Bash Reference Manual. Node: Shell Arithmetic

PREVBash Variables UPBash Features NEXTAliases

5.8: Shell Arithmetic

The shell allows arithmetic expressions to be evaluated, as one of the shell expansions or by the let builtin.

Evaluation is done in long integers with no check for overflow, though division by 0 is trapped and flagged as an error. The following list of operators is grouped into levels of equal-precedence operators. The levels are listed in order of decreasing precedence.

- +

unary minus and plus

! ~

logical and bitwise negation



* / %

multiplication, division, remainder

+ -

addition, subtraction

<< >>

left and right bitwise shifts

<= >= < >


== !=

equality and inequality


bitwise AND


bitwise exclusive OR


bitwise OR


logical AND


logical OR

expr ? expr : expr

conditional evaluation

= *= /= %= += -= <<= >>= &= ^= |=


Shell variables are allowed as operands; parameter expansion is performed before the expression is evaluated. The value of a parameter is coerced to a long integer within an expression. A shell variable need not have its integer attribute turned on to be used in an expression.

Constants with a leading 0 are interpreted as octal numbers. A leading `0x' or `0X' denotes hexadecimal. Otherwise, numbers take the form [base#]n, where base is a decimal number between 2 and 64 representing the arithmetic base, and n is a number in that base. If base is omitted, then base 10 is used. The digits greater than 9 are represented by the lowercase letters, the uppercase letters, `_', and `@', in that order. If base is less than or equal to 36, lowercase and uppercase letters may be used interchangably to represent numbers between 10 and 35.

Operators are evaluated in order of precedence. Sub-expressions in parentheses are evaluated first and may override the precedence rules above.

PREVBash Variables UPBash Features NEXTAliases