After finishing our previous tutorial on Python variables in this series, you should now have a good grasp of creating and naming Python objects of different types. Let’s do some work with them!
Here’s what you’ll learn in this tutorial: You’ll see how calculations can be performed on objects in Python. By the end of this tutorial, you will be able to create complex expressions by combining objects and operators.
Take the Quiz: Test your knowledge with our interactive “Python Operators and Expressions” quiz. Upon completion you will receive a score so you can track your learning progress over time.
In Python, operators are special symbols that designate that some sort of computation should be performed. The values that an operator acts on are called operands.
Here is an example:
>>> a = 10
>>> b = 20
>>> a + b
30
In this case, the +
operator adds the operands a
and b
together. An operand can be either a literal value or a variable that references an object:
>>> a = 10
>>> b = 20
>>> a + b  5
25
A sequence of operands and operators, like a + b  5
, is called an expression. Python supports many operators for combining data objects into expressions. These are explored below.
Arithmetic Operators
The following table lists the arithmetic operators supported by Python:
Operator  Example  Meaning  Result 

+ (unary) 
+a 
Unary Positive  a In other words, it doesn’t really do anything. It mostly exists for the sake of completeness, to complement Unary Negation. 
+ (binary) 
a + b 
Addition  Sum of a and b 
 (unary) 
a 
Unary Negation  Value equal to a but opposite in sign 
 (binary) 
a  b 
Subtraction  b subtracted from a 
* 
a * b 
Multiplication  Product of a and b 
/ 
a / b 
Division  Quotient when a is divided by b .The result always has type float . 
% 
a % b 
Modulo  Remainder when a is divided by b 
// 
a // b 
Floor Division (also called Integer Division)  Quotient when a is divided by b , rounded to the next smallest whole number 
** 
a ** b 
Exponentiation  a raised to the power of b 
Here are some examples of these operators in use:
>>> a = 4
>>> b = 3
>>> +a
4
>>> b
3
>>> a + b
7
>>> a  b
1
>>> a * b
12
>>> a / b
1.3333333333333333
>>> a % b
1
>>> a ** b
64
The result of standard division (/
) is always a float
, even if the dividend is evenly divisible by the divisor:
>>> 10 / 5
2.0
>>> type(10 / 5)
<class 'float'>
When the result of floor division (//
) is positive, it is as though the fractional portion is truncated off, leaving only the integer portion. When the result is negative, the result is rounded down to the next smallest (greater negative) integer:
>>> 10 / 4
2.5
>>> 10 // 4
2
>>> 10 // 4
3
>>> 10 // 4
3
>>> 10 // 4
2
Note, by the way, that in a REPL session, you can display the value of an expression by just typing it in at the >>>
prompt without print()
, the same as you can with a literal value or variable:
>>> 25
25
>>> x = 4
>>> y = 6
>>> x
4
>>> y
6
>>> x * 25 + y
106
Comparison Operators
Operator  Example  Meaning  Result 

