$((Arithmetic Expansion))

Arithmetic expansion (returns the result as a string).

result=$(( expression ))

Arithmetic command (returns true/false via exit status).

(( expression ))

Using the let command.

let "variable=expression"

Legacy external command (not recommended).

result=$(expr expression)

Operator	Description
+ - * / %	Addition, subtraction, multiplication, integer division, and remainder.
**	Exponentiation (e.g., 2**10 = 1024).
++ --	Increment and decrement (both prefix and postfix forms are supported).
+= -= *= /= %=	Compound assignment operators.
== != < > <= >=	Comparison operators (return 1 for true, 0 for false).
&& ||	Logical AND and OR.
! ~ & | ^ << >>	Logical NOT and bitwise operations (NOT, AND, OR, XOR, and shift).
condition ? true : false	Ternary operator.

Basic arithmetic operations. Inside $(( )), you can reference variables without the $ prefix.

calc.sh

a=10
b=3
echo "Addition:       $(( a + b ))"
echo "Subtraction:    $(( a - b ))"
echo "Multiplication: $(( a * b ))"
echo "Division:       $(( a / b ))"
echo "Remainder:      $(( a % b ))"

bash calc.sh
Addition:       13
Subtraction:    7
Multiplication: 30
Division:       3
Remainder:      1

Use ** for exponentiation.

echo "2 to the power of 10: $(( 2**10 ))"
2 to the power of 10: 1024

Use increment and compound assignment operators to update a variable's value.

increment.sh

count=0
(( count++ ))
echo "After increment: $count"

(( count += 5 ))
echo "After +=: $count"

bash increment.sh
After increment: 1
After +=: 6

(( )) can also be used in conditionals. A non-zero result returns exit status 0 (true).

compare.sh

num=7
if (( num > 5 )); then
    echo "$num is greater than 5"
fi

bash compare.sh
7 is greater than 5

You can also enter an if statement directly in the terminal. After pressing Enter after then, a > prompt appears — this means the shell is waiting for more input. Enter fi to execute.

if (( 7 > 5 )); then
    echo "7 is greater than 5"
fi
7 is greater than 5

Use a C-style for loop to iterate with a counter.

sum.sh

sum=0
for (( i=1; i<=10; i++ )); do
    (( sum += i ))
done
echo "Sum of 1 to 10: $sum"

bash sum.sh
Sum of 1 to 10: 55

You can also enter a for loop directly in the terminal. After pressing Enter after do, a > prompt appears — this means the shell is waiting for more input. Enter done to execute.

sum=0; for (( i=1; i<=10; i++ )); do
    (( sum += i ))
done
echo "Sum of 1 to 10: $sum"
Sum of 1 to 10: 55

The ternary operator is also available.

ternary.sh

x=15
result=$(( x > 10 ? x * 2 : x + 10 ))
echo "result: $result"

bash ternary.sh
result: 30

Bitwise operations (AND and shift).

bitwise.sh

echo "Bitwise AND: $(( 0b1010 & 0b1100 ))"
echo "Left shift:  $(( 1 << 4 ))"

bash bitwise.sh
Bitwise AND: 8
Left shift:  16

Bash arithmetic supports integers only. For decimal calculations, use the bc command (e.g., $ echo "scale=2; 10/3" | bc → 3.33).

Inside $(( )), you can reference variables without the $ prefix (adding it also works). String variables and undefined variables are treated as 0.

For details on command substitution ($()), see Command Substitution.