math

Properties

e

Type: const float

The mathematical constant e (Euler's number), approximately 2.71828.

The base of natural logarithms and the limit of (1 + 1/n)^n as n approaches infinity.

phi

Type: const float

The golden ratio φ (phi), approximately 1.61803.

Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity. Common in natural patterns and technical analysis (Fibonacci retracements).

pi

Type: const float

The mathematical constant π (pi), approximately 3.14159.

Represents the ratio of a circle's circumference to its diameter.

rphi

Type: const float

The reciprocal of the golden ratio (1/φ), approximately 0.61803.

Equal to φ - 1. Used in Fibonacci analysis where 61.8% is a key retracement level.

Functions

abs

Returns the absolute value of n.

For positive numbers, returns n unchanged. For negative numbers, returns -n. For zero, returns zero.

Parameters

Name	Type	Default	Description
`n`	`int`		The integer value.

Returns: int

Name	Type	Default	Description
`n`	`float`		The float value.

acos

pine

math.acos(float value) → float

Returns the arccosine (inverse cosine) of value in degrees.

Given a cosine value, returns the angle that produces it.

Parameters

Name	Type	Default	Description
`value`	`float`		The cosine value (must be between -1 and 1).

Returns: float — An angle in degrees in the range [0, 180].

asin

pine

math.asin(float value) → float

Returns the arcsine (inverse sine) of value in degrees.

Given a sine value, returns the angle that produces it.

Parameters

Name	Type	Default	Description
`value`	`float`		The sine value (must be between -1 and 1).

Returns: float — An angle in degrees in the range [-90, 90].

atan

pine

math.atan(float value) → float

Returns the arctangent (inverse tangent) of value in degrees.

Given a tangent value, returns the angle that produces it.

Parameters

Name	Type	Default	Description
`value`	`float`		The tangent value (any real number).

Returns: float — An angle in degrees in the range (-90, 90).

avg

Returns the average (arithmetic mean) of all provided arguments.

Accepts a variable number of integer arguments.

Parameters

Name	Type	Default	Description
`numbers`	`int`		Two or more integer values to average.

Returns: float

Name	Type	Default	Description
`numbers`	`float`		Two or more float values to average.

ceil

pine

math.ceil(float n) → int

Returns the ceiling of n: the smallest integer greater than or equal to n.

E.g., ceil(2.3) = 3, ceil(-2.3) = -2.

Parameters

Name	Type	Default	Description
`n`	`float`		The value to round up.

Returns: int

cos

pine

math.cos(float angle) → float

Returns the cosine of angle.

Note: Pine Script uses degrees, not radians (unlike most programming languages).

Parameters

Name	Type	Default	Description
`angle`	`float`		The angle in degrees.

Returns: float — A value between -1 and 1.

exp

pine

math.exp(float n) → float

Returns e (Euler's number) raised to the power of n.

The inverse of log(). Useful for exponential growth/decay calculations.

Parameters

Name	Type	Default	Description
`n`	`float`		The exponent value.

Returns: float

floor

pine

math.floor(float n) → int

Returns the floor of n: the largest integer less than or equal to n.

E.g., floor(2.7) = 2, floor(-2.3) = -3.

Parameters

Name	Type	Default	Description
`n`	`float`		The value to round down.

Returns: int

log

pine

math.log(float n) → float

Returns the natural logarithm (base e) of n.

The inverse of exp(). Returns na for non-positive values.

Parameters

Name	Type	Default	Description
`n`	`float`		The value (must be positive).

Returns: float

log10

pine

math.log10(float n) → float

Returns the base-10 (common) logarithm of n.

Useful for calculating orders of magnitude. Returns na for non-positive values.

Parameters

Name	Type	Default	Description
`n`	`float`		The value (must be positive).

Returns: float

max

Returns the maximum value among all provided arguments.

Accepts a variable number of integer arguments.

Parameters

Name	Type	Default	Description
`numbers`	`int`		Two or more integer values to compare.

Returns: int

Name	Type	Default	Description
`numbers`	`float`		Two or more float values to compare.

min

Returns the minimum value among all provided arguments.

