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---
mapped_pages:
- https://www.elastic.co/guide/en/elasticsearch/reference/current/sql-functions-math.html
---
# Mathematical functions [sql-functions-math]
All math and trigonometric functions require their input (where applicable) to be numeric.
## Generic [sql-functions-math-generic]
## `ABS` [sql-functions-math-abs]
```sql
ABS(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: numeric
**Description**: Returns the [absolute value](https://en.wikipedia.org/wiki/Absolute_value) of `numeric_exp`. The return type is the same as the input type.
```sql
SELECT ABS(-123.5), ABS(55);
ABS(-123.5) | ABS(55)
---------------+---------------
123.5 |55
```
## `CBRT` [sql-functions-math-cbrt]
```sql
CBRT(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [cube root](https://en.wikipedia.org/wiki/Cube_root) of `numeric_exp`.
```sql
SELECT CBRT(-125.5);
CBRT(-125.5)
-------------------
-5.0066577974783435
```
## `CEIL/CEILING` [sql-functions-math-ceil]
```sql
CEIL(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: integer or long numeric value
**Description**: Returns the smallest integer greater than or equal to `numeric_exp`.
```sql
SELECT CEIL(125.01), CEILING(-125.99);
CEIL(125.01) |CEILING(-125.99)
---------------+----------------
126 |-125
```
## `E` [sql-functions-math-e]
```sql
E()
```
**Input**: *none*
**Output**: `2.718281828459045`
**Description**: Returns [Euler’s number](https://en.wikipedia.org/wiki/E_%28mathematical_constant%29).
```sql
SELECT E(), CEIL(E());
E() | CEIL(E())
-----------------+---------------
2.718281828459045|3
```
## `EXP` [sql-functions-math-exp]
```sql
EXP(numeric_exp) <1>
```
**Input**:
1. float numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns [Euler’s number at the power](https://en.wikipedia.org/wiki/Exponential_function) of `numeric_exp` enumeric_exp.
```sql
SELECT EXP(1), E(), EXP(2), E() * E();
EXP(1) | E() | EXP(2) | E() * E()
-----------------+-----------------+----------------+------------------
2.718281828459045|2.718281828459045|7.38905609893065|7.3890560989306495
```
## `EXPM1` [sql-functions-math-expm1]
```sql
EXPM1(numeric_exp) <1>
```
**Input**:
1. float numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns [Euler’s number at the power](https://en.wikipedia.org/wiki/Exponential_function) of `numeric_exp` minus 1 (enumeric_exp - 1).
```sql
SELECT E(), EXP(2), EXPM1(2);
E() | EXP(2) | EXPM1(2)
-----------------+----------------+----------------
2.718281828459045|7.38905609893065|6.38905609893065
```
## `FLOOR` [sql-functions-math-floor]
```sql
FLOOR(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: integer or long numeric value
**Description**: Returns the largest integer less than or equal to `numeric_exp`.
```sql
SELECT FLOOR(125.01), FLOOR(-125.99);
FLOOR(125.01) |FLOOR(-125.99)
---------------+---------------
125 |-126
```
## `LOG` [sql-functions-math-log]
```sql
LOG(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [natural logarithm](https://en.wikipedia.org/wiki/Natural_logarithm) of `numeric_exp`.
```sql
SELECT EXP(3), LOG(20.085536923187668);
EXP(3) |LOG(20.085536923187668)
------------------+-----------------------
20.085536923187668|3.0
```
## `LOG10` [sql-functions-math-log10]
```sql
LOG10(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [base 10 logarithm](https://en.wikipedia.org/wiki/Common_logarithm) of `numeric_exp`.
```sql
SELECT LOG10(5), LOG(5)/LOG(10);
LOG10(5) | LOG(5)/LOG(10)
------------------+-----------------------
0.6989700043360189|0.6989700043360187
```
## `PI` [sql-functions-math-pi]
```sql
PI()
```
**Input**: *none*
**Output**: `3.141592653589793`
**Description**: Returns [PI number](https://en.wikipedia.org/wiki/Pi).
```sql
SELECT PI();
PI()
-----------------
3.141592653589793
```
## `POWER` [sql-functions-math-power]
```sql
POWER(
numeric_exp, <1>
integer_exp) <2>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
2. integer expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the value of `numeric_exp` to the power of `integer_exp`.
