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[comment]: # (terms: abs, acos, asin, atan, atan2, avg, cbrt, ceil, cos, cosh, cot, degrees, e, exp, expm1, floor, log, log10, max, min, mod, pi, power, radians, rand, round, signum, sin, sinh, sqrt, sum, tan, truncate )

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# 6 Mathematical functions

All functions listed here are supported in:

-   [Trigger expressions](/manual/config/triggers/expression)
-   [Calculated items](/manual/config/items/itemtypes/calculated)
-   [Expression macros](/manual/config/macros/expression_macros)

Mathematical functions are supported with float and integer value types,
unless stated otherwise.

The functions are listed without additional information. Click the function to see the full details.

|Function|Description|
|--|--------|
|[abs](#abs)|The absolute value of a value.|
|[acos](#acos)|The arccosine of a value as an angle, expressed in radians.|
|[asin](#asin)|The arcsine of a value as an angle, expressed in radians.|
|[atan](#atan)|The arctangent of a value as an angle, expressed in radians.|
|[atan2](#atan2)|The arctangent of the ordinate (value) and abscissa coordinates specified as an angle, expressed in radians.|
|[avg](#avg)|The average value of the referenced item values.|
|[cbrt](#cbrt)|The cube root of a value.|
|[ceil](#ceil)|Round the value up to the nearest greater or equal integer.|
|[cos](#cos)|The cosine of a value, where the value is an angle expressed in radians.|
|[cosh](#cosh)|The hyperbolic cosine of a value.|
|[cot](#cot)|The cotangent of a value, where the value is an angle expressed in radians.|
|[degrees](#degrees)|Converts a value from radians to degrees.|
|[e](#e)|The Euler's number (2.718281828459045).|
|[exp](#exp)|The Euler's number at a power of a value.|
|[expm1](#expm1)|The Euler's number at a power of a value minus 1.|
|[floor](#floor)|Round the value down to the nearest smaller or equal integer.|
|[log](#log)|The natural logarithm.|
|[log10](#log10)|The decimal logarithm.|
|[max](#max)|The highest value of the referenced item values.|
|[min](#min)|The lowest value of the referenced item values.|
|[mod](#mod)|The division remainder.|
|[pi](#pi)|The Pi constant (3.14159265358979).|
|[power](#power)|The power of a value.|
|[radians](#radians)|Converts a value from degrees to radians.|
|[rand](#rand)|Return a random integer value.|
|[round](#round)|Round the value to decimal places.|
|[signum](#signum)|Returns '-1' if a value is negative, '0' if a value is zero, '1' if a value is positive.|
|[sin](#sin)|The sine of a value, where the value is an angle expressed in radians.|
|[sinh](#sinh)|The hyperbolical sine of a value, where the value is an angle expressed in radians.|
|[sqrt](#sqrt)|The square root of a value.|
|[sum](#sum)|The sum of the referenced item values.| 
|[tan](#tan)|The tangent of a value.|
|[truncate](#truncate)|Truncate the value to decimal places.|

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### Function details

Some general notes on function parameters:

-   Function parameters are separated by a comma
-   Expressions are accepted as parameters
-   Optional function parameters (or parameter parts) are indicated by
    `<` `>`

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##### abs(value) {#abs}

The absolute value (from 0) of a value.

Parameter: 

-   **value** - the value to check

For example, the absolute value of either '3' or '-3' will be '3'.

Example:

    abs(last(/host/key))>10

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##### acos(value) {#acos}

The arccosine of a value as an angle, expressed in radians.

Parameter: 

-   **value** - the value to check

The value must be between -1 and 1. For example, the arccosine of a value '0.5' will be '2.0943951'.

Example:

    acos(last(/host/key))

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##### asin(value) {#asin}

The arcsine of a value as an angle, expressed in radians.

Parameter: 

-   **value** - the value to check

The value must be between -1 and 1. For example, the arcsine of a value '0.5' will be '-0.523598776'.

Example:

    asin(last(/host/key)) 

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##### atan(value) {#atan}

The arctangent of a value as an angle, expressed in radians.

Parameter: 

-   **value** - the value to check

For example, the arctangent of a value '1' will be '0.785398163'.

Example:

    atan(last(/host/key))

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##### atan2(value,abscissa) {#atan2}

The arctangent of the ordinate (value) and abscissa coordinates specified as an angle, expressed in radians.

Parameters: 

-   **value** - the value to check;
-   **abscissa** - the abscissa value.

For example, the arctangent of the ordinate and abscissa coordinates of a value '1' will be '2.21429744'.

Example:

    atan2(last(/host/key),2)

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##### avg(<value1>,<value2>,...) {#avg}

The average value of the referenced item values.

Parameter: 

-   **valueX** - the value returned by another function that is working with item history.

Example:

    avg(avg(/host/key,1h),avg(/host2/key2,1h))

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##### cbrt(value) {#cbrt}

The cube root of a value.

Parameter: 

-   **value** - the value to check

For example, the cube root of '64' will be '4', of '63' will be '3.97905721'.

Example:

    cbrt(last(/host/key))

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##### ceil(value) {#ceil}

Round the value up to the nearest greater or equal integer.

Parameter: 

-   **value** - the value to check

For example, '2.4' will be rounded up to '3'. See also [floor()](#floor).

Example:

    ceil(last(/host/key))

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##### cos(value) {#cos}

The cosine of a value, where the value is an angle expressed in radians.

Parameter: 

-   **value** - the value to check

For example, the cosine of a value '1' will be '0.54030230586'.