Accepts a variable number of integer arguments.

Parameters

Name	Type	Default	Description
`numbers`	`int`		Two or more integer values to compare.

Returns: int

Name	Type	Default	Description
`numbers`	`float`		Two or more float values to compare.

pow

pine

math.pow(float base, float exponent) → float

Returns base raised to the power of exponent.

Parameters

Name	Type	Default	Description
`base`	`float`		The base value.
`exponent`	`float`		The power to raise the base to.

Returns: float

random

pine

math.random(
    series float min = 0,
    series float max = 1,
    series int seed = na
  ) → series float

Generates a pseudo-random number in the range [min, max).

The same seed produces the same sequence of numbers, useful for reproducible results.

Parameters

Name	Type	Default	Description
`min`	`series float`	`0`	Lower bound of the range (inclusive). Defaults to 0.
`max`	`series float`	`1`	Upper bound of the range (exclusive). Defaults to 1.
`seed`	`series int`	`na`	Optional seed for reproducibility. If `na`, uses system randomness.

Returns: series float — A float in the half-open interval [min, max).

round

pine

math.round(float n, int precision = 0) → int

Rounds n to the nearest integer, or to precision decimal places.

Uses round-half-up: 0.5 rounds to 1.

Parameters

Name	Type	Default	Description
`n`	`float`		The value to round.
`precision`	`int`	`0`	Number of decimal places (0 for integer rounding).

Returns: int

round_to_mintick

Rounds n to the nearest tick value for the current symbol.

The result is always a valid price that can be used for orders. Uses syminfo.mintick as the rounding increment.

Parameters

Name	Type	Default	Description
`n`	`float`		The price value to round.

Returns: float

sign

pine

math.sign(float n) → float

Returns the sign of n: 1.0 for positive, -1.0 for negative, 0.0 for zero.

Useful for determining direction without magnitude.

Parameters

Name	Type	Default	Description
`n`	`float`		The value to check.

Returns: float — 1.0, -1.0, or 0.0.

sin

pine

math.sin(float angle) → float

Returns the sine of angle.

Note: Pine Script uses degrees, not radians (unlike most programming languages).

Parameters

Name	Type	Default	Description
`angle`	`float`		The angle in degrees.

Returns: float — A value between -1 and 1.

sqrt

pine

math.sqrt(float n) → float

Returns the square root of n.

Parameters

Name	Type	Default	Description
`n`	`float`		The value (must be non-negative).

Returns: float — The square root, or na for negative values.

sum

pine

math.sum(series float source, series int length) → series float

Calculates the rolling sum of source over the last length bars.

Parameters

Name	Type	Default	Description
`source`	`series float`		The series to sum.
`length`	`series int`		Number of bars to include (must be >= 1).

Returns: series float — The total of the most recent length values in the series.

tan

pine

math.tan(float angle) → float

Returns the tangent of angle.

Note: Pine Script uses degrees, not radians. Undefined (returns very large values) at ±90°, ±270°, etc.

Parameters

Name	Type	Default	Description
`angle`	`float`		The angle in degrees.

Returns: float

todegrees

pine

math.todegrees(float rad) → float

Converts an angle from radians to degrees.

Parameters

Name	Type	Default	Description
`rad`	`float`		The angle in radians.

Returns: float

toradians

pine

math.toradians(float deg) → float

Converts an angle from degrees to radians.

Parameters

Name	Type	Default	Description
`deg`	`float`		The angle in degrees.

Returns: float

math ​

Properties ​

e ​

phi ​

pi ​

rphi ​

Functions ​

abs ​

acos ​

asin ​

atan ​

avg ​

ceil ​

cos ​

exp ​

floor ​

log ​

log10 ​

max ​

min ​

pow ​

random ​

round ​

round_to_mintick ​

sign ​

sin ​

sqrt ​

sum ​

tan ​

todegrees ​

toradians ​

math

Properties

e

phi

pi

rphi

Functions

abs

acos

asin

atan

avg

ceil

cos

exp

floor

log

log10

max

min

pow

random

round

round_to_mintick

sign

sin

sqrt

sum

tan

todegrees

toradians