Chapter introduction
This chapter builds on top of the concepts from lesson 1.9  Introduction to literals and operators. A quick review follows:
In mathematics, an operation is a mathematical calculation involving zero or more input values (called operands) that produces a new value (called an output value). The specific operation to be performed is denoted by a construct (typically a symbol or pair of symbols) called an operator.
For example, as children we all learn that 2 + 3 equals 5. In this case, the literals 2 and 3 are the operands, and the symbol + is the operator that tells us to apply mathematical addition on the operands to produce the new value 5.
In this chapter, we’ll discuss topics related to operators, and explore many of the common operators that C++ supports.
Operator precedence
Now, let’s consider a more complicated expression, such as 4 + 2 * 3. In order to evaluate this expression, we must understand both what the operators do, and the correct order to apply them. The order in which operators are evaluated in a compound expression is determined by an operator’s precedence. Using normal mathematical precedence rules (which state that multiplication is resolved before addition), we know that the above expression should evaluate as 4 + (2 * 3) to produce the value 10.
In C++, when the compiler encounters an expression, it must similarly analyze the expression and determine how it should be evaluated. To assist with this, all operators are assigned a level of precedence. Operators with the highest level of precedence are evaluated first.
You can see in the table below that multiplication and division (precedence level 5) have more precedence than addition and subtraction (precedence level 6). Thus, 4 + 2 * 3 evaluates as 4 + (2 * 3) because multiplication has a higher level of precedence than addition.
Operator associativity
What happens if two operators in the same expression have the same precedence level? For example, in the expression 3 * 4 / 2, the multiplication and division operators are both precedence level 5. In this case, the compiler can’t rely upon precedence alone to determine how to evaluate the result.
If two operators with the same precedence level are adjacent to each other in an expression, the operator’s associativity tells the compiler whether to evaluate the operators from left to right or from right to left. The operators in precedence level 5 have an associativity of left to right, so the expression is resolved from left to right: (3 * 4) / 2 = 6.
Table of operators
The below table is primarily meant to be a reference chart that you can refer back to in the future to resolve any precedence or associativity questions you have.
Notes:
 Precedence level 1 is the highest precedence level, and level 17 is the lowest. Operators with a higher precedence level get evaluated first.
 L>R means left to right associativity.
 R>L means right to left associativity.
Prec/Ass  Operator  Description  Pattern 

1 None 
:: :: 
Global scope (unary) Namespace scope (binary) 
::name class_name::member_name 
2 L>R 
() () () {} type() type{} [] . > ++ –– typeid const_cast dynamic_cast reinterpret_cast static_cast sizeof… noexcept alignof 
Parentheses Function call Initialization Uniform initialization (C++11) Functional cast Functional cast (C++11) Array subscript Member access from object Member access from object ptr Postincrement Postdecrement Runtime type information Cast away const Runtime typechecked cast Cast one type to another Compiletime typechecked cast Get parameter pack size Compiletime exception check Get type alignment 
(expression) function_name(parameters) type name(expression) type name{expression} new_type(expression) new_type{expression} pointer[expression] object.member_name object_pointer>member_name lvalue++ lvalue–– typeid(type) or typeid(expression) const_cast<type>(expression) dynamic_cast<type>(expression) reinterpret_cast<type>(expression) static_cast<type>(expression) sizeof…(expression) noexcept(expression) alignof(Type) 
3 R>L 
+  ++ –– ! ~ (type) sizeof co_await & * new new[] delete delete[] 
Unary plus Unary minus Preincrement Predecrement Logical NOT Bitwise NOT Cstyle cast Size in bytes Await asynchronous call Address of Dereference Dynamic memory allocation Dynamic array allocation Dynamic memory deletion Dynamic array deletion 
+expression expression ++lvalue ––lvalue !expression ~expression (new_type)expression sizeof(type) or sizeof(expression) co_await expression &lvalue *expression new type new type[expression] delete pointer delete[] pointer 
4 L>R 
>* .* 
Member pointer selector Member object selector 
object_pointer>*pointer_to_member object.*pointer_to_member 
5 L>R 
* / % 
Multiplication Division Modulus 
expression * expression expression / expression expression % expression 
6 L>R 
+

Addition Subtraction 
expression + expression expression  expression 
7 L>R 
<< >> 
Bitwise shift left Bitwise shift right 
expression << expression expression >> expression 
8 L>R  <=>  Threeway comparison  expression <=> expression 
9 L>R 
< <= > >= 
Comparison less than Comparison less than or equals Comparison greater than Comparison greater than or equals 
expression < expression expression <= expression expression > expression expression >= expression 
10 L>R 
== != 
Equality Inequality 
expression == expression expression != expression 
11 L>R  &  Bitwise AND  expression & expression 
12 L>R  ^  Bitwise XOR  expression ^ expression 
13 L>R    Bitwise OR  expression  expression 
14 L>R  &&  Logical AND  expression && expression 
15 L>R    Logical OR  expression  expression 
16 R>L 
throw co_yield ?: = *= /= %= += = <<= >>= &= = ^= 
Throw expression Yield expression Conditional Assignment Multiplication assignment Division assignment Modulus assignment Addition assignment Subtraction assignment Bitwise shift left assignment Bitwise shift right assignment Bitwise AND assignment Bitwise OR assignment Bitwise XOR assignment 
throw expression co_yield expression expression ? expression : expression lvalue = expression lvalue *= expression lvalue /= expression lvalue %= expression lvalue += expression lvalue = expression lvalue <<= expression lvalue >>= expression lvalue &= expression lvalue = expression lvalue ^= expression 
17 L>R  ,  Comma operator  expression, expression 
You should already recognize a few of these operators, such as +, , *, /, (), and sizeof. However, unless you have experience with another programming language, the majority of the operators in this table will probably be incomprehensible to you right now. That’s expected at this point. We’ll cover many of them in this chapter, and the rest will be introduced as there is a need for them.
