$((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)

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

sample_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 ))"

Run the following command:

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.

sample_increment.sh

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

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

Run the following command:

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

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

sample_compare.sh

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

The following example demonstrates this:

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.

sample_sum.sh

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

The following example demonstrates this:

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.

sample_ternary.sh

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

The following example demonstrates this:

bash ternary.sh
result: 30

Bitwise operations (AND and shift).

sample_bitwise.sh

echo "Bitwise AND: $(( 0x0A & 0x0C ))"
echo "Left shift:  $(( 1 << 4 ))"

Run the following command:

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

Common Mistake 1: Adding spaces around the operator causes an error

Inside $(( )), spaces around operators are fine. However, spaces in the assignment itself cause a command-not-found error.

result = $(( 1 + 2 ))
bash: result: command not found

Write the assignment without spaces around =.

result=$(( 1 + 2 ))
echo $result
3

Common Mistake 2: Trying to compute floating-point numbers

$(( )) handles integers only. Division is integer division and fractional parts are discarded.

echo $(( 10 / 3 ))
3

Use bc for floating-point arithmetic.

echo "scale=2; 10 / 3" | bc
3.33

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.