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 operators and their precedence
and associativity are the same as in the C language.

The following list of operators is grouped into levels of equal-precedence operators.
The levels are listed in order of decreasing precedence.

* Multiplication / Division % Remainder + Addition - Subtraction << Left bitwise shift >> Right bitwise shift ++id --id Variable pre-increment and pre-decrement Increment the value of a variablebeforeusing it in an expression. id++ id-- Variable post-increment and post-decrement. Increment the value of variable after executing the expression completely. In Post-Increment, the value is first used in the expression and then incremented. - + Unary minus and plus ! ~ Logical and bitwise negation ** Exponentiation <= >= < > comparison == != Equality and Inequality & Bitwise AND ^ Bitwise exclusive OR | Bitwise OR && Logical AND || Logical OR expr ? expr : expr Conditional evaluation = *= /= %= += -= <<= >>= &= ^= |= Assignment expr1 , expr2 Comma

Shell variables are allowed as operands; parameter expansion is performed before the expression is evaluated. Within an expression, shell variables can also be referenced by name without using the parameter expansion syntax. The value of a variable is evaluated as an arithmetic expression when it is referenced. 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 can 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 can override the precedence rules above.

**Related linux commands:**

Bash Syntax

NIST Digital Library of Mathematical Functions

Windows equivalent command: SET /A - Display, set, or remove Windows environment variables