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

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	float		The float value.

Returns: float

---

acos

math.acos(value: float): 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

math.asin(value: float): 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

math.atan(value: float): 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

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

Parameters

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

Returns: float

---

ceil

math.ceil(n: float): 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

math.cos(angle: float): float

Returns the cosine of angle.

Note: Navi 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

math.exp(n: float): 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

math.floor(n: float): 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

math.log(n: float): 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

math.log10(n: float): 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

Returns the maximum value among all provided arguments.

Parameters

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

Returns: float

---

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

Returns the minimum value among all provided arguments.

Parameters

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

Returns: float

---

pow

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

math.random(
    min: series float = 0,
    max: series float = 1,
    seed: series int = 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

math.round(n: float, precision: int = 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

math.round_to_mintick(n: float): float

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.min_tick as the rounding increment.

Parameters

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

Returns: float

---

sign

math.sign(n: float): 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

math.sin(angle: float): float

Returns the sine of angle.

Note: Navi 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

math.sqrt(n: float): 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

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

math.tan(angle: float): float

Returns the tangent of angle.

Note: Navi 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

math.todegrees(rad: float): float

Converts an angle from radians to degrees.

Parameters

Name	Type	Default	Description
rad	float		The angle in radians.

Returns: float

---

toradians

math.toradians(deg: float): float

Converts an angle from degrees to radians.

Parameters

Name	Type	Default	Description
deg	float		The angle in degrees.

Returns: float