## Chapter 13. Arithmetic Expansion

Arithmetic expansion provides a
powerful tool for performing (integer) arithmetic
operations in scripts. Translating a string into a
numerical expression is relatively straightforward using
*backticks*, *double
parentheses*, or *let*.

**Variations**

- Arithmetic expansion with backticks (often used in
conjunction with expr)
z=`expr $z + 3` # The 'expr' command performs the expansion.

- Arithmetic expansion with double
parentheses, and using let
The use of *backticks*
(*backquotes*) in arithmetic
expansion has been superseded by *double
parentheses* --
`((...))`

and
`$((...))`

-- and also by the very
convenient let construction.

z=$(($z+3))
z=$((z+3)) # Also correct.
# Within double parentheses,
#+ parameter dereferencing
#+ is optional.
# $((EXPRESSION)) is arithmetic expansion. # Not to be confused with
#+ command substitution.
# You may also use operations within double parentheses without assignment.
n=0
echo "n = $n" # n = 0
(( n += 1 )) # Increment.
# (( $n += 1 )) is incorrect!
echo "n = $n" # n = 1
let z=z+3
let "z += 3" # Quotes permit the use of spaces in variable assignment.
# The 'let' operator actually performs arithmetic evaluation,
#+ rather than expansion.

Examples of arithmetic expansion in scripts: