bash-hackers-wiki/docs/syntax/expansion/arith.md

# Arithmetic expansion

    $(( <EXPRESSION> ))

    $[ <EXPRESSION> ]

The [arithmetic expression](../../syntax/arith_expr.md) `<EXPRESSION>` is
evaluated and expands to the result. The output of the arithmetic
expansion is guaranteed to be one word and a digit in Bash.

Please **do not use the second form `$[ ... ]`**! It's deprecated. The
preferred and standardized form is `$(( ... ))`!

Example

``` bash
function printSum {
    typeset -A args
    typeset name
    for name in first second; do
        [[ -t 0 ]] && printf 'Enter %s positive integer: ' "$name" >&2
        read -r ${BASH_VERSION+-e} "args[$name]"
        [[ ${args[$name]} == +([[:digit:]]) ]] || return 1 # Validation is extremely important whenever user input is used in arithmetic.
    done
    printf 'The sum is %d.' $((${args[first]} + ${args[second]}))
}
```

**Note** that in Bash you don't need the arithmetic expansion to check
for the boolean value of an arithmetic expression. This can be done
using the [arithmetic evaluation compound
command](../../syntax/ccmd/arithmetic_eval.md):

``` bash
printf %s 'Enter a number: ' >&2
read -r number
if ((number == 1234)); then
    echo 'Good guess'
else
    echo 'Haha... :-P'
fi
```

**Variables** used inside the arithmetic expansion, as in all arithmetic
contexts, can be used with or without variable expansion:

``` bash
x=1

echo $((x))       # Good.
echo $(($x))      # Ok. Avoid expansions within arithmetic. Use variables directly.
echo $(("$x"))    # Error. There is no quote-removal in arithmetic contexts. It expands to $(("1")), which is an invalid arithmetic expression.
echo $((x[0]))    # Good.
echo $((${x[0]})) # Ok. Nested expansion again.
echo $((${x[$((${x[!$x]}-$x))]})) # Same as above but more ridiculous.
echo $(($x[0]))   # Error. This expands to $((1[0])), an invalid expression.
```

## Bugs and Portability considerations

-   The original Bourne shell doesn't have arithmetic expansions. You
    have to use something like `expr(1)` within backticks instead. Since
    `expr` is horrible (as are backticks), and arithmetic expansion is
    required by POSIX, you should not worry about this, and preferably
    fix any code you find that's still using `expr`.

## See also

-   [arithmetic expressions](../../syntax/arith_expr.md)
-   [arithmetic evaluation compound
    command](../../syntax/ccmd/arithmetic_eval.md)
-   [Introduction to expansion and
    substitution](../../syntax/expansion/intro.md)
-   [POSIX
    definition](http://pubs.opengroup.org/onlinepubs/9699919799/utilities/V3_chap02.html#tag_18_06_04)