# ATan2 function

## Overview

Calculates the inverse tangent (based on x,y) of the pixels in a raster.

## Notes

ATan2 function converts rectangular coordinates (x,y) to polar (r,θ), where r is the distance from the origin, and θ is the angle from the x-axis.

The equation for determining ATan2 is as follows:

``tanθ = y / x ``
(where θ is the angle). The ATan2 operation represents all quadrants in a Cartesian matrix (based on sign).

The value of the first specified input is used as the numerator in the calculation of the tangent angle (y). The value of the second specified input is used as the denominator in the calculation of the angle (x).

In mathematics, all trigonometric functions have a defined range of valid input values, called the domain. The output values from each function also have a defined range. For this tool, the domain and range are as follows:

• Domain: -∞ < [in_value] < ∞
• Range: -pi < [out_value] ≤ pi
This domain applies to both inputs.

If both input values are 0, the output will be NoData. If the first input value is 0, the output will be 0.

The input values to the ATan2 function are interpreted as being in linear units; to give meaningful results, they should both be in the same unit.

The output raster is always a floating-point type, regardless of the input value type.

The output values from this tool are interpreted as unitless.

For further assistance, a procedure to follow, and some examples of converting output from radians to degrees, are available.

If both inputs are single band rasters, or one of the inputs is a constant, the output will be a single band raster.

If both inputs are multiband rasters, the function will perform the operation on each band from one input, and the output will be a multiband raster. The number of bands in each multiband input must be the same.

If one of the inputs is a multiband raster and the other input is a constant, the function will perform the operation against the constant value for each band in the multiband input, and the output will be a multiband raster.

If both inputs are multidimensional rasters with same number of variables, the function will perform the operation for all slices with same dimension value, and the output will be a multidimensional raster. The variables in the inputs must have same dimensions or a common dimension but no uncommon dimensions.

If one of the inputs is a multidimensional raster and the other input is a constant, the function will perform the operation for all slices for all variables against the constant value, and the output will be a multidimensional raster.

## Parameters

Parameter nameDescription

Raster

The input that specifies the numerator, or y value, to use when calculating the inverse tangent.

Raster2

The input that specifies the denominator, or x value, to use when calculating the inverse tangent.

Extent Type

Choose which extent should be used in the output raster:

• First Of—Use the extent of the first input raster to determine the processing extent.

• Intersection Of—Use the extent of the overlapping pixels to determine the processing extent. This is the default.
• Union Of—Use the extent of all the rasters to determine the processing extent.
• Last Of—Use the extent of the last input raster to determine the processing extent.

Cellsize Type

Choose which cell size to use in the output raster. If all the input cell sizes are the same, all the options will yield the same results.

• First Of—Use the first cell size of the input rasters.
• Min Of—Use the smallest cell size of all the input rasters.
• Max Of—Use the largest cell size of all the input rasters. This is the default.
• Mean Of—Use the mean cell size of all the input rasters.
• Last Of—Use the last cell size of the input rasters.