diff --git a/core/math/expression.h b/core/math/expression.h
index 59a9a2f4ed4..f2cfe6b1a6c 100644
--- a/core/math/expression.h
+++ b/core/math/expression.h
@@ -343,7 +343,7 @@ protected:
 
 public:
 	Error parse(const String &p_expression, const Vector<String> &p_input_names = Vector<String>());
-	Variant execute(Array p_inputs, Object *p_base = nullptr, bool p_show_error = true);
+	Variant execute(Array p_inputs = Array(), Object *p_base = nullptr, bool p_show_error = true);
 	bool has_execute_failed() const;
 	String get_error_text() const;
 
diff --git a/doc/classes/Expression.xml b/doc/classes/Expression.xml
index fcd1aa43c0c..f2611dc850b 100644
--- a/doc/classes/Expression.xml
+++ b/doc/classes/Expression.xml
@@ -5,7 +5,7 @@
 	</brief_description>
 	<description>
 		An expression can be made of any arithmetic operation, built-in math function call, method call of a passed instance, or built-in type construction call.
-		An example expression text using the built-in math functions could be [code]sqrt(pow(3,2) + pow(4,2))[/code].
+		An example expression text using the built-in math functions could be [code]sqrt(pow(3, 2) + pow(4, 2))[/code].
 		In the following example we use a [LineEdit] node to write our expression and show the result.
 		[codeblock]
 		onready var expression = Expression.new()
diff --git a/tests/test_expression.h b/tests/test_expression.h
new file mode 100644
index 00000000000..85d37d14609
--- /dev/null
+++ b/tests/test_expression.h
@@ -0,0 +1,431 @@
+/*************************************************************************/
+/*  test_expression.h                                                    */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef TEST_EXPRESSION_H
+#define TEST_EXPRESSION_H
+
+#include "core/math/expression.h"
+
+#include "tests/test_macros.h"
+
+namespace TestExpression {
+
+TEST_CASE("[Expression] Integer arithmetic") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("-123456") == OK,
+			"Integer identity should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == -123456,
+			"Integer identity should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("2 + 3") == OK,
+			"Integer addition should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 5,
+			"Integer addition should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("999999999999 + 999999999999") == OK,
+			"Large integer addition should parse successfully.");
+	CHECK_MESSAGE(
+			int64_t(expression.execute()) == 1'999'999'999'998,
+			"Large integer addition should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("25 / 10") == OK,
+			"Integer / integer division should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 2,
+			"Integer / integer divsion should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("2 * (6 + 14) / 2 - 5") == OK,
+			"Integer multiplication-addition-subtraction-division should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 15,
+			"Integer multiplication-addition-subtraction-division should return the expected result.");
+}
+
+TEST_CASE("[Expression] Floating-point arithmetic") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("-123.456") == OK,
+			"Float identity should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), -123.456),
+			"Float identity should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("2.0 + 3.0") == OK,
+			"Float addition should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 5),
+			"Float addition should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("3.0 / 10") == OK,
+			"Float / integer division should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 0.3),
+			"Float / integer divsion should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("3 / 10.0") == OK,
+			"Basic integer / float division should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 0.3),
+			"Basic integer / float divsion should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("3.0 / 10.0") == OK,
+			"Float / float division should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 0.3),
+			"Float / float divsion should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("2.5 * (6.0 + 14.25) / 2.0 - 5.12345") == OK,
+			"Float multiplication-addition-subtraction-division should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 20.18905),
+			"Float multiplication-addition-subtraction-division should return the expected result.");
+}
+
+TEST_CASE("[Expression] Scientific notation") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("2.e5") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 200'000),
+			"The expression should return the expected result.");
+
+	// The middle "e" is ignored here.
