Input:

Calculate Clear

Output:

Named Constants▼

Numeric Constants▼

The following operators are available for use in expressions:

When a named constant is immediately followed by a numeric constant or named function, implicit multiplication is not recognizable. For example, pi2 and esin4 are in error, whereas 2pi, pi 2, and e sin 4 are valid.

The following functions are available for use in expressions. Function names are case sensitive.

The operand of a unary function need not be parenthesized. For example, ln 2 and sin sqrt 2 are valid. When used in this manner, the function name behaves as a prefix operator. For example, sin 2π is parsed as (sin 2) × π and ln 2 ^ 4 is parsed as ln(2⁴).

Rounding▼

Roots, Exponents, and Logarithms▼

Trigonometry▼

Miscellaneous▼

The following EBNF-like notation describes the expression syntax:

expression:
    | additive-expression
    ;

additive-expression:
    | multiplicative-expression
    | additive-expression '+' multiplicative-expression
    | additive-expression '-' multiplicative-expression
    ;

multiplicative-expression:
    | prefix-expression
    | multiplicative-expression prefix-expression
    | multiplicative-expression '*' prefix-expression
    | multiplicative-expression '/' prefix-expression
    | multiplicative-expression '%' prefix-expression
    ;

prefix-expression:
    | '+' prefix-expression
    | '-' prefix-expression
    | '√' prefix-expression
    | unary-function prefix-expression
    | power-expression
    ;

    unary-function:
        | 'ceil'    | 'floor'
        | 'int'     | 'trunc'
        | 'round'
        | 'sqrt'    | 'cbrt'
        | 'exp'     | 'exp2'    | 'exp10'
        | 'ln'      | 'log'     | 'log2'    | 'log10'
        | 'sin'     | 'asin'    | 'sinh'    | 'asinh'   | 'sinc'
        | 'cos'     | 'acos'    | 'cosh'    | 'acosh'
        | 'tan'     | 'tanh'    | 'atan'    | 'atanh'
        | 'sec'     | 'asec'    | 'sech'    | 'asech'
        | 'csc'     | 'acsc'    | 'csch'    | 'acsch'
        | 'cot'     | 'acot'    | 'coth'    | 'acoth'
        | 'abs'     | 'nabs'    | 'sign'
        ;

power-expression:
    | postfix-expression
    | postfix-expression '^' prefix-expression
    ;

postfix-expression:
    | function
    | primary-expression
    | postfix-expression '!'
    ;

    function:
        | function-name '(' argument-list ')'
        ;

        function-name:
            | 'floor'   | 'ceil'
            | 'int'     | 'trunc'
            | 'round'
            | 'sqrt'    | 'cbrt'
            | 'exp'     | 'exp2'    | 'exp10'
            | 'ln'      | 'log'     | 'log2'    | 'log10'
            | 'hypot'
            | 'sin'     | 'asin'    | 'sinh'    | 'asinh'   | 'sinc'
            | 'cos'     | 'acos'    | 'cosh'    | 'acosh'
            | 'tan'     | 'tanh'    | 'atan'    | 'atanh'   | 'atan2'
            | 'sec'     | 'asec'    | 'sech'    | 'asech'
            | 'csc'     | 'acsc'    | 'csch'    | 'acsch'
            | 'cot'     | 'acot'    | 'coth'    | 'acoth'
            | 'abs'     | 'nabs'    | 'sign'
            | 'min'     | 'max'     | 'avg'
            | 'gcd'     | 'lcm'
            | 'combin'  | 'permut'  | 'hgd'
            | 'interp'
            ;

        argument-list:
            | expression
            | argument-list ',' expression
            ;

primary-expression:
    | constant
    | '(' expression ')'
    ;

    constant:
        | named-constant
        | numeric-constant
        ;

        named-constant:
            | 'e'
            | 'π' | 'pi'
            | 'τ' | 'tau'
            ;

        numeric-constant:
            | integer-part [ fraction-part ] [ exponent-part ]
            | fraction-part [ exponent-part ]
            ;

            integer-part:
                | digit { digit }
                ;

                digit:
                    | '0' | '1' | '2' | '3' | '4'
                    | '5' | '6' | '7' | '8' | '9'
                    ;

            fraction-part:
                | '.' integer-part
                ;

            exponent-part:
                | exponent-char [ exponent-sign ] integer-part
                ;

                exponent-char:
                    | 'E'
                    | 'e'
                    ;

                exponent-sign:
                    | '+'
                    | '-'
                    ;