Q: Where’s the exponent operator?
C++ doesn’t include an operator to do exponentiation (operator^ has a different function in C++). We discuss exponentiation more in lesson 5.3  Modulus and Exponentiation.
Parenthesization
In normal arithmetic, you learned that you can use parentheses to change the order of application of operations. For example, we know that 4 + 2 * 3 evaluates as 4 + (2 * 3), but if you want it to evaluate as (4 + 2) * 3 instead, you can explicitly parenthesize the expression to make it evaluate the way you want. This works in C++ because parentheses have one of the highest precedence levels, so parentheses generally evaluate before whatever is inside them.
Now consider an expression like x && y  z. Does this evaluate as (x && y)  z or x && (y  z)? You could look up in the table and see that && takes precedence over . But there are so many operators and precedence levels that it’s hard to remember them all. In order to reduce mistakes and make your code easier to understand without referencing a precedence table, it’s a good idea to parenthesize any nontrivial compound expression, so it’s clear what your intent is.
Best practice
Use parentheses to make it clear how an expression should evaluate, even if they are technically unnecessary.
The order of evaluation of expressions is mostly unspecified
Consider the following expression:
a + b * c
We know from the precedence and associativity rules above that this expression will evaluate as if we had typed:
a + (b * c)
If a is 1, b is 2, and c is 3, this expression will evaluate to the answer 7.
However, the precedence and associativity rules only tell us how operators evaluate in relation to other operators. It does not tell us anything about the order in which the rest of the expression evaluates. For example, does variable a, b, or c get evaluated first?
Perhaps surprisingly, in many cases, the order of evaluation of any part of a compound expression (including function calls and argument evaluation) is unspecified. In such cases, the compiler is free to choose any evaluation order it believes is optimal.
Warning
In many cases, the parts of a compound expression (including function calls and argument evaluation) may evaluate in any order.
For most expressions, this is irrelevant. In our sample expression above, it doesn’t matter whether in which order variables a, b, or c are evaluated for their values: the answer will always be 7. There is no ambiguity here.
But it is possible to write expressions where the order of evaluation does matter. Consider this program, which contains a mistake often made by new C++ programmers:
#include <iostream>
int getValue()
{
int x{};
std::cin >> x;
return x;
}
int main()
{
std::cout << getValue() + (getValue() * getValue()); // a + (b * c)
return 0;
}
If you run this program and enter inputs 1, 2, and 3, you might assume that this program would print 7. But that is making the assumption that the calls to getValue() will evaluate in lefttoright order. The compiler may choose a different order. For example, if the compiler chose a righttoleft order instead, the program would print 5 for the same set of inputs.
Best practice
Outside of the operator precedence and associativity rules, assume that the parts of an expression could evaluate in any order. Ensure that the expressions you write are not dependent on the order of evaluation of those parts.
Related content
There are some additional examples of cases where order of evaluation problems can occur in lesson 5.4  Increment/decrement operators, and side effects.
Quiz time
Question #1
You know from everyday mathematics that expressions inside of parentheses get evaluated first. For example, in the expression (2 + 3) * 4
, the (2 + 3)
part is evaluated first.
For this exercise, you are given a set of expressions that have no parentheses. Using the operator precedence and associativity rules in the table above, add parentheses to each expression to make it clear how the compiler will evaluate the expression.
Sample problem: x = 2 + 3 % 4
Binary operator % has higher precedence than operator + or operator =, so it gets evaluated first: x = 2 + (3 % 4) Binary operator + has a higher precedence than operator =, so it gets evaluated next: Final answer: x = (2 + (3 % 4)) We now no longer need the table above to understand how this expression will evaluate. 
a) x = 3 + 4 + 5;
b) x = y = z;
c) z *= ++y + 5;
d) a  b && c  d;