Advanced Bash−Scripting Guide

Chapter 15. Arithmetic Expansion
Arithmetic expansion provides a powerful tool for performing 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The use of backticks in arithmetic expansion has been superseded by double parentheses $((...))
or the very convenient let construction.
z=$(($z+3))
# $((EXPRESSION)) is arithmetic expansion. # Not to be confused with
#+ command substitution.
let z=z+3
let "z += 3" # Quotes permit the use of spaces and special operators.
# The 'let' operator actually performs arithmetic evaluation,
#+ rather than expansion.
All the above are equivalent. You may use whichever one "rings your chimes".
Examples of arithmetic expansion in scripts:
1. Example 12−6
2. Example 10−14
3. Example 26−1
4. Example 26−6
5. Example A−18
Chapter 15. Arithmetic Expansion 241