Arc tangent (inverse tangent): atan

The atan template function returns the arc tangent (inverse tangent) of a value. The result is in radians, in the range [-pi/2, pi/2]. Unlike atan2, this function takes a single value and cannot distinguish between quadrants.

This is useful for converting a slope or ratio back into an angle, for example when calculating an incline angle from rise-over-run sensorSensors return information about a thing, for instance the level of water in a tank. [Learn more] data.

Usage

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

{{ atan(1) }}

0.7853981633974483

{{ 1 | atan }}

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.

atan(
    value: Any,
    default: Any = None,
) -> float

Function parameters

The following parameters can be provided to this function.

Good to know

• Cannot tell quadrants apart because the sign information is lost. Use atan2 when you need the correct angle in all four quadrants.
• The result is in radians. Multiply by 180 / pi to convert to degrees.

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.

Using a default value

If the 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 sensorSensors return information about a thing, for instance the level of water in a tank. [Learn more] is temporarily unavailable.

{{ atan(states("sensor.slope"), default=0) }}

0

Convert arc tangent to degrees

Turn a slope ratio (rise over run) into an angle in degrees.

{{ (atan(1) * 180 / pi) | round(1) }}

45.0

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:

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

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

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

• Four-quadrant arc tangent: atan2 - Returns the four-quadrant arc tangent of y/x, in radians.