diff --git a/datafusion/functions/src/math/factorial.rs b/datafusion/functions/src/math/factorial.rs
index b4c41838e164f..3b4f973f19d62 100644
--- a/datafusion/functions/src/math/factorial.rs
+++ b/datafusion/functions/src/math/factorial.rs
@@ -32,7 +32,7 @@ use datafusion_macros::user_doc;
 
 #[user_doc(
     doc_section(label = "Math Functions"),
-    description = "Factorial. Returns 1 if value is less than 2.",
+    description = "Factorial of a non-negative integer. Errors if the argument is negative or the result overflows.",
     syntax_example = "factorial(numeric_expression)",
     sql_example = r#"```sql
 > SELECT factorial(5);
@@ -143,7 +143,7 @@ const FACTORIALS: [i64; 21] = [
 
 fn compute_factorial(n: i64) -> Result<i64> {
     if n < 0 {
-        Ok(1)
+        exec_err!("factorial of a negative number is undefined")
     } else if n < FACTORIALS.len() as i64 {
         Ok(FACTORIALS[n as usize])
     } else {
diff --git a/datafusion/sqllogictest/test_files/math.slt b/datafusion/sqllogictest/test_files/math.slt
index e00edf47c176b..8f7245365f1e3 100644
--- a/datafusion/sqllogictest/test_files/math.slt
+++ b/datafusion/sqllogictest/test_files/math.slt
@@ -826,6 +826,10 @@ select
 ----
 39 Decimal128(2, 1)
 
+# factorial negative (PostgreSQL-compatible domain error)
+query error DataFusion error: Execution error: factorial of a negative number is undefined
+select factorial(-1);
+
 # factorial overflow
 query error DataFusion error: Execution error: Overflow happened on FACTORIAL\(350943270\)
 select FACTORIAL(350943270);
diff --git a/docs/source/user-guide/sql/scalar_functions.md b/docs/source/user-guide/sql/scalar_functions.md
index 7010a2b7c1e6c..4786163cb59f6 100644
--- a/docs/source/user-guide/sql/scalar_functions.md
+++ b/docs/source/user-guide/sql/scalar_functions.md
@@ -420,7 +420,7 @@ exp(numeric_expression)
 
 ### `factorial`
 
-Factorial. Returns 1 if value is less than 2.
+Factorial of a non-negative integer. Errors if the argument is negative or the result overflows.
 
 ```sql
 factorial(numeric_expression)