== 
a == b 
Equal to  True if the value of a is equal to the value of b False otherwise 
!= 
a != b 
Not equal to  True if a is not equal to b False otherwise 
< 
a < b 
Less than  True if a is less than b False otherwise 
<= 
a <= b 
Less than or equal to  True if a is less than or equal to b False otherwise 
> 
a > b 
Greater than  True if a is greater than b False otherwise 
>= 
a >= b 
Greater than or equal to  True if a is greater than or equal to b False otherwise 
Here are examples of the comparison operators in use:
>>> a = 10
>>> b = 20
>>> a == b
False
>>> a != b
True
>>> a <= b
True
>>> a >= b
False
>>> a = 30
>>> b = 30
>>> a == b
True
>>> a <= b
True
>>> a >= b
True
Comparison operators are typically used in Boolean contexts like conditional and loop statements to direct program flow, as you will see later.
Equality Comparison on FloatingPoint Values
Recall from the earlier discussion of floatingpoint numbers that the value stored internally for a float
object may not be precisely what you’d think it would be. For that reason, it is poor practice to compare floatingpoint values for exact equality. Consider this example:
>>> x = 1.1 + 2.2
>>> x == 3.3
False
Yikes! The internal representations of the addition operands are not exactly equal to 1.1
and 2.2
, so you cannot rely on x
to compare exactly to 3.3
.
The preferred way to determine whether two floatingpoint values are “equal” is to compute whether they are close to one another, given some tolerance. Take a look at this example:
>>> tolerance = 0.00001
>>> x = 1.1 + 2.2
>>> abs(x  3.3) < tolerance
True
abs()
returns absolute value. If the absolute value of the difference between the two numbers is less than the specified tolerance, they are close enough to one another to be considered equal.
Logical Operators
The logical operators not
, or
, and and
modify and join together expressions evaluated in Boolean context to create more complex conditions.
Logical Expressions Involving Boolean Operands
As you have seen, some objects and expressions in Python actually are of Boolean type. That is, they are equal to one of the Python objects True
or False
. Consider these examples:
>>> x = 5
>>> x < 10
True
>>> type(x < 10)
<class 'bool'>
>>> t = x > 10
>>> t
False
>>> type(t)
<class 'bool'>
>>> callable(x)
False
>>> type(callable(x))
<class 'bool'>
>>> t = callable(len)
>>> t
True
>>> type(t)
<class 'bool'>
In the examples above, x < 10
, callable(x)
, and t
are all Boolean objects or expressions.
Interpretation of logical expressions involving not
, or
, and and
is straightforward when the operands are Boolean:
Operator  Example  Meaning 

not 
not x 
True if x is False False if x is True (Logically reverses the sense of x ) 
or 
x or y 
True if either x or y is True False otherwise 
and 
x and y 
True if both x and y are True False otherwise 
Take a look at how they work in practice below.
“not
” and Boolean Operands
x = 5
not x < 10
False
not callable(x)
True
Operand  Value  Logical Expression  Value 

x < 10 
True 
not x < 10 
False 
callable(x) 
False 
not callable(x) 
True 
“or
” and Boolean Operands
x = 5
x < 10 or callable(x)
True
x < 0 or callable(x)
False
Operand  Value  Operand  Value  Logical Expression  Value 

x < 10 
True 
callable(x) 
False 
x < 10 or callable(x) 
True 
x < 0 
False 
callable(x) 
False 
x < 0 or callable(x) 
False 
“and
” and Boolean Operands
x = 5
x < 10 and callable(x)
False
x < 10 and callable(len)
True
Operand  Value  Operand  Value  Logical Expression  Value 

x < 10 
True 
callable(x) 
False 
x < 10 and callable(x) 
False 
x < 10 
True 
callable(len) 
True 
x < 10 or callable(len) 
True 
Evaluation of NonBoolean Values in Boolean Context
Many objects and expressions are not equal to True
or False
. Nonetheless, they may still be evaluated in Boolean context and determined to be “truthy” or “falsy.”
So what is true and what isn’t? As a philosophical question, that is outside the scope of this tutorial!
But in Python, it is welldefined. All the following are considered false when evaluated in Boolean context:
 The Boolean value
False
 Any value that is numerically zero (
0
,0.0
,0.0+0.0j
)  An empty string
 An object of a builtin composite data type which is empty (see below)
 The special value denoted by the Python keyword
None
Virtually any other object built into Python is regarded as true.
You can determine the “truthiness” of an object or expression with the builtin bool()
function. bool()
returns True
if its argument is truthy and False
if it is falsy.
Numeric Value
A zero value is false.
A nonzero value is true.
>>> print(bool(0), bool(0.0), bool(0.0+0j))
False False False
>>> print(bool(3), bool(3.14159), bool(1.0+1j))
True True True
String
An empty string is false.
A nonempty string is true.
>>> print(bool(''), bool(""), bool(""""""))
False False False
>>> print(bool('foo'), bool(" "), bool(''' '''))
True True True
BuiltIn Composite Data Object
Python provides builtin composite data types called
list
,tuple
,dict
, andset
. These are “container” types that contain other objects. An object of one of these types is considered false if it is empty and true if it is nonempty.The examples below demonstrate this for the
list
type. (Lists are defined in Python with square brackets.)For more information on the
list
,tuple
,dict
, andset
types, see the upcoming tutorials.
>>> type([])
<class 'list'>
>>> bool([])
False
>>> type([1, 2, 3])
<class 'list'>
>>> bool([1, 2, 3])
True
The “None
” Keyword
None
is always false:
>>> bool(None)
False
Logical Expressions Involving NonBoolean Operands
NonBoolean values can also be modified and joined by not
, or
and, and
. The result depends on the “truthiness” of the operands.
“not
” and NonBoolean Operands
Here is what happens for a nonBoolean value x
:
If x is 
not x is 

“truthy”  False 
“falsy”  True 
Here are some concrete examples:
>>> x = 3
>>> bool(x)
True
>>> not x
False
>>> x = 0.0
>>> bool(x)
False
>>> not x
True
“or
” and NonBoolean Operands
This is what happens for two nonBoolean values x
and y
:
If x is 
x or y is 

truthy  x 
falsy  y 
Note that in this case, the expression x or y
does not evaluate to either True
or False
, but instead to one of either x
or y
:
>>> x = 3
>>> y = 4
>>> x or y
3
>>> x = 0.0
>>> y = 4.4
>>> x or y
4.4
Even so, it is still the case that the expression x or y
will be truthy if either x
or y
is truthy, and falsy if both x
and y
are falsy.
“and
” and NonBoolean Operands
Here’s what you’ll get for two nonBoolean values x
and y
:
If x is 
x and y is 

“truthy”  y 
“falsy”  x 
>>> x = 3
>>> y = 4
>>> x and y
4
>>> x = 0.0
>>> y = 4.4
>>> x and y
0.0
As with or
, the expression x and y
does not evaluate to either True
or False
, but instead to one of either x
or y
. x and y
will be truthy if both x
and y
are truthy, and falsy otherwise.
Compound Logical Expressions and ShortCircuit Evaluation
So far, you have seen expressions with only a single or
or and
operator and two operands:
x or y
x and y
Multiple logical operators and operands can be strung together to form compound logical expressions.
Compound “or
” Expressions
Consider the following expression:
x_{1}
or
x_{2}or
x_{3}or
… x_{n}
This expression is true if any of the x_{i} are true.
In an expression like this, Python uses a methodology called shortcircuit evaluation, also called McCarthy evaluation in honor of computer scientist John McCarthy. The x_{i} operands are evaluated in order from left to right. As soon as one is found to be true, the entire expression is known to be true. At that point, Python stops and no more terms are evaluated. The value of the entire expression is that of the x_{i} that terminated evaluation.
To help demonstrate shortcircuit evaluation, suppose that you have a simple “identity” function f()
that behaves as follows:
f()
takes a single argument. It displays the argument to the console.
 It returns the argument passed to it as its return value.
(You will see how to define such a function in the upcoming tutorial on Functions.)
Several example calls to f()
are shown below:
>>> f(0)
> f(0) = 0
0
>>> f(False)
> f(False) = False
False
>>> f(1.5)
> f(1.5) = 1.5
1.5
Because f()
simply returns the argument passed to it, we can make the expression f(arg)
be truthy or falsy as needed by specifying a value for arg
that is appropriately truthy or falsy. Additionally, f()
displays its argument to the console, which visually confirms whether or not it was called.
Now, consider the following compound logical expression:
>>> f(0) or f(False) or f(1) or f(2) or f(3)
> f(0) = 0
> f(False) = False
> f(1) = 1
1
The interpreter first evaluates f(0)
, which is 0
. A numeric value of 0
is false. The expression is not true yet, so evaluation proceeds left to right. The next operand, f(False)
, returns False
. That is also false, so evaluation continues.
Next up is f(1)
. That evaluates to 1
, which is true. At that point, the interpreter stops because it now knows the entire expression to be true. 1
is returned as the value of the expression, and the remaining operands, f(2)
and f(3)
, are never evaluated. You can see from the display that the f(2)
and f(3)
calls do not occur.
Compound “and
” Expressions
A similar situation exists in an expression with multiple and
operators:
x_{1}
and
x_{2}and
x_{3}and
… x_{n}
This expression is true if all the x_{i} are true.
In this case, shortcircuit evaluation dictates that the interpreter stop evaluating as soon as any operand is found to be false, because at that point the entire expression is known to be false. Once that is the case, no more operands are evaluated, and the falsy operand that terminated evaluation is returned as the value of the expression:
>>> f(1) and f(False) and f(2) and f(3)
> f(1) = 1
> f(False) = False
False
>>> f(1) and f(0.0) and f(2) and f(3)
> f(1) = 1
> f(0.0) = 0.0
0.0
In both examples above, evaluation stops at the first term that is false—f(False)
in the first case, f(0.0)
in the second case—and neither the f(2)
nor f(3)
call occurs. False
and 0.0
, respectively, are returned as the value of the expression.
If all the operands are truthy, they all get evaluated and the last (rightmost) one is returned as the value of the expression:
>>> f(1) and f(2.2) and f('bar')
> f(1) = 1
> f(2.2) = 2.2
> f(bar) = bar
'bar'
Idioms That Exploit ShortCircuit Evaluation
There are some common idiomatic patterns that exploit shortcircuit evaluation for conciseness of expression.
Avoiding an Exception
Suppose you have defined two variables a
and b
, and you want to know whether (b / a) > 0
:
>>> a = 3
>>> b = 1
>>> (b / a) > 0
True
But you need to account for the possibility that a
might be 0
, in which case the interpreter will raise an exception:
>>> a = 0
>>> b = 1
>>> (b / a) > 0
Traceback (most recent call last):
File "<pyshell#2>", line 1, in <module>
(b / a) > 0
ZeroDivisionError: division by zero
You can avoid an error with an expression like this:
>>> a = 0
>>> b = 1
>>> a != 0 and (b / a) > 0
False
When a
is 0
, a != 0
is false. Shortcircuit evaluation ensures that evaluation stops at that point. (b / a)
is not evaluated, and no error is raised.
If fact, you can be even more concise than that. When a
is 0
, the expression a
by itself is falsy. There is no need for the explicit comparison a != 0
:
>>> a = 0
>>> b = 1
>>> a and (b / a) > 0
0
Selecting a Default Value
Another idiom involves selecting a default value when a specified value is zero or empty. For example, suppose you want to assign a variable s
to the value contained in another variable called string
. But if string
is empty, you want to supply a default value.
Here is a concise way of expressing this using shortcircuit evaluation:
s = string or '<default_value>'
If string
is nonempty, it is truthy, and the expression string or '<default_value>'
will be true at that point. Evaluation stops, and the value of string
is returned and assigned to s
:
>>> string = 'foo bar'
>>> s = string or '<default_value>'
>>> s
'foo bar'
On the other hand, if string
is an empty string, it is falsy. Evaluation of string or '<default_value>'
continues to the next operand, '<default_value>'
, which is returned and assigned to s
:
>>> string = ''
>>> s = string or '<default_value>'
>>> s
'<default_value>'
Chained Comparisons
Comparison operators can be chained together to arbitrary length. For example, the following expressions are nearly equivalent:
x < y <= z
x < y and y <= z
They will both evaluate to the same Boolean value. The subtle difference between the two is that in the chained comparison x < y <= z
, y
is evaluated only once. The longer expression x < y and y <= z
will cause y
to be evaluated twice.
Note: In cases where y
is a static value, this will not be a significant distinction. But consider these expressions:
x < f() <= z
x < f() and f() <= z
If f()
is a function that causes program data to be modified, the difference between its being called once in the first case and twice in the second case may be important.
More generally, if op_{1}, op_{2}, …, op_{n} are comparison operators, then the following have the same Boolean value:
x_{1} op_{1} x_{2} op_{2} x_{3} … x_{n1} op_{n} x_{n}
x_{1} op_{1} x_{2}
and
x_{2} op_{2} x_{3}and
… x_{n1} op_{n} x_{n}
In the former case, each x_{i} is only evaluated once. In the latter case, each will be evaluated twice except the first and last, unless shortcircuit evaluation causes premature termination.
Bitwise Operators
Bitwise operators treat operands as sequences of binary digits and operate on them bit by bit. The following operators are supported:
Operator  Example  Meaning  Result 

& 
a & b 
bitwise AND  Each bit position in the result is the logical AND of the bits in the corresponding position of the operands. (1 if both are 1 , otherwise 0 .) 
 
a  b 
bitwise OR  Each bit position in the result is the logical OR of the bits in the corresponding position of the operands. (1 if either is 1 , otherwise 0 .) 
~ 
~a 
bitwise negation  Each bit position in the result is the logical negation of the bit in the corresponding position of the operand. (1 if 0 , 0 if 1 .) 
^ 
a ^ b 
bitwise XOR (exclusive OR)  Each bit position in the result is the logical XOR of the bits in the corresponding position of the operands. (1 if the bits in the operands are different, 0 if they are the same.) 
>> 
a >> n 
Shift right n places 
Each bit is shifted right n places. 
<< 
a << n 
Shift left n places 
Each bit is shifted left n places. 
Here are some examples:
>>> '0b{:04b}'.format(0b1100 & 0b1010)
'0b1000'
>>> '0b{:04b}'.format(0b1100  0b1010)
'0b1110'
>>> '0b{:04b}'.format(0b1100 ^ 0b1010)
'0b0110'
>>> '0b{:04b}'.format(0b1100 >> 2)
'0b0011'
>>> '0b{:04b}'.format(0b0011 << 2)
'0b1100'
Note: The purpose of the '0b{:04b}'.format()
is to format the numeric output of the bitwise operations, to make them easier to read. You will see the format()
method in much more detail later. For now, just pay attention to the operands of the bitwise operations, and the results.
Identity Operators
Python provides two operators, is
and is not
, that determine whether the given operands have the same identity—that is, refer to the same object. This is not the same thing as equality, which means the two operands refer to objects that contain the same data but are not necessarily the same object.
Here is an example of two object that are equal but not identical:
>>> x = 1001
>>> y = 1000 + 1
>>> print(x, y)
1001 1001
>>> x == y
True
>>> x is y
False
Here, x
and y
both refer to objects whose value is 1001
. They are equal. But they do not reference the same object, as you can verify:
>>> id(x)
60307920
>>> id(y)
60307936
x
and y
do not have the same identity, and x is y
returns False
.
You saw previously that when you make an assignment like x = y
, Python merely creates a second reference to the same object, and that you could confirm that fact with the id()
function. You can also confirm it using the is
operator:
>>> a = 'I am a string'
>>> b = a
>>> id(a)
55993992
>>> id(b)
55993992
>>> a is b
True
>>> a == b
True
In this case, since a
and b
reference the same object, it stands to reason that a
and b
would be equal as well.
Unsurprisingly, the opposite of is
is is not
:
>>> x = 10
>>> y = 20
>>> x is not y
True
Operator Precedence
Consider this expression:
>>> 20 + 4 * 10
60
There is ambiguity here. Should Python perform the addition 20 + 4
first and then multiply the sum by 10
? Or should the multiplication 4 * 10
be performed first, and the addition of 20
second?
Clearly, since the result is 60
, Python has chosen the latter; if it had chosen the former, the result would be 240
. This is standard algebraic procedure, found universally in virtually all programming languages.
All operators that the language supports are assigned a precedence. In an expression, all operators of highest precedence are performed first. Once those results are obtained, operators of the next highest precedence are performed. So it continues, until the expression is fully evaluated. Any operators of equal precedence are performed in lefttoright order.
Here is the order of precedence of the Python operators you have seen so far, from lowest to highest:
Operator  Description  

lowest precedence  or 
Boolean OR 
and 
Boolean AND  
not 
Boolean NOT  
== , != , < , <= , > , >= , is , is not 
comparisons, identity  
 
bitwise OR  
^ 
bitwise XOR  
& 
bitwise AND  
<< , >> 
bit shifts  
+ ,  
addition, subtraction  
* , / , // , % 
multiplication, division, floor division, modulo  
+x , x , ~x 
unary positive, unary negation, bitwise negation  
highest precedence  ** 
exponentiation 
Operators at the top of the table have the lowest precedence, and those at the bottom of the table have the highest. Any operators in the same row of the table have equal precedence.
It is clear why multiplication is performed first in the example above: multiplication has a higher precedence than addition.
Similarly, in the example below, 3
is raised to the power of 4
first, which equals 81
, and then the multiplications are carried out in order from left to right (2 * 81 * 5 = 810
):
>>> 2 * 3 ** 4 * 5
810
Operator precedence can be overridden using parentheses. Expressions in parentheses are always performed first, before expressions that are not parenthesized. Thus, the following happens:
>>> 20 + 4 * 10
60
>>> (20 + 4) * 10
240
>>> 2 * 3 ** 4 * 5
810
>>> 2 * 3 ** (4 * 5)
6973568802
In the first example, 20 + 4
is computed first, then the result is multiplied by 10
. In the second example, 4 * 5
is calculated first, then 3
is raised to that power, then the result is multiplied by 2
.
There is nothing wrong with making liberal use of parentheses, even when they aren’t necessary to change the order of evaluation. In fact, it is considered good practice, because it can make the code more readable, and it relieves the reader of having to recall operator precedence from memory. Consider the following:
(a < 10) and (b > 30)
Here the parentheses are fully unnecessary, as the comparison operators have higher precedence than and
does and would have been performed first anyhow. But some might consider the intent of the parenthesized version more immediately obvious than this version without parentheses:
a < 10 and b > 30
On the other hand, there are probably those who would prefer the latter; it’s a matter of personal preference. The point is, you can always use parentheses if you feel it makes the code more readable, even if they aren’t necessary to change the order of evaluation.
Augmented Assignment Operators
You have seen that a single equal sign (=
) is used to assign a value to a variable. It is, of course, perfectly viable for the value to the right of the assignment to be an expression containing other variables:
>>> a = 10
>>> b = 20
>>> c = a * 5 + b
>>> c
70
In fact, the expression to the right of the assignment can include references to the variable that is being assigned to:
>>> a = 10
>>> a = a + 5
>>> a
15
>>> b = 20
>>> b = b * 3
>>> b
60
The first example is interpreted as “a
is assigned the current value of a
plus 5
,” effectively increasing the value of a
by 5
. The second reads “b
is assigned the current value of b
times 3
,” effectively increasing the value of b
threefold.
Of course, this sort of assignment only makes sense if the variable in question has already previously been assigned a value:
>>> z = z / 12
Traceback (most recent call last):
File "<pyshell#11>", line 1, in <module>
z = z / 12
NameError: name 'z' is not defined
Python supports a shorthand augmented assignment notation for these arithmetic and bitwise operators:
Arithmetic  Bitwise 

+  * / % // ** 
&  ^ >> << 
For these operators, the following are equivalent:
x <op>= y
x = x <op> y
Take a look at these examples:
Augmented Assignment 
Standard Assignment 


a += 5 
is equivalent to  a = a + 5 
a /= 10 
is equivalent to  a = a / 10 
a ^= b 
is equivalent to  a = a ^ b 
Conclusion
In this tutorial, you learned about the diverse operators Python supports to combine objects into expressions.
Most of the examples you have seen so far have involved only simple atomic data, but you saw a brief introduction to the string data type. The next tutorial will explore string objects in much more detail.
Take the Quiz: Test your knowledge with our interactive “Python Operators and Expressions” quiz. Upon completion you will receive a score so you can track your learning progress over time.