Arithmetic¶

Bash supports integer arithmetic natively. For floating-point calculations, external tools are needed.

Arithmetic Expansion¶

The $(( )) syntax evaluates arithmetic expressions:

echo $((5 + 3))       # 8
echo $((10 - 4))      # 6
echo $((6 * 7))       # 42
echo $((20 / 3))      # 6 (integer division)
echo $((20 % 3))      # 2 (modulo)
echo $((2 ** 10))     # 1024 (exponentiation)

Operators¶

Operator	Meaning
`+`	Addition
`-`	Subtraction
`*`	Multiplication
`/`	Division (integer)
`%`	Modulo (remainder)
`**`	Exponentiation
`++`	Increment
`--`	Decrement

Compound Assignment¶

x=10
((x += 5))     # x = 15
((x -= 3))     # x = 12
((x *= 2))     # x = 24
((x /= 4))     # x = 6
((x %= 4))     # x = 2

Increment and Decrement¶

x=5
echo $((x++))  # 5 (post-increment: use then increment)
echo $x        # 6

x=5
echo $((++x))  # 6 (pre-increment: increment then use)
echo $x        # 6

The (( )) Command¶

For arithmetic evaluation without output:

((count++))         # Increment, no output
((total = a + b))   # Calculate and assign

# As a condition
if ((count > 10)); then
    echo "Large"
fi

Exit Status¶

(( )) returns 0 (success) if result is non-zero, 1 (failure) if zero:

((5 > 3)) && echo "True"    # Prints True
((5 < 3)) && echo "True"    # Prints nothing

((0)) && echo "True"        # Prints nothing (0 = false)
((1)) && echo "True"        # Prints True (non-zero = true)

Variables in Arithmetic¶

Variables don't need $ inside (( )):

a=5
b=3
echo $((a + b))     # 8
echo $((a * b))     # 15

# With $ works too, but not needed
echo $(($a + $b))   # 8

Undefined variables are treated as 0:

unset x
echo $((x + 5))     # 5

Comparison Operators¶

Inside (( )):

Operator	Meaning
`<`	Less than
`>`	Greater than
`<=`	Less than or equal
`>=`	Greater than or equal
`==`	Equal
`!=`	Not equal

a=5
b=10

((a < b)) && echo "a is smaller"
((a == 5)) && echo "a equals 5"

Logical Operators¶

Operator	Meaning
`&&`	Logical AND
`\\|\\|`	Logical OR
`!`	Logical NOT

a=5
b=10

((a > 0 && b > 0)) && echo "Both positive"
((a > 10 || b > 5)) && echo "At least one condition true"
((!0)) && echo "NOT 0 is true"

Bitwise Operators¶

Operator	Meaning
`&`	Bitwise AND
`\\|`	Bitwise OR
`^`	Bitwise XOR
`~`	Bitwise NOT
`<<`	Left shift
`>>`	Right shift

echo $((5 & 3))     # 1  (0101 & 0011 = 0001)
echo $((5 | 3))     # 7  (0101 | 0011 = 0111)
echo $((5 ^ 3))     # 6  (0101 ^ 0011 = 0110)
echo $((~5))        # -6 (bitwise NOT)
echo $((1 << 4))    # 16 (0001 << 4 = 10000)
echo $((16 >> 2))   # 4  (10000 >> 2 = 100)

The let Command¶

Alternative syntax for arithmetic:

let "a = 5 + 3"
let a++
let "b = a * 2"
echo $a $b    # 9 18

Multiple expressions:

let "a = 1" "b = 2" "c = a + b"
echo $c    # 3

The expr Command¶

External command (POSIX compatible, but slower):

result=$(expr 5 + 3)
echo $result    # 8

# Operators need escaping
expr 5 \* 3     # 15
expr 10 / 3     # 3

Prefer $(( ))

expr is slower and more cumbersome. Use $(( )) in bash scripts.

Floating-Point Arithmetic¶

Bash only handles integers. For floating-point, use external tools.

