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## 13.4. Mathematical functions

These functions all operate on numerical expressions only, and will return an error if used on any other values.

See also Section 8.4.1, “Mathematical operators”.

Figure 13.4. Graph

### 13.4.1. ABS

`ABS` returns the absolute value of a number.

Syntax: `ABS( expression )`

Arguments:

- expression: A numeric expression.

Query.

    MATCH (a),(e)
    WHERE a.name = 'Alice' AND e.name = 'Eskil'
    RETURN a.age, e.age, abs(a.age - e.age)

The absolute value of the age difference is returned.

Result

a.age | e.age | abs(a.age - e.age)
--- | --- | ---
1 row
`38` | `41` | `3.0`

### 13.4.2. ACOS

`ACOS` returns the arccosine of the expression, in radians.

Syntax: `ACOS( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN acos(0.5)

The arccosine of 0.5.

Result

acos(0.5)
1 row
`1.0471975511965979`

### 13.4.3. ASIN

`ASIN` returns the arcsine of the expression, in radians.

Syntax: `ASIN( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN asin(0.5)

The arcsine of 0.5.

Result

asin(0.5)
1 row
`0.5235987755982989`

### 13.4.4. ATAN

`ATAN` returns the arctangent of the expression, in radians.

Syntax: `ATAN( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN atan(0.5)

The arctangent of 0.5.

Result

atan(0.5)
1 row
`0.4636476090008061`

### 13.4.5. ATAN2

`ATAN2` returns the arctangent2 of a set of coordinates, in radians.

Syntax: `ATAN2( expression , expression)`

Arguments:

- expression: A numeric expression for y.
- expression: A numeric expression for x.

Query.

    RETURN atan2(0.5, 0.6)

The arctangent2 of 0.5, 0.6.

Result

atan2(0.5, 0.6)
1 row
`0.6947382761967033`

### 13.4.6. COS

`COS` returns the cosine of the expression.

Syntax: `COS( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN cos(0.5)

The cosine of 0.5 is returned.

Result

cos(0.5)
1 row
`0.8775825618903728`

### 13.4.7. COT

`COT` returns the cotangent of the expression.

Syntax: `COT( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN cot(0.5)

The cotangent of 0.5 is returned.

Result

cot(0.5)
1 row
`1.830487721712452`

### 13.4.8. DEGREES

`DEGREES` converts radians to degrees.

Syntax: `DEGREES( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN degrees(3.14159)

The number of degrees in something close to pi.

Result

degrees(3.14159)
1 row
`179.99984796050427`

### 13.4.9. E

`E` returns the constant, e.

Syntax: `E()`

Arguments:

Query.

    RETURN e()

The constant e is returned (the base of natural log).

Result

e()
1 row
`2.718281828459045`

### 13.4.10. EXP

`EXP` returns the value e raised to the power of the expression.

Syntax: `EXP( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN exp(2)

The exp of 2 is returned: e2.

Result

exp(2)
1 row
`7.38905609893065`

### 13.4.11. FLOOR

`FLOOR` returns the greatest integer less than or equal to the expression.

Syntax: `FLOOR( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN floor(0.9)

The floor of 0.9 is returned.

Result

floor(0.9)
1 row
`0.0`

### 13.4.12. HAVERSIN

`HAVERSIN` returns the half versine of the expression.

Syntax: `HAVERSIN( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN haversin(0.5)

The haversine of 0.5 is returned.

Result

haversin(0.5)
1 row
`0.06120871905481362`

#### Spherical distance using the haversin function

The `haversin` function may be used to compute the distance on the surface of a sphere between two points (each given by their latitude and longitude). In this example the spherical distance (in km) between Berlin in Germany (at lat 52.5, lon 13.4) and San Mateo in California (at lat 37.5, lon -122.3) is calculated using an average earth radius of 6371 km.

Query.

    CREATE (ber:City { lat: 52.5, lon: 13.4 }),(sm:City { lat: 37.5, lon: -122.3 })
    RETURN 2 * 6371 * asin(sqrt(haversin(radians(sm.lat - ber.lat))+ cos(radians(sm.lat))*
      cos(radians(ber.lat))* haversin(radians(sm.lon - ber.lon)))) AS dist

The distance between Berlin and San Mateo is returned (about 9129 km).

Result

dist
1 row
Nodes created: 2
Properties set: 4
Labels added: 2
`9129.969740051658`

### 13.4.13. LOG

`LOG` returns the natural logarithm of the expression.

Syntax: `LOG( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN log(27)

The log of 27 is returned.

Result

log(27)
1 row
`3.295836866004329`

### 13.4.14. LOG10

`LOG10` returns the base 10 logarithm of the expression.

Syntax: `LOG10( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN log10(27)

The log10 of 27 is returned.

Result

log10(27)
1 row
`1.4313637641589874`

### 13.4.15. PI

`PI` returns the mathmatical constant pi.

Syntax: `PI()`

Arguments:

Query.

    RETURN pi()

The constant pi is returned.

Result

pi()
1 row
`3.141592653589793`

### 13.4.16. RADIANS

`RADIANS` converts degrees to radians.

Syntax: `RADIANS( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN radians(180)

The number of radians in 180 is returned (pi).

Result

radians(180)
1 row
`3.141592653589793`

### 13.4.17. RAND

`RAND` returns a random double between 0 and 1.0.

Syntax: `RAND( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN rand() AS x1

A random number is returned.

Result

x1
1 row
`0.2649907229190529`

### 13.4.18. ROUND

`ROUND` returns the numerical expression, rounded to the nearest integer.

Syntax: `ROUND( expression )`

Arguments:

- expression: A numerical expression.

Query.

    RETURN round(3.141592)

Result

round(3.141592)
1 row
`3`

### 13.4.19. SIGN

`SIGN` returns the signum of a number — zero if the expression is zero, `-1` for any negative number, and `1` for any positive number.

Syntax: `SIGN( expression )`

Arguments:

- expression: A numerical expression

Query.

    RETURN sign(-17), sign(0.1)

Result

sign(-17) | sign(0.1)
--- | ---
1 row
`-1.0` | `1.0`

### 13.4.20. SIN

`SIN` returns the sine of the expression.

Syntax: `SIN( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN sin(0.5)

The sine of 0.5 is returned.

Result

sin(0.5)
1 row
`0.479425538604203`

### 13.4.21. SQRT

`SQRT` returns the square root of a number.

Syntax: `SQRT( expression )`

Arguments:

- expression: A numerical expression

Query.

    RETURN sqrt(256)

Result

sqrt(256)
1 row
`16.0`

### 13.4.22. TAN

`TAN` returns the tangent of the expression.

Syntax: `TAN( expression )`

Arguments:

- expression: A numeric expression.

Query.

    RETURN tan(0.5)

The tangent of 0.5 is returned.

Result

tan(0.5)
1 row
`0.5463024898437905`

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