diff --git a/datafusion/expr/src/columnar_value.rs b/datafusion/expr/src/columnar_value.rs
index bfefb37c98d7..7b614ba9c491 100644
--- a/datafusion/expr/src/columnar_value.rs
+++ b/datafusion/expr/src/columnar_value.rs
@@ -17,8 +17,7 @@
 
 //! [`ColumnarValue`] represents the result of evaluating an expression.
 
-use arrow::array::ArrayRef;
-use arrow::array::NullArray;
+use arrow::array::{Array, ArrayRef, NullArray};
 use arrow::compute::{kernels, CastOptions};
 use arrow::datatypes::{DataType, TimeUnit};
 use datafusion_common::format::DEFAULT_CAST_OPTIONS;
@@ -218,6 +217,17 @@ impl ColumnarValue {
             }
         }
     }
+
+    /// Converts an [`ArrayRef`] to a [`ColumnarValue`] based on the supplied arguments.
+    /// This is useful for scalar UDF implementations to fulfil their contract:
+    /// if all arguments are scalar values, the result should also be a scalar value.
+    pub fn from_args_and_result(args: &[Self], result: ArrayRef) -> Result<Self> {
+        if result.len() == 1 && args.iter().all(|arg| matches!(arg, Self::Scalar(_))) {
+            Ok(Self::Scalar(ScalarValue::try_from_array(&result, 0)?))
+        } else {
+            Ok(Self::Array(result))
+        }
+    }
 }
 
 #[cfg(test)]
diff --git a/datafusion/functions/src/macros.rs b/datafusion/functions/src/macros.rs
index cae689b3e0cb..1aadaae6c1d6 100644
--- a/datafusion/functions/src/macros.rs
+++ b/datafusion/functions/src/macros.rs
@@ -222,9 +222,8 @@ macro_rules! make_math_unary_udf {
                     $OUTPUT_ORDERING(input)
                 }
 
-                fn invoke(&self, args: &[ColumnarValue]) -> Result<ColumnarValue> {
-                    let args = ColumnarValue::values_to_arrays(args)?;
-
+                fn invoke(&self, col_args: &[ColumnarValue]) -> Result<ColumnarValue> {
+                    let args = ColumnarValue::values_to_arrays(col_args)?;
                     let arr: ArrayRef = match args[0].data_type() {
                         DataType::Float64 => {
                             Arc::new(make_function_scalar_inputs_return_type!(
@@ -251,7 +250,8 @@ macro_rules! make_math_unary_udf {
                             )
                         }
                     };
-                    Ok(ColumnarValue::Array(arr))
+
+                    ColumnarValue::from_args_and_result(col_args, arr)
                 }
             }
         }
@@ -332,9 +332,8 @@ macro_rules! make_math_binary_udf {
                     $OUTPUT_ORDERING(input)
                 }
 
-                fn invoke(&self, args: &[ColumnarValue]) -> Result<ColumnarValue> {
-                    let args = ColumnarValue::values_to_arrays(args)?;
-
+                fn invoke(&self, col_args: &[ColumnarValue]) -> Result<ColumnarValue> {
+                    let args = ColumnarValue::values_to_arrays(col_args)?;
                     let arr: ArrayRef = match args[0].data_type() {
                         DataType::Float64 => Arc::new(make_function_inputs2!(
                             &args[0],
@@ -360,7 +359,8 @@ macro_rules! make_math_binary_udf {
                             )
                         }
                     };
-                    Ok(ColumnarValue::Array(arr))
+
+                    ColumnarValue::from_args_and_result(col_args, arr)
                 }
             }
         }