_endianess();
diff --git a/test/src/unit-regression.cpp b/test/src/unit-regression.cpp
index c4ca93d91..01e689570 100644
--- a/test/src/unit-regression.cpp
+++ b/test/src/unit-regression.cpp
@@ -114,6 +114,13 @@ struct nocopy
 };
 }
 
+/////////////////////////////////////////////////////////////////////
+// for #1021
+/////////////////////////////////////////////////////////////////////
+
+using float_json = nlohmann::basic_json<std::map, std::vector, std::string, bool, std::int64_t, std::uint64_t, float>;
+
+
 TEST_CASE("regression tests")
 {
     SECTION("issue #60 - Double quotation mark is not parsed correctly")
@@ -1597,4 +1604,15 @@ TEST_CASE("regression tests")
         auto j = json::parse(geojsonExample, cb, true);
         CHECK(j == json());
     }
+
+    SECTION("issue #1021 - to/from_msgpack only works with standard typization")
+    {
+        float_json j = 1000.0;
+        CHECK(float_json::from_cbor(float_json::to_cbor(j)) == j);
+        CHECK(float_json::from_msgpack(float_json::to_msgpack(j)) == j);
+        CHECK(float_json::from_ubjson(float_json::to_ubjson(j)) == j);
+
+        float_json j2 = {1000.0, 2000.0, 3000.0};
+        CHECK(float_json::from_ubjson(float_json::to_ubjson(j2, true, true)) == j2);
+    }
 }