---
title: math.atan2
summary: null
url: >-
  https://www.fastly.com/documentation/reference/vcl/functions/math-trig/math-atan2
---

```
FLOAT math.atan2(FLOAT y, FLOAT x)
```

**Available in:** all subroutines

Computes the principal value of the arc tangent of `y`/`x`, using the signs of
both arguments to determine the quadrant of the return value.

## Parameters

- `y` - Floating point value.
- `x` - Floating point value.

## Return Value

Upon successful completion, this function returns the arc tangent of `y`/`x` in
the range -`math.PI` to
`math.PI` radians inclusive.

If `y` is ±0 and `x` is < 0, ±`math.PI`
will be returned.

If `y` is ±0 and `x` is > 0, ±0 will be returned.

If `y` is < 0 and `x` is ±0, -`math.PI_2`
will be returned.

If `y` is > 0 and `x` is ±0, `math.PI_2`
will be returned.

If `x` is 0, a pole error will not occur.

If either `x` or `y` is `math.NAN`,
a NaN will be returned.

If `y` is ±0 and `x` is +0, ±0 will be returned.

For finite values of ±`y` > 0, if `x` is
`math.NEG_INFINITY`,
±`math.PI` will be returned.

For finite values of ±`y` > 0, if `x` is
`math.POS_INFINITY`, ±0 will be returned.

For finite values of `x`, if `y` is
`math.POS_INFINITY` or
`math.NEG_INFINITY`,
±`math.PI_2` will be returned.

If `y` is `math.POS_INFINITY` or
`math.NEG_INFINITY` and `x` is
`math.NEG_INFINITY`,
±(3\*math.PI_4) will be returned.

If `y` is `math.POS_INFINITY` or
`math.NEG_INFINITY` and `x` is
`math.POS_INFINITY`,
±math.PI_4 will be returned.

If both arguments are 0, a domain error will not occur.

If the result would cause an underflow, a range error occurs
and `math.atan2()` will return `y`/`x`.

## Example

```vcl
declare local var.fo FLOAT;

set var.fo = math.atan2(7, -0);
```