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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}.

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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:

ToPolarCoordinates[pt] is a special case of CoordinateTransform:

ToPolarCoordinates inverts FromPolarCoordinates:

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:

Wolfram Research (2015), ToPolarCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/ToPolarCoordinates.html.

Text

Wolfram Research (2015), ToPolarCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/ToPolarCoordinates.html.

CMS

Wolfram Language. 2015. "ToPolarCoordinates." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToPolarCoordinates.html.

APA

Wolfram Language. (2015). ToPolarCoordinates. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToPolarCoordinates.html

BibTeX

@misc{reference.wolfram_2025_topolarcoordinates, author="Wolfram Research", title="{ToPolarCoordinates}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/ToPolarCoordinates.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_topolarcoordinates, organization={Wolfram Research}, title={ToPolarCoordinates}, year={2015}, url={https://reference.wolfram.com/language/ref/ToPolarCoordinates.html}, note=[Accessed: 13-August-2025]}