```sql
SELECT POWER(3, 2), POWER(3, 3);
POWER(3, 2) | POWER(3, 3)
---------------+---------------
9.0 |27.0
```
```sql
SELECT POWER(5, -1), POWER(5, -2);
POWER(5, -1) | POWER(5, -2)
---------------+---------------
0.2 |0.04
```
## `RANDOM/RAND` [sql-functions-math-random]
```sql
RANDOM(seed) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns a random double using the given seed.
```sql
SELECT RANDOM(123);
RANDOM(123)
------------------
0.7231742029971469
```
## `ROUND` [sql-functions-math-round]
```sql
ROUND(
numeric_exp <1>
[, integer_exp]) <2>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
2. integer expression; optional. If `null`, the function returns `null`.
**Output**: numeric
**Description**: Returns `numeric_exp` rounded to `integer_exp` places right of the decimal point. If `integer_exp` is negative, `numeric_exp` is rounded to |`integer_exp`| places to the left of the decimal point. If `integer_exp` is omitted, the function will perform as if `integer_exp` would be 0. The returned numeric data type is the same as the data type of `numeric_exp`.
```sql
SELECT ROUND(-345.153, 1) AS rounded;
rounded
---------------
-345.2
```
```sql
SELECT ROUND(-345.153, -1) AS rounded;
rounded
---------------
-350.0
```
## `SIGN/SIGNUM` [sql-functions-math-sign]
```sql
SIGN(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: [-1, 0, 1]
**Description**: Returns an indicator of the sign of `numeric_exp`. If `numeric_exp` is less than zero, –1 is returned. If `numeric_exp` equals zero, 0 is returned. If `numeric_exp` is greater than zero, 1 is returned.
```sql
SELECT SIGN(-123), SIGN(0), SIGN(415);
SIGN(-123) | SIGN(0) | SIGN(415)
---------------+---------------+---------------
-1 |0 |1
```
## `SQRT` [sql-functions-math-sqrt]
```sql
SQRT(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns [square root](https://en.wikipedia.org/wiki/Square_root) of `numeric_exp`.
```sql
SELECT SQRT(EXP(2)), E(), SQRT(25);
SQRT(EXP(2)) | E() | SQRT(25)
-----------------+-----------------+---------------
2.718281828459045|2.718281828459045|5.0
```
## `TRUNCATE/TRUNC` [sql-functions-math-truncate]
```sql
TRUNCATE(
numeric_exp <1>
[, integer_exp]) <2>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
2. integer expression; optional. If `null`, the function returns `null`.
**Output**: numeric
**Description**: Returns `numeric_exp` truncated to `integer_exp` places right of the decimal point. If `integer_exp` is negative, `numeric_exp` is truncated to |`integer_exp`| places to the left of the decimal point. If `integer_exp` is omitted, the function will perform as if `integer_exp` would be 0. The returned numeric data type is the same as the data type of `numeric_exp`.
```sql
SELECT TRUNC(-345.153, 1) AS trimmed;
trimmed
---------------
-345.1
```
```sql
SELECT TRUNCATE(-345.153, -1) AS trimmed;
trimmed
---------------
-340.0
```
## Trigonometric [sql-functions-math-trigonometric]
## `ACOS` [sql-functions-math-acos]
```sql
ACOS(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [arccosine](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) of `numeric_exp` as an angle, expressed in radians.
```sql
SELECT ACOS(COS(PI())), PI();
ACOS(COS(PI())) | PI()
-----------------+-----------------
3.141592653589793|3.141592653589793
```
## `ASIN` [sql-functions-math-asin]
```sql
ASIN(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [arcsine](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) of `numeric_exp` as an angle, expressed in radians.
```sql
SELECT ROUND(DEGREES(ASIN(0.7071067811865475))) AS "ASIN(0.707)", ROUND(SIN(RADIANS(45)), 3) AS "SIN(45)";
ASIN(0.707) | SIN(45)
---------------+---------------
45.0 |0.707
```
## `ATAN` [sql-functions-math-atan]
```sql
ATAN(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [arctangent](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) of `numeric_exp` as an angle, expressed in radians.
```sql
SELECT DEGREES(ATAN(TAN(RADIANS(90))));
DEGREES(ATAN(TAN(RADIANS(90))))
-------------------------------
90.0
```
## `ATAN2` [sql-functions-math-atan2]
```sql
ATAN2(
ordinate, <1>
abscisa) <2>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
2. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [arctangent of the `ordinate` and `abscisa` coordinates](https://en.wikipedia.org/wiki/Atan2) specified as an angle, expressed in radians.
```sql
SELECT ATAN2(5 * SIN(RADIANS(45)), 5 * COS(RADIANS(45))) AS "ATAN2(5*SIN(45), 5*COS(45))", RADIANS(45);
ATAN2(5*SIN(45), 5*COS(45))| RADIANS(45)
---------------------------+------------------
0.7853981633974483 |0.7853981633974483
```
## `COS` [sql-functions-math-cos]
```sql
COS(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [cosine](https://en.wikipedia.org/wiki/Trigonometric_functions#cosine) of `numeric_exp`, where `numeric_exp` is an angle expressed in radians.
```sql
SELECT COS(RADIANS(180)), POWER(SIN(RADIANS(54)), 2) + POWER(COS(RADIANS(54)), 2) AS pythagorean_identity;
COS(RADIANS(180))|pythagorean_identity
-----------------+--------------------
-1.0 |1.0
```
## `COSH` [sql-functions-math-cosh]
```sql
COSH(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [hyperbolic cosine](https://en.wikipedia.org/wiki/Hyperbolic_function) of `numeric_exp`.
```sql
SELECT COSH(5), (POWER(E(), 5) + POWER(E(), -5)) / 2 AS "(e^5 + e^-5)/2";
COSH(5) | (e^5 + e^-5)/2
-----------------+-----------------
74.20994852478785|74.20994852478783
```
## `COT` [sql-functions-math-cot]
```sql
COT(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [cotangent](https://en.wikipedia.org/wiki/Trigonometric_functions#Cosecant,_secant,_and_cotangent) of `numeric_exp`, where `numeric_exp` is an angle expressed in radians.
```sql
SELECT COT(RADIANS(30)) AS "COT(30)", COS(RADIANS(30)) / SIN(RADIANS(30)) AS "COS(30)/SIN(30)";
COT(30) | COS(30)/SIN(30)
------------------+------------------
1.7320508075688774|1.7320508075688776
```
## `DEGREES` [sql-functions-math-degrees]
```sql
DEGREES(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Convert from [radians](https://en.wikipedia.org/wiki/Radian) to [degrees](https://en.wikipedia.org/wiki/Degree_(angle)).
```sql
SELECT DEGREES(PI() * 2), DEGREES(PI());
DEGREES(PI() * 2)| DEGREES(PI())
-----------------+---------------
360.0 |180.0
```
## `RADIANS` [sql-functions-math-radians]
```sql
RADIANS(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Convert from [degrees](https://en.wikipedia.org/wiki/Degree_(angle)) to [radians](https://en.wikipedia.org/wiki/Radian).
```sql
SELECT RADIANS(90), PI()/2;
RADIANS(90) | PI()/2
------------------+------------------
1.5707963267948966|1.5707963267948966
```
## `SIN` [sql-functions-math-sin]
```sql
SIN(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [sine](https://en.wikipedia.org/wiki/Trigonometric_functions#sine) of `numeric_exp`, where `numeric_exp` is an angle expressed in radians.
```sql
SELECT SIN(RADIANS(90)), POWER(SIN(RADIANS(67)), 2) + POWER(COS(RADIANS(67)), 2) AS pythagorean_identity;
SIN(RADIANS(90))|pythagorean_identity
----------------+--------------------
1.0 |1.0
```
## `SINH` [sql-functions-math-sinh]
```sql
SINH(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [hyperbolic sine](https://en.wikipedia.org/wiki/Hyperbolic_function) of `numeric_exp`.
```sql
SELECT SINH(5), (POWER(E(), 5) - POWER(E(), -5)) / 2 AS "(e^5 - e^-5)/2";
SINH(5) | (e^5 - e^-5)/2
-----------------+-----------------
74.20321057778875|74.20321057778874
```
## `TAN` [sql-functions-math-tan]
```sql
TAN(numeric_exp) <1>
```
**Input**:
1. numeric expression. If `null`, the function returns `null`.
**Output**: double numeric value
**Description**: Returns the [tangent](https://en.wikipedia.org/wiki/Trigonometric_functions#tangent) of `numeric_exp`, where `numeric_exp` is an angle expressed in radians.
```sql
SELECT TAN(RADIANS(66)) AS "TAN(66)", SIN(RADIANS(66))/COS(RADIANS(66)) AS "SIN(66)/COS(66)=TAN(66)";
TAN(66) |SIN(66)/COS(66)=TAN(66)
------------------+-----------------------
2.2460367739042164|2.246036773904216
```
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