diff --git a/lib/logger_json/formatters/datadog_logger.ex b/lib/logger_json/formatters/datadog_logger.ex
index fec2f90..3b6c8c6 100644
--- a/lib/logger_json/formatters/datadog_logger.ex
+++ b/lib/logger_json/formatters/datadog_logger.ex
@@ -67,7 +67,7 @@ defmodule LoggerJSON.Formatters.DatadogLogger do
     LoggerJSON.take_metadata(md, md_keys, @processed_metadata_keys)
     |> convert_tracing_keys(md)
     |> JasonSafeFormatter.format()
-    |> FormatterUtils.maybe_put(:error, FormatterUtils.format_process_crash(md))
+    |> FormatterUtils.maybe_put(:error, format_process_crash(md))
   end
 
   # To connect logs and traces, span_id and trace_id keys are respectively dd.span_id and dd.trace_id
@@ -113,6 +113,38 @@ defmodule LoggerJSON.Formatters.DatadogLogger do
     _ -> ""
   end
 
+  # This follows the DataDog standard attributes for error tracking, allowing
+  # errors to automatically be aggregated by error tracking.
+  defp format_process_crash(metadata) do
+    case Keyword.get(metadata, :crash_reason) do
+      {reason, stacktrace} ->
+        initial_call = Keyword.get(metadata, :initial_call)
+
+        json_map(
+          initial_call: format_initial_call(initial_call),
+          stack: Exception.format_stacktrace(stacktrace),
+          message: format_exception_message(reason),
+          kind: format_exception_kind(reason)
+        )
+
+      nil ->
+        nil
+    end
+  end
+
+  defp format_initial_call(nil), do: nil
+
+  defp format_initial_call({module, function, arity}),
+    do: FormatterUtils.format_function(module, function, arity)
+
+  defp format_exception_message(%{message: message}), do: message
+  defp format_exception_message(other), do: JasonSafeFormatter.format(other)
+
+  defp format_exception_kind(:throw), do: "throw"
+  defp format_exception_kind(:exit), do: "exit"
+  defp format_exception_kind(%exception{}), do: inspect(exception)
+  defp format_exception_kind(other), do: inspect(other)
+
   defp method_name(metadata) do
     function = Keyword.get(metadata, :function)
     module = Keyword.get(metadata, :module)
diff --git a/test/unit/logger_json/formatters/datadog_logger_test.exs b/test/unit/logger_json/formatters/datadog_logger_test.exs
index a2ef055..1bf8b9d 100644
--- a/test/unit/logger_json/formatters/datadog_logger_test.exs
+++ b/test/unit/logger_json/formatters/datadog_logger_test.exs
@@ -413,14 +413,25 @@ defmodule LoggerJSONDatadogTest do
 
   test "logs crash reason when present" do
     Logger.configure_backend(LoggerJSON, metadata: [:crash_reason])
-    Logger.metadata(crash_reason: {%RuntimeError{message: "oops"}, []})
+
+    Logger.metadata(
+      crash_reason:
+        {%RuntimeError{message: "oops"},
+         [
+           {Exception, :exception, [[message: "stacktrace test"]], []},
+           {LoggerJSONDatadogTest, :"test logs crash reason when present", 1,
+            [file: 'test/unit/logger_json/formatters/datadog_logger_test.exs', line: 414]}
+         ]}
+    )
 
     log =
       capture_log(fn -> Logger.debug("hello") end)
       |> Jason.decode!()
 
     assert is_nil(log["error"]["initial_call"])
-    assert log["error"]["reason"] == "** (RuntimeError) oops"
+    assert log["error"]["kind"] == "RuntimeError"
+    assert log["error"]["message"] == "oops"
+    assert log["error"]["stack"] =~ "stacktrace test"
   end
 
   test "logs erlang style crash reasons" do
@@ -432,7 +443,7 @@ defmodule LoggerJSONDatadogTest do
       |> Jason.decode!()
 
     assert is_nil(log["error"]["initial_call"])
-    assert log["error"]["reason"] == "{:socket_closed_unexpectedly, []}"
+    assert log["error"]["message"] == "socket_closed_unexpectedly"
   end
 
   test "logs initial call when present" do