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 the section called “Mathematical operators”.

Figure 13.4. Graph

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.agee.ageabs(a.age - e.age)
1 row

38

41

3.0

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

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

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

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

CEIL

CEIL returns the smallest integer greater than or equal to the number.

Syntax: CEIL( expression )

Arguments:

  • expression: A numeric expression.

Query 

RETURN ceil(0.1)

The ceil of 0.1

Result

ceil(0.1)
1 row

1.0

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

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

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

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

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

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

HAVERSIN

HAVERSIN returns half the 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

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

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

PI

PI returns the mathematical constant pi.

Syntax: PI()

Arguments:

Query 

RETURN pi()

The constant pi is returned.

Result

pi()
1 row

3.141592653589793

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

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

0.8536190468465595

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

3.0

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

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

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

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