diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index ee59af149..451bb4f15 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -1593,6 +1593,14 @@ class binary_writer
                 {
                     oa->write_character(to_char_type(0xFD));
                 }
+                else if (std::isnan(j.m_value.number_float))
+                {
+                    oa->write_character(to_char_type(0x8E));
+                    oa->write_character(to_char_type(0x7F));
+                    oa->write_character(to_char_type(0x80));
+                    oa->write_character(to_char_type(0x00));
+                    oa->write_character(to_char_type(0x01));
+                }
                 else
                 {
                     // write float with prefix
@@ -1839,9 +1847,9 @@ class binary_writer
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wfloat-equal"
 #endif
-        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
-                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
-                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        if (std::isnan(n) || std::isinf(n) || (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                                               static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
+                                               static_cast<double>(static_cast<float>(n)) == static_cast<double>(n)))
         {
             switch (format)
             {
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index eae9dedb4..1c13057e1 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -15167,6 +15167,14 @@ class binary_writer
                 {
                     oa->write_character(to_char_type(0xFD));
                 }
+                else if (std::isnan(j.m_value.number_float))
+                {
+                    oa->write_character(to_char_type(0x8E));
+                    oa->write_character(to_char_type(0x7F));
+                    oa->write_character(to_char_type(0x80));
+                    oa->write_character(to_char_type(0x00));
+                    oa->write_character(to_char_type(0x01));
+                }
                 else
                 {
                     // write float with prefix
@@ -15413,9 +15421,9 @@ class binary_writer
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wfloat-equal"
 #endif
-        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
-                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
-                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        if (std::isnan(n) || std::isinf(n) || (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                                               static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
+                                               static_cast<double>(static_cast<float>(n)) == static_cast<double>(n)))
         {
             switch (format)
             {
diff --git a/test/src/unit-bon8.cpp b/test/src/unit-bon8.cpp
index 9f6848cf6..06cf57073 100644
--- a/test/src/unit-bon8.cpp
+++ b/test/src/unit-bon8.cpp
@@ -468,6 +468,30 @@ TEST_CASE("BON8")
                     const auto result = json::to_bon8(j);
                     CHECK(result == expected);
                 }
+
+                SECTION("NAN")
+                {
+                    json j = NAN;
+                    std::vector<uint8_t> expected = {0x8E, 0x7F, 0x80, 0x00, 0x01};
+                    const auto result = json::to_bon8(j);
+                    CHECK(result == expected);
+                }
+
+                SECTION("infinity")
+                {
+                    json j = INFINITY;
+                    std::vector<uint8_t> expected = {0x8E, 0x7F, 0x80, 0x00, 0x00};
+                    const auto result = json::to_bon8(j);
+                    CHECK(result == expected);
+                }
+
+                SECTION("-infinity")
+                {
+                    json j = -INFINITY;
+                    std::vector<uint8_t> expected = {0x8E, 0xFF, 0x80, 0x00, 0x00};
+                    const auto result = json::to_bon8(j);
+                    CHECK(result == expected);
+                }
             }
 
             SECTION("floats")