Four-quadrant arc tangent: atan2

The atan2 template function returns the four-quadrant arc tangent of y/x in radians. Unlike atan, which takes a single ratio, atan2 takes two separate values (y and x) and correctly determines the angle in all four quadrants. The result is in the range [-pi, pi].

This is useful when you need to compute a true bearing or direction angle from two coordinate components. For example, you could calculate the angle to a point on a map, or determine wind direction from separate north-south and east-west wind speed sensorsSensors return information about a thing, for instance the level of water in a tank. [Learn more].

Usage

Here’s how to use this template function. Copy any example and adjust it to your setup.

{{ atan2(1, 1) }}

0.7853981633974483

{{ (1, 1) | atan2 }}

0.7853981633974483

Function signature

The signature is a technical summary of this template function. It shows the name of the function, the values (called parameters) it accepts, and what type of data each parameter expects (for example, a piece of text or a number).

Function parameters that have a = with a value after them are optional. If you leave them out, the default value shown is used automatically. Function parameters without a default are required.

atan2(
    y: Any,
    x: Any,
    default: Any = None,
) -> float

Function parameters

The following parameters can be provided to this function.

Using a default value

If either input might not be numeric, provide a default to avoid errors. This keeps your templateA template is an automation definition that can include variables for the action or data from the trigger values. This allows automations to generate dynamic actions. [Learn more] from breaking when a sensor is temporarily unavailable.

{{
  atan2(
    states("sensor.wind_ns") | float(0),
    states("sensor.wind_ew") | float(0),
    default=0
  )
}}

0

Good to know

• The argument order is y, x, not x, y. Swapping them flips your angle.
• The result is in radians and covers all four quadrants, unlike atan.
• When x and y are both zero, the result is 0.0.

Try it yourself

Ready to test this? Open Developer tools > Template, paste the example into the Template editor, and watch the result update on the right. Edit the values to see how the function adapts to your own entitiesAn entity represents a sensor, actor, or function in Home Assistant. Entities are used to monitor physical properties or to control other entities. An entity is usually part of a device or a service. [Learn more].

More examples

Real scenarios where this function comes up in automations and templates. Copy any example and adapt it to your setup.

Passing values as a list

You can also pass the y and x values as a list or tuple, which is convenient when working with coordinate pairs.

{{ atan2([1, 0]) }}

1.5707963267948966

Still stuck?

The Home Assistant community is quick to help: join Discord for real-time chat, post on the community forum with your template and expected result, or share on our subreddit /r/homeassistant.

Related template functions

These functions work well alongside this one:

• Arc tangent (inverse tangent): atan - Returns the arc tangent (inverse tangent) of a value, in radians.

• Sine: sin - Returns the sine of a value given in radians.

• Cosine: cos - Returns the cosine of a value given in radians.

• Tangent: tan - Returns the tangent of a value given in radians.