diff --git a/include/nlohmann/detail/input/lexer.hpp b/include/nlohmann/detail/input/lexer.hpp
index 8c13cd6d8..aec10c5d2 100644
--- a/include/nlohmann/detail/input/lexer.hpp
+++ b/include/nlohmann/detail/input/lexer.hpp
@@ -14,6 +14,7 @@
 #include <cstdio> // snprintf
 #include <cstring> // memcmp
 #include <initializer_list> // initializer_list
+#include <limits> // numeric_limits
 #include <string> // char_traits, string
 #include <utility> // move
 #include <vector> // vector
@@ -1816,6 +1817,15 @@ scan_number_done:
     /// significand (see scan_number_bulk_contiguous())
     bool convert_accumulated_float(const float_significand& s, std::true_type /*native*/) noexcept
     {
+        // accept() only needs to know that the value is finite (see the parser):
+        // w < 10^19, so a value below 10^max_exponent10 cannot overflow, and a
+        // value that underflows is a finite number as well. Only a token that
+        // may overflow has to be converted to find out.
+        if (JSON_HEDLEY_UNLIKELY(discard_number_values && s.exponent + 19 <= std::numeric_limits<number_float_t>::max_exponent10))
+        {
+            value_float = 0;
+            return true;
+        }
         value_float = decimal_to_float<number_float_t>(s);
         return true;
     }
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 4dbec78fb..f36721a6a 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -9723,6 +9723,7 @@ NLOHMANN_JSON_NAMESPACE_END
 #include <cstdio> // snprintf
 #include <cstring> // memcmp
 #include <initializer_list> // initializer_list
+#include <limits> // numeric_limits
 #include <string> // char_traits, string
 #include <utility> // move
 #include <vector> // vector
@@ -14071,6 +14072,15 @@ scan_number_done:
     /// significand (see scan_number_bulk_contiguous())
     bool convert_accumulated_float(const float_significand& s, std::true_type /*native*/) noexcept
     {
+        // accept() only needs to know that the value is finite (see the parser):
+        // w < 10^19, so a value below 10^max_exponent10 cannot overflow, and a
+        // value that underflows is a finite number as well. Only a token that
+        // may overflow has to be converted to find out.
+        if (JSON_HEDLEY_UNLIKELY(discard_number_values && s.exponent + 19 <= std::numeric_limits<number_float_t>::max_exponent10))
+        {
+            value_float = 0;
+            return true;
+        }
         value_float = decimal_to_float<number_float_t>(s);
         return true;
     }
diff --git a/tests/src/unit-class_parser.cpp b/tests/src/unit-class_parser.cpp
index 1d1b5f40b..a97652243 100644
--- a/tests/src/unit-class_parser.cpp
+++ b/tests/src/unit-class_parser.cpp
@@ -2952,3 +2952,32 @@ TEST_CASE("diagnostic positions: value lifetime, input adapters, and SAX")
     }
 }
 #endif
+
+TEST_CASE("accept() agrees with parse() on floats around the overflow limit")
+{
+    // accept() does not convert a float that cannot overflow; the tokens
+    // around the limit (and beyond it) must still be rejected exactly as
+    // parse() rejects them
+    const char* const numbers[] =
+    {
+        "1e0", "123.456e-5", "1e-400", "-1e-400", "1e307", "1e308", "1e309", "-1e309",
+        "10e307", "100e307", "0.1e309", "0.1e310", "1E+308", "1E+309",
+        "1.7976931348623157e308", "1.7976931348623159e308", "1.8e308", "-1.7976931348623157e308",
+        "12345678901234567e291", "12345678901234567e292", "123456789012345678e290", "123456789012345678e291",
+        "1234567890123456789e289", "1234567890123456789e290", "9999999999999999999e289", "9999999999999999999e290",
+        "0.00000000000000000001e328", "0.00000000000000000001e329"
+    };
+
+    for (const char* number : numbers)
+    {
+        for (const std::string text :
+                {
+                    std::string(number), "[" + std::string(number) + "]", "{\"a\":" + std::string(number) + "}"
+                })
+        {
+            INFO(text);
+            const bool parses = !json::parse(text, nullptr, false).is_discarded();
+            CHECK(json::accept(text) == parses);
+        }
+    }
+}