# ToPolarCoordinates

ToPolarCoordinates[{x,y}]

gives the {r,θ} polar coordinates corresponding to the Cartesian coordinates {x,y}.

ToPolarCoordinates[{x1,x2,,xn}]

gives the hyperspherical coordinates corresponding to the Cartesian coordinates {x1,x2,,xn}.

# Details • ToPolarCoordinates produces points in the standard range , in two dimensions, and , , in higher dimensions.
• ToPolarCoordinates automatically threads over arrays of coordinate lists.

# Examples

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## Basic Examples(3)

Convert a general point:

A specific point:

A conversion in dimension 3:

## Scope(3)

Convert several points:

A matrix of points:

Five-dimensional hyperspherical coordinates:

## Properties & Relations(6)

ToPolarCoordinates preserves the shape of arrays:

This includes empty arrays:

is a special case of CoordinateTransform:

ToPolarCoordinates converts pairs of real numbers to their polar representation:

AbsArg converts complex numbers to their polar representation:

ToPolarCoordinates[{x,y,z}] uses spherical coordinates about the axis:

ToSphericalCoordinates[{x,y,z}] uses spherical coordinates about the axis:

ToPolarCoordinates changes the coordinate values of points:

TransformedField changes the coordinate expressions for fields: