About Arithmetic Operators
SHORT DESCRIPTION
Describes the operators that perform arithmetic in PowerShell.
LONG DESCRIPTION
Arithmetic operators calculate numeric values. You can use one or more arithmetic operators to add, subtract, multiply, and divide values, and to calculate the remainder (modulus) of a division operation.
In addition, the addition operator (+
) and multiplication operator (*
)
also operate on strings, arrays, and hash tables. The addition operator
concatenates the input. The multiplication operator returns multiple copies
of the input. You can even mix object types in an arithmetic statement. The
method that is used to evaluate the statement is determined by the type of
the leftmost object in the expression.
Beginning in PowerShell 2.0, all arithmetic operators work on 64bit numbers.
Beginning in PowerShell 3.0, the shr
(shiftright) and shl
(shiftleft) are added to support bitwise arithmetic in PowerShell.
PowerShell supports the following arithmetic operators:
Operator  Description  Example 

+  Adds integers; concatenates  6 + 2 
strings, arrays, and hash tables.  "file" + "name" 

@(1, "one") + @(2.0, "two") 

@{"one" = 1} + @{"two" = 2} 

  Subtracts one value from another  6  2 
value  
  Makes a number a negative number  6 
(GetDate).AddDays(1) 

*  Multiply numbers or copy strings  6 * 2 
and arrays the specified number  @("!") * 4 

of times.  "!" * 3 

/  Divides two values.  6 / 2 
%  Modulus  returns the remainder of  7 % 2 
a division operation.  
band  Bitwise AND  5 band 3 
bnot  Bitwise NOT  bnot 5 
bor  Bitwise OR  5 bor 0x03 
bxor  Bitwise XOR  5 bxor 3 
shl  Shifts bits to the left  102 shl 2 
shr  Shifts bits to the right  102 shr 2 
The bitwise operators only work on integer types.
OPERATOR PRECEDENCE
PowerShell processes arithmetic operators in the following order:
Precedence  Operator  Description 

1  () 
Parentheses 
2   
For a negative number or unary operator 
3  * , / , % 
For multiplication and division 
4  + ,  
For addition and subtraction 
5  band , bnot 
For bitwise operations 
5  bor , bxor 
For bitwise operations 
5  shr , shl 
For bitwise operations 
PowerShell processes the expressions from left to right according to the precedence rules. The following examples show the effect of the precedence rules:
Expression  Result 

3+6/3*4 
11 
3+6/(3*4) 
3.5 
(3+6)/3*4 
12 
The order in which PowerShell evaluates expressions might differ from other programming and scripting languages that you have used. The following example shows a complicated assignment statement.
$a = 0
$b = @(1,2)
$c = @(1,2)
$b[$a] = $c[$a++]
In this example, the expression $a++
is evaluated before $b[$a]
.
Evaluating $a++
changes the value of $a
after it is used in the
statement $c[$a++]
; but, before it is used in $b[$a]
. The variable $a
in $b[$a]
equals 1
, not 0
; so, the statement assigns a value to
$b[1]
, not $b[0]
.
The above code is equivalent to:
$a = 0
$b = @(1,2)
$c = @(1,2)
$tmp = $c[$a]
$a = $a + 1
$b[$a] = $tmp
DIVISION AND ROUNDING
When the quotient of a division operation is an integer, PowerShell rounds
the value to the nearest integer. When the value is .5
, it rounds to the
nearest even integer.
The following example shows the effect of rounding to the nearest even integer.
Expression  Result 

[int]( 5 / 2 ) 
2 
[int]( 7 / 2 ) 
4 
Notice how 5/2 = 2.5 gets rounded to 2. But, 7/2 = 3.5 gets rounded to 4.
You can use the [Math]
class to get different rounding behavior.
Expression  Result 

[int][Math]::Round(5 / 2,[MidpointRounding]::AwayFromZero) 
3 
[int][Math]::Ceiling(5 / 2) 
3 
[int][Math]::Floor(5 / 2) 
2 
For more information, see the Math.Round method.
ADDING AND MULTIPLYING NONNUMERIC TYPES
You can add numbers, strings, arrays, and hash tables. And, you can multiply numbers, strings, and arrays. However, you cannot multiply hash tables.
When you add strings, arrays, or hash tables, the elements are concatenated. When you concatenate collections, such as arrays or hash tables, a new object is created that contains the objects from both collections. If you try to concatenate hash tables that have the same key, the operation fails.
For example, the following commands create two arrays and then add them:
$a = 1,2,3
$b = "A","B","C"
$a + $b
1
2
3
A
B
C
You can also perform arithmetic operations on objects of different types. The operation that PowerShell performs is determined by the Microsoft .NET Framework type of the leftmost object in the operation. PowerShell tries to convert all the objects in the operation to the .NET Framework type of the first object. If it succeeds in converting the objects, it performs the operation appropriate to the .NET Framework type of the first object. If it fails to convert any of the objects, the operation fails.
The following examples demonstrate the use of the addition and
multiplication operators; in operations that include different object
types. Assume $array = 1,2,3
:
Expression  Result 

"file" + 16 
file16 
$array + 16 
1 ,2 ,3 ,16 
$array + "file" 
1 ,2 ,3 ,file 
$array * 2 
1 ,2 ,3 ,1 ,2 ,3 
"file" * 3 
filefilefile 
Because the method that is used to evaluate statements is determined by the
leftmost object, addition and multiplication in PowerShell are not strictly
commutative. For example, (a + b)
does not always equal (b + a)
, and
(ab)
does not always equal (ba)
.
The following examples demonstrate this principle:
Expression  Result 

"file" + 16 
file16 
16 + "file" 
Cannot convert value "file" to type "System.Int32". 
Error: "Input string was not in a correct format." 

At line:1 char:1 

+ 16 + "file"` 
Hash tables are a slightly different case. You can add hash tables to another hash table, as long as, the added hash tables don't have duplicate keys.
The following example show how to add hash tables to each other.
$hash1 = @{a=1; b=2; c=3}
$hash2 = @{c1="Server01"; c2="Server02"}
$hash1 + $hash2
Name Value
 
c2 Server02
a 1
b 2
c1 Server01
c 3
The following example throws an error because one of the keys is duplicated in both hash tables.
$hash1 = @{a=1; b=2; c=3}
$hash2 = @{c1="Server01"; c="Server02"}
$hash1 + $hash2
Item has already been added. Key in dictionary: 'c' Key being added: 'c'
At line:3 char:1
+ $hash1 + $hash2
+ ~~~~~~~~~~~~~~~
+ CategoryInfo : OperationStopped: (:) [], ArgumentException
+ FullyQualifiedErrorId : System.ArgumentException
Also, you can add a hash table to an array; and, the entire hash table becomes an item in the array.
$array1 = @(0, "Hello World", [datetime]::Now)
$hash1 = @{a=1; b=2}
$array2 = $array1 + $hash1
$array2
0
Hello World
Monday, June 12, 2017 3:05:46 PM
Key : a
Value : 1
Name : a
Key : b
Value : 2
Name : b
However, you cannot add any other type to a hash table.
$hash1 + 2
A hash table can only be added to another hash table.
At line:3 char:1
+ $hash1 + 2
Although the addition operators are very useful, use the assignment
operators to add elements to hash tables and arrays. For more information
see about_assignment_operators. The
following examples use the +=
assignment operator to add items to an
array:
$array = @()
(0..9).foreach{ $array += $_ }
$array
0
1
2
TYPE CONVERSION TO ACCOMMODATE RESULT
PowerShell automatically selects the .NET Framework numeric type that best expresses the result without losing precision. For example:
2 + 3.1
(2). GetType().FullName
(2 + 3.1).GetType().FullName
5.1
System.Int32
System.Double
If the result of an operation is too large for the type, the type of the result is widened to accommodate the result, as in the following example:
(512MB).GetType().FullName
(512MB * 512MB).GetType().FullName
System.Int32
System.Double
The type of the result will not necessarily be the same as one of the
operands. In the following example, the negative value cannot be cast to an
unsigned integer, and the unsigned integer is too large to be cast to
Int32
:
([int32]::minvalue + [uint32]::maxvalue).gettype().fullname
System.Int64
In this example, Int64
can accommodate both types.
The System.Decimal
type is an exception. If either operand has the
Decimal type, the result will be of the Decimal type. If the result is too
large for the Decimal type, it will not be cast to Double. Instead, an
error results.
Expression  Result 

[Decimal]::maxvalue 
79228162514264337593543950335 
[Decimal]::maxvalue + 1 
Value was either too large or too small for a 
Decimal. 
ARITHMETIC OPERATORS AND VARIABLES
You can also use arithmetic operators with variables. The operators act on the values of the variables. The following examples demonstrate the use of arithmetic operators with variables:
Expression  Result 

$intA = 6 $intB = 4 $intA + $intB 
10 
$a = "Power" $b = "Shell" $a + $b 
PowerShell 
ARITHMETIC OPERATORS AND COMMANDS
Typically, you use the arithmetic operators in expressions with numbers, strings, and arrays. However, you can also use arithmetic operators with the objects that commands return and with the properties of those objects.
The following examples show how to use the arithmetic operators in expressions with PowerShell commands:
(getdate) + (newtimespan day 1)
The parenthesis operator forces the evaluation of the getdate
cmdlet and
the evaluation of the newtimespan day 1
cmdlet expression, in that
order. Both results are then added using the +
operator.
GetProcess  WhereObject { ($_.ws * 2) gt 50mb }
Handles NPM(K) PM(K) WS(K) VM(M) CPU(s) Id ProcessName
       
1896 39 50968 30620 264 1,572.55 1104 explorer
12802 78 188468 81032 753 3,676.39 5676 OUTLOOK
660 9 36168 26956 143 12.20 988 PowerShell
561 14 6592 28144 110 1,010.09 496 services
3476 80 34664 26092 234 ...45.69 876 svchost
967 30 58804 59496 416 930.97 2508 WINWORD
In the above expression, each process working space ($_.ws
) is multiplied
by 2
; and, the result, compared against 50mb
to see if it is greater
than that.
Bitwise Operators
PowerShell supports the standard bitwise operators, including bitwiseAND
(bAnd
), the inclusive and exclusive bitwiseOR operators (bOr
and
bXor
), and bitwiseNOT (bNot
).
Beginning in PowerShell 2.0, all bitwise operators work with 64bit integers.
Beginning in PowerShell 3.0, the shr
(shiftright) and shl
(shiftleft) are introduced to support bitwise arithmetic in PowerShell.
PowerShell supports the following bitwise operators.
Operator  Description  Expression  Result 

band 
Bitwise AND  10 band 3 
2 
bor 
Bitwise OR (inclusive)  10 bor 3 
11 
bxor 
Bitwise OR (exclusive)  10 bxor 3 
9 
bnot 
Bitwise NOT  bNot 10 
11 
shl 
Shiftleft  102 shl 2 
408 
shr 
Shiftright  102 shr 1 
51 
Bitwise operators act on the binary format of a value. For example, the bit structure for the number 10 is 00001010 (based on 1 byte), and the bit structure for the number 3 is 00000011. When you use a bitwise operator to compare 10 to 3, the individual bits in each byte are compared.
In a bitwise AND operation, the resulting bit is set to 1 only when both input bits are 1.
1010 (10)
0011 ( 3)
 bAND
0010 ( 2)
In a bitwise OR (inclusive) operation, the resulting bit is set to 1 when either or both input bits are 1. The resulting bit is set to 0 only when both input bits are set to 0.
1010 (10)
0011 ( 3)
 bOR (inclusive)
1011 (11)
In a bitwise OR (exclusive) operation, the resulting bit is set to 1 only when one input bit is 1.
1010 (10)
0011 ( 3)
 bXOR (exclusive)
1001 ( 9)
The bitwise NOT operator is a unary operator that produces the binary complement of the value. A bit of 1 is set to 0 and a bit of 0 is set to 1.
For example, the binary complement of 0 is 1, the maximum unsigned integer (0xffffffff), and the binary complement of 1 is 0.
bNot 10
11
0000 0000 0000 1010 (10)
 bNOT
1111 1111 1111 0101 (11, xfffffff5)
In a bitwise shiftleft operation, all bits are moved "n" places to the left, where "n" is the value of the right operand. A zero is inserted in the ones place.
When the left operand is an Integer (32bit) value, the lower 5 bits of the right operand determine how many bits of the left operand are shifted.
When the left operand is a Long (64bit) value, the lower 6 bits of the right operand determine how many bits of the left operand are shifted.
Expression  Result  Binary Result 

21 shl 0 
21  0001 0101 
21 shl 1 
42  0010 1010 
21 shl 2 
84  0101 0100 
In a bitwise shiftright operation, all bits are moved "n" places to the right, where "n" is specified by the right operand. The shiftright operator (shr) inserts a zero in the leftmost place when shifting a positive or unsigned value to the right.
When the left operand is an Integer (32bit) value, the lower 5 bits of the right operand determine how many bits of the left operand are shifted.
When the left operand is a Long (64bit) value, the lower 6 bits of the right operand determine how many bits of the left operand are shifted.
Expression  Result  Binary  Hex 

21 shr 0 
21  0001 0101  0x15 
21 shr 1 
10  0000 1010  0x0A 
21 shr 2 
5  0000 0101  0x05 
21 shr 31 
0  0000 0000  0x00 
21 shr 32 
21  0001 0101  0x15 
21 shr 64 
21  0001 0101  0x15 
21 shr 65 
10  0000 1010  0x0A 
21 shr 66 
5  0000 0101  0x05 
[int]::MaxValue shr 1 
1073741823  0x3FFFFFFF  
[int]::MinValue shr 1 
1073741824  0xC0000000  
1 shr 1 
1  0xFFFFFFFF 