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.

RECIPROCAL_PHI

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

navi

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].

See Also: math.cos

asin

navi

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].

See Also: math.sin

atan

navi

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).

See Also: math.tan, math.atan2

atan2

navi

atan2(y: float, x: float): float

Returns the four-quadrant arctangent of y/x in degrees.

Unlike atan, this function takes two arguments and determines the correct quadrant using the signs of both. Useful for computing angles between vectors or points.

Parameters

Name	Type	Default	Description
`y`	`float`		The Y component (numerator).
`x`	`float`		The X component (denominator).

Returns: float — An angle in degrees in the range (-180, 180].

See Also: math.atan

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.

cbrt

navi

cbrt(n: float): float

Returns the cube root of n.

Correctly handles negative inputs (e.g., cbrt(-8.0) = -2.0), unlike pow(n, 1.0/3.0) which returns na for negatives.

Parameters

Name	Type	Default	Description
`n`	`float`		The value to take the cube root of.

Returns: float

See Also: math.pow, math.sqrt

ceil

navi

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

See Also: math.floor, math.trunc

clamp

navi

clamp(value: float, min: float, max: float): float

Clamps value to the closed interval [min, max].

Returns min if value < min, max if value > max, otherwise value. Avoids the verbose math.max(min, math.min(max, x)) pattern.

Parameters

Name	Type	Description
`value`	`float`	The value to clamp.
`min`	`float`	The lower bound (inclusive).
`max`	`float`	The upper bound (inclusive).

Returns: float

cos

navi

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.

See Also: math.acos

exp

navi

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

See Also: math.log

floor

navi

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

See Also: math.ceil, math.trunc

hypot

navi

hypot(x: float, y: float): float

Returns the hypotenuse of a right triangle with legs x and y.

Equivalent to sqrt(x*x + y*y) but numerically stable (avoids overflow for large inputs).

Parameters

Name	Type	Default	Description
`x`	`float`		The length of the first leg.
`y`	`float`		The length of the second leg.

Returns: float

log

navi

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

See Also: math.exp, math.log10

log10

navi

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

See Also: math.log

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

navi

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

See Also: math.sqrt, math.cbrt

random

navi

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

navi

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

navi

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 symbol_info.min_tick as the rounding increment.

Parameters

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

Returns: float

sign

navi

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.

See Also: math.abs

sin

navi

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.

See Also: math.asin

sqrt

navi

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.

See Also: math.pow, math.cbrt

sum

navi

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

navi

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

See Also: math.atan, math.atan2

to_degrees

navi

to_degrees(rad: float): float

Converts an angle from radians to degrees.

Parameters

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

Returns: float

See Also: math.to_radians

to_radians

navi

to_radians(deg: float): float

Converts an angle from degrees to radians.

Parameters

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

Returns: float

See Also: math.to_degrees

trunc

navi

trunc(n: float): int

Truncates n toward zero (removes the fractional part).

Unlike floor, truncation toward zero is symmetric: trunc(-1.9) = -1, whereas floor(-1.9) = -2.

Parameters

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

Returns: int

See Also: math.floor, math.ceil

math ​

Properties ​

E ​

PHI ​

PI ​

RECIPROCAL_PHI ​

Functions ​

abs ​

acos ​

asin ​

atan ​

atan2 ​

avg ​

cbrt ​

ceil ​

clamp ​

cos ​

exp ​

floor ​

hypot ​

log ​

log10 ​

max ​

min ​

pow ​

random ​

round ​

round_to_mintick ​

sign ​

sin ​

sqrt ​

sum ​

tan ​

to_degrees ​

to_radians ​

trunc ​

math

Properties

E

PHI

PI

RECIPROCAL_PHI

Functions

abs

acos

asin

atan

atan2

avg

cbrt

ceil

clamp

cos

exp

floor

hypot

log

log10

max

min

pow

random

round

round_to_mintick

sign

sin

sqrt

sum

tan

to_degrees

to_radians

trunc