Example:

    cos(last(/host/key))

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##### cosh(value) {#cosh}

The hyperbolic cosine of a value.
Returns the value as a real number, not as scientific notation.

Parameter: 

-   **value** - the value to check

For example, the hyperbolic cosine of a value '1' will be '1.54308063482'.

Example:

    cosh(last(/host/key))

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##### cot(value) {#cot}

The cotangent of a value, where the value is an angle expressed in radians.

Parameter: 

-   **value** - the value to check

For example, the cotangent of a value '1' will be '0.54030230586'.

Example:

    cot(last(/host/key))

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##### degrees(value) {#degrees}

Converts a value from radians to degrees.

Parameter: 

-   **value** - the value to check

For example, a value '1' converted to degrees will be '57.2957795'.

Example:

    degrees(last(/host/key))

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##### e {#e}

The Euler's number (2.718281828459045).

Example:

    e()

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##### exp(value) {#exp}

The Euler's number at a power of a value.

Parameter: 

-   **value** - the value to check

For example, Euler's number at a power of a value '2' will be '7.38905609893065'.

Example:

    exp(last(/host/key))

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##### expm1(value) {#expm1}

The Euler's number at a power of a value minus 1.

Parameter: 

-   **value** - the value to check

For example, Euler's number at a power of a value '2' minus 1 will be '6.38905609893065'.

Example:

    expm1(last(/host/key))

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##### floor(value) {#floor}

Round the value down to the nearest smaller or equal integer.

Parameter: 

-   **value** - the value to check

For example, '2.6' will be rounded down to '2'. See also [ceil()](#ceil).

Example:

    floor(last(/host/key))

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##### log(value) {#log}

The natural logarithm.

Parameter: 

-   **value** - the value to check

For example, the natural logarithm of a value '2' will be '0.69314718055994529'.

Example:

    log(last(/host/key))

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##### log10(value) {#log10}

The decimal logarithm.

Parameter: 

-   **value** - the value to check

For example, the decimal logarithm of a value '5' will be '0.69897000433'.

Example:

    log10(last(/host/key))

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##### max(<value1>,<value2>,...) {#max}

The highest value of the referenced item values.

Parameter: 

-   **valueX** - the value returned by another function that is working with item history.

Example:

    max(avg(/host/key,1h),avg(/host2/key2,1h))

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##### min(<value1>,<value2>,...) {#min}

The lowest value of the referenced item values.

Parameter: 

-   **valueX** - the value returned by another function that is working with item history.

Example:

    min(avg(/host/key,1h),avg(/host2/key2,1h))

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##### mod(value,denominator) {#mod}

The division remainder.

Parameters: 

-   **value** - the value to check;
-   **denominator** - the division denominator.

For example, division remainder of a value '5' with division denominator '2' will be '1'.

Example:

    mod(last(/host/key),2)

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##### pi {#pi}

The Pi constant (3.14159265358979).

Example:

    pi()

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##### power(value,power value) {#power}

The power of a value.

Parameters: 

-   **value** - the value to check;
-   **power value** - the Nth power to use.

For example, the 3rd power of a value '2' will be '8'.

Example:

    power(last(/host/key),3)

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##### radians(value) {#radians}

Converts a value from degrees to radians.

Parameter: 

-   **value** - the value to check

For example, a value '1' converted to radians will be '0.0174532925'.

Example:

    radians(last(/host/key))

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##### rand {#rand}

Return a random integer value. A pseudo-random generated number using time as seed (enough for mathematical purposes, but not cryptography).

Example:

    rand()

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##### round(value,decimal places) {#round}

Round the value to decimal places.

Parameters: 

-   **value** - the value to check;
-   **decimal places** - specify decimal places for rounding (0 is also possible).

For example, a value '2.5482' rounded to 2 decimal places will be '2.55'.

Example:

    round(last(/host/key),2)

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##### signum(value) {#signum}

Returns '-1' if a value is negative, '0' if a value is zero, '1' if a value is positive.

Parameter: 

-   **value** - the value to check.

Example:

    signum(last(/host/key))

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##### sin(value) {#sin}

The sine of a value, where the value is an angle expressed in radians.

Parameter: 

-   **value** - the value to check

For example, the sine of a value '1' will be '0.8414709848'.

Example:

    sin(last(/host/key))

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##### sinh(value) {#sinh}

The hyperbolical sine of a value.

Parameter: 

-   **value** - the value to check

For example, the hyperbolical sine of a value '1' will be '1.17520119364'.

Example:

    sinh(last(/host/key))

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##### sqrt(value) {#sqrt}

The square root of a value.<br>
This function will fail with a negative value.

Parameter: 

-   **value** - the value to check

For example, the square root of a value '3.5' will be '1.87082869339'.

Example:

    sqrt(last(/host/key))

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##### sum(<value1>,<value2>,...) {#sum}

The sum of the referenced item values.

Parameter: 

-   **valueX** - the value returned by another function that is working with item history.

Example:

    sum(avg(/host/key,1h),avg(/host2/key2,1h))

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##### tan(value) {#tan}

The tangent of a value.

Parameter: 

-   **value** - the value to check

For example, the tangent of a value '1' will be '1.55740772465'.

Example:

    tan(last(/host/key))

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##### truncate(value,decimal places) {#truncate}

Truncate the value to decimal places.

Parameters: 

-   **value** - the value to check;
-   **decimal places** - specify decimal places for truncating (0 is also possible).

For example, a value '2.5482' truncated to 2 decimal places will be '2.54'.

Example:

    truncate(last(/host/key),2)

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See [all supported functions](/manual/appendix/functions).  

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