+	CHECK_MESSAGE(
+			expression.parse("2e5") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 25),
+			"The expression should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("2e.5") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 2),
+			"The expression should return the expected result.");
+}
+
+TEST_CASE("[Expression] Built-in functions") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("sqrt(pow(3, 2) + pow(4, 2))") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 5,
+			"`sqrt(pow(3, 2) + pow(4, 2))` should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("stepify(sin(0.5), 0.01)") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_equal_approx(float(expression.execute()), 0.48),
+			"`stepify(sin(0.5), 0.01)` should return the expected result.");
+
+	CHECK_MESSAGE(
+			expression.parse("pow(2.0, -2500)") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			Math::is_zero_approx(float(expression.execute())),
+			"`pow(2.0, -2500)` should return the expected result (asymptotically zero).");
+}
+
+TEST_CASE("[Expression] Boolean expressions") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("24 >= 12") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			bool(expression.execute()),
+			"The boolean expression should evaluate to `true`.");
+
+	CHECK_MESSAGE(
+			expression.parse("1.0 < 1.25 && 1.25 < 2.0") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			bool(expression.execute()),
+			"The boolean expression should evaluate to `true`.");
+
+	CHECK_MESSAGE(
+			expression.parse("!2") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			!bool(expression.execute()),
+			"The boolean expression should evaluate to `false`.");
+
+	CHECK_MESSAGE(
+			expression.parse("!!2") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			bool(expression.execute()),
+			"The boolean expression should evaluate to `true`.");
+
+	CHECK_MESSAGE(
+			expression.parse("!0") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			bool(expression.execute()),
+			"The boolean expression should evaluate to `true`.");
+
+	CHECK_MESSAGE(
+			expression.parse("!!0") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			!bool(expression.execute()),
+			"The boolean expression should evaluate to `false`.");
+
+	CHECK_MESSAGE(
+			expression.parse("2 && 5") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			bool(expression.execute()),
+			"The boolean expression should evaluate to `true`.");
+
+	CHECK_MESSAGE(
+			expression.parse("0 || 0") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			!bool(expression.execute()),
+			"The boolean expression should evaluate to `false`.");
+
+	CHECK_MESSAGE(
+			expression.parse("(2 <= 4) && (2 > 5)") == OK,
+			"The boolean expression should parse successfully.");
+	CHECK_MESSAGE(
+			!bool(expression.execute()),
+			"The boolean expression should evaluate to `false`.");
+}
+
+TEST_CASE("[Expression] Expressions with variables") {
+	Expression expression;
+
+	PackedStringArray parameter_names;
+	parameter_names.push_back("foo");
+	parameter_names.push_back("bar");
+	CHECK_MESSAGE(
+			expression.parse("foo + bar + 50", parameter_names) == OK,
+			"The expression should parse successfully.");
+	Array values;
+	values.push_back(60);
+	values.push_back(20);
+	CHECK_MESSAGE(
+			int(expression.execute(values)) == 130,
+			"The expression should return the expected value.");
+
+	PackedStringArray parameter_names_invalid;
+	parameter_names_invalid.push_back("foo");
+	parameter_names_invalid.push_back("baz"); // Invalid parameter name.
+	CHECK_MESSAGE(
+			expression.parse("foo + bar + 50", parameter_names_invalid) == OK,
+			"The expression should parse successfully.");
+	Array values_invalid;
+	values_invalid.push_back(60);
+	values_invalid.push_back(20);
+	// Invalid parameters will parse successfully but print an error message when executing.
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			int(expression.execute(values_invalid)) == 0,
+			"The expression should return the expected value.");
+	ERR_PRINT_ON;
+
+	// Mismatched argument count (more values than parameters).
+	PackedStringArray parameter_names_mismatch;
+	parameter_names_mismatch.push_back("foo");
+	parameter_names_mismatch.push_back("bar");
+	CHECK_MESSAGE(
+			expression.parse("foo + bar + 50", parameter_names_mismatch) == OK,
+			"The expression should parse successfully.");
+	Array values_mismatch;
+	values_mismatch.push_back(60);
+	values_mismatch.push_back(20);
+	values_mismatch.push_back(110);
+	CHECK_MESSAGE(
+			int(expression.execute(values_mismatch)) == 130,
+			"The expression should return the expected value.");
+
+	// Mismatched argument count (more parameters than values).
+	PackedStringArray parameter_names_mismatch2;
+	parameter_names_mismatch2.push_back("foo");
+	parameter_names_mismatch2.push_back("bar");
+	parameter_names_mismatch2.push_back("baz");
+	CHECK_MESSAGE(
+			expression.parse("foo + bar + baz + 50", parameter_names_mismatch2) == OK,
+			"The expression should parse successfully.");
+	Array values_mismatch2;
+	values_mismatch2.push_back(60);
+	values_mismatch2.push_back(20);
+	// Having more parameters than values will parse successfully but print an
+	// error message when executing.
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			int(expression.execute(values_mismatch2)) == 0,
+			"The expression should return the expected value.");
+	ERR_PRINT_ON;
+}
+
+TEST_CASE("[Expression] Invalid expressions") {
+	Expression expression;
+
+	CHECK_MESSAGE(
+			expression.parse("\\") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("0++") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("()") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("()()") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("() - ()") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("() * 12345") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("() * 12345") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("123'456") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+
+	CHECK_MESSAGE(
+			expression.parse("123\"456") == ERR_INVALID_PARAMETER,
+			"The expression shouldn't parse successfully.");
+}
+
+TEST_CASE("[Expression] Unusual expressions") {
+	Expression expression;
+
+	// Redundant parentheses don't cause a parse error as long as they're matched.
+	CHECK_MESSAGE(
+			expression.parse("(((((((((((((((666)))))))))))))))") == OK,
+			"The expression should parse successfully.");
+
+	// Using invalid identifiers doesn't cause a parse error.
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			expression.parse("hello + hello") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 0,
+			"The expression should return the expected result.");
+	ERR_PRINT_ON;
+
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			expression.parse("$1.00 + €5") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 0,
+			"The expression should return the expected result.");
+	ERR_PRINT_ON;
+
+	// Commas can't be used as a decimal parameter.
+	CHECK_MESSAGE(
+			expression.parse("123,456") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 123,
+			"The expression should return the expected result.");
+
+	// Spaces can't be used as a separator for large numbers.
+	CHECK_MESSAGE(
+			expression.parse("123 456") == OK,
+			"The expression should parse successfully.");
+	CHECK_MESSAGE(
+			int(expression.execute()) == 123,
+			"The expression should return the expected result.");
+
+	// Division by zero is accepted, even though it prints an error message normally.
+	CHECK_MESSAGE(
+			expression.parse("-25.4 / 0") == OK,
+			"The expression should parse successfully.");
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			Math::is_zero_approx(float(expression.execute())),
+			"`-25.4 / 0` should return 0.");
+	ERR_PRINT_ON;
+
+	CHECK_MESSAGE(
+			expression.parse("0 / 0") == OK,
+			"The expression should parse successfully.");
+	ERR_PRINT_OFF;
+	CHECK_MESSAGE(
+			int(expression.execute()) == 0,
+			"`0 / 0` should return 0.");
+	ERR_PRINT_ON;
+
+	// The tests below currently crash the engine.
+	//
+	//CHECK_MESSAGE(
+	//		expression.parse("(-9223372036854775807 - 1) % -1") == OK,
+	//		"The expression should parse successfully.");
+	//CHECK_MESSAGE(
+	//		int64_t(expression.execute()) == 0,
+	//		"`(-9223372036854775807 - 1) % -1` should return the expected result.");
+	//
+	//CHECK_MESSAGE(
+	//		expression.parse("(-9223372036854775807 - 1) / -1") == OK,
+	//		"The expression should parse successfully.");
+	//CHECK_MESSAGE(
+	//		int64_t(expression.execute()) == 0,
+	//		"`(-9223372036854775807 - 1) / -1` should return the expected result.");
+}
+
+} // namespace TestExpression
+
+#endif // TEST_EXPRESSION_H
diff --git a/tests/test_main.cpp b/tests/test_main.cpp
index 137882841c3..91a7dbba36a 100644
--- a/tests/test_main.cpp
+++ b/tests/test_main.cpp
@@ -36,6 +36,7 @@
 #include "test_basis.h"
 #include "test_class_db.h"
 #include "test_color.h"
+#include "test_expression.h"
 #include "test_gdscript.h"
 #include "test_gui.h"
 #include "test_math.h"