Using bc¶

echo "5.5 + 3.2" | bc           # 8.7
echo "scale=2; 10 / 3" | bc     # 3.33
echo "scale=4; 22 / 7" | bc     # 3.1428

In scripts:

result=$(echo "scale=2; 10 / 3" | bc)
echo $result    # 3.33

bc features:

# Math functions
echo "scale=4; sqrt(2)" | bc -l     # 1.4142
echo "scale=4; s(3.14159/2)" | bc -l  # sin(pi/2) = 1.0000
echo "scale=4; c(0)" | bc -l        # cos(0) = 1.0000
echo "scale=4; l(2.71828)" | bc -l  # ln(e) = .9999

Using awk¶

awk "BEGIN {print 5.5 + 3.2}"           # 8.7
awk "BEGIN {printf \"%.2f\n\", 10/3}"   # 3.33

In scripts:

result=$(awk "BEGIN {printf \"%.2f\", 10/3}")
echo $result    # 3.33

Using Python¶

python3 -c "print(5.5 + 3.2)"           # 8.7
python3 -c "print(f'{10/3:.2f}')"       # 3.33

Number Bases¶

Specify Base¶

echo $((16#FF))       # 255 (hex)
echo $((2#1111))      # 15 (binary)
echo $((8#77))        # 63 (octal)
echo $((36#z))        # 35 (base 36)

Convert to Base¶

# Decimal to hex
printf '%x\n' 255     # ff
printf '%X\n' 255     # FF

# Decimal to octal
printf '%o\n' 64      # 100

# Binary (using bc)
echo "obase=2; 255" | bc    # 11111111

Random Numbers¶

echo $RANDOM              # 0-32767
echo $((RANDOM % 100))    # 0-99
echo $((RANDOM % 100 + 1)) # 1-100

Random in range:

# Random between min and max
min=10
max=20
echo $((RANDOM % (max - min + 1) + min))

Practical Examples¶

Sum Numbers¶

nums=(1 2 3 4 5)
sum=0
for n in "${nums[@]}"; do
    ((sum += n))
done
echo "Sum: $sum"    # 15

Average¶

nums=(10 20 30 40 50)
sum=0
for n in "${nums[@]}"; do
    ((sum += n))
done
avg=$(echo "scale=2; $sum / ${#nums[@]}" | bc)
echo "Average: $avg"    # 30.00

Factorial¶

factorial() {
    local n=$1
    local result=1
    for ((i=2; i<=n; i++)); do
        ((result *= i))
    done
    echo $result
}

factorial 5    # 120

Power of Two Check¶

is_power_of_two() {
    local n=$1
    ((n > 0 && (n & (n - 1)) == 0))
}

is_power_of_two 16 && echo "Yes"    # Yes
is_power_of_two 15 && echo "Yes"    # (nothing)

Temperature Conversion¶

# Celsius to Fahrenheit
c_to_f() {
    echo "scale=1; ($1 * 9 / 5) + 32" | bc
}

c_to_f 0     # 32.0
c_to_f 100   # 212.0

File Size Formatting¶

format_bytes() {
    local bytes=$1
    if ((bytes < 1024)); then
        echo "${bytes}B"
    elif ((bytes < 1048576)); then
        echo "$(echo "scale=1; $bytes / 1024" | bc)K"
    elif ((bytes < 1073741824)); then
        echo "$(echo "scale=1; $bytes / 1048576" | bc)M"
    else
        echo "$(echo "scale=1; $bytes / 1073741824" | bc)G"
    fi
}

format_bytes 500         # 500B
format_bytes 5000        # 4.8K
format_bytes 5000000     # 4.7M
format_bytes 5000000000  # 4.6G

Try It¶

Basic arithmetic:

a=10
b=3
echo "Sum: $((a + b))"
echo "Product: $((a * b))"
echo "Division: $((a / b))"
echo "Modulo: $((a % b))"

Compound assignment:

x=5
((x += 10))
echo $x    # 15
((x *= 2))
echo $x    # 30

Floating-point:

echo "scale=4; 22 / 7" | bc
awk "BEGIN {printf \"%.2f\n\", 355/113}"

Random number:

echo "Random 1-100: $((RANDOM % 100 + 1))"

Summary¶

Method	Use Case
`$((expr))`	Integer arithmetic, returns value
`((expr))`	Integer arithmetic, no return (for conditions)
`let`	Alternative integer arithmetic
`bc`	Floating-point, advanced math
`awk`	Floating-point, inline calculations

Key points:

$(( )) is for integer arithmetic only
Variables don't need $ inside (( ))
Use bc or awk for floating-point
(( )) returns true (0) for non-zero results
Division is integer division (truncates)