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FromPolarCoordinates
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FromPolarCoordinates

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

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FromPolarCoordinates[{r,θ1,…,θn-2,ϕ}]

gives the coordinates corresponding to the hyperspherical coordinates {r,θ1,…,θn-2,ϕ}

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Convert a general point in polar coordinates:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-bw55q1
Out[1]=1

A specific point:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-rar2fc
Out[1]=1

A conversion in dimension 3:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-350pd4
Out[1]=1

Scope  (3)Survey of the scope of standard use cases

Convert several points:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-eu2xfu
Out[1]=1

A matrix of points:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-q4xfmf
Out[1]=1

Five-dimensional hyperspherical coordinates:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-yifv2u
Out[1]=1

Properties & Relations  (6)Properties of the function, and connections to other functions

FromPolarCoordinates checks that inputs obey the normal restrictions of polar coordinates:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-2dx7ao
Out[1]=1

This point violates the condition on the angle :

In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-xynf1u
Out[2]=2

Extract the symbolic transform from CoordinateTransformData to apply it to singular points:

In[3]:=3
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https://wolfram.com/xid/0e49ng57pglmdy-dtet27
Out[4]=4

FromPolarCoordinates preserves the shape of arrays:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-bv0cjq
Out[1]=1

This includes empty arrays:

In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-jjfwrv
Out[2]=2

FromPolarCoordinates[pt] is a special case of CoordinateTransform:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-17wv03
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-yao322
Out[2]=2

FromPolarCoordinates inverts ToPolarCoordinates:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-6bo2ei
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-fbe72w
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-mxdwg7
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-fs682w
Out[2]=2

FromPolarCoordinates changes the coordinate values of points:

In[1]:=1
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https://wolfram.com/xid/0e49ng57pglmdy-8ymbgz
Out[1]=1

TransformedField changes the coordinate expressions for fields:

In[2]:=2
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https://wolfram.com/xid/0e49ng57pglmdy-4naww
Out[2]=2
Wolfram Research (2015), FromPolarCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/FromPolarCoordinates.html.
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Wolfram Research (2015), FromPolarCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/FromPolarCoordinates.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_frompolarcoordinates, author="Wolfram Research", title="{FromPolarCoordinates}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FromPolarCoordinates.html}", note=[Accessed: 15-July-2025 ]}

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@misc{reference.wolfram_2025_frompolarcoordinates, author="Wolfram Research", title="{FromPolarCoordinates}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FromPolarCoordinates.html}", note=[Accessed: 15-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_frompolarcoordinates, organization={Wolfram Research}, title={FromPolarCoordinates}, year={2015}, url={https://reference.wolfram.com/language/ref/FromPolarCoordinates.html}, note=[Accessed: 15-July-2025 ]}

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@online{reference.wolfram_2025_frompolarcoordinates, organization={Wolfram Research}, title={FromPolarCoordinates}, year={2015}, url={https://reference.wolfram.com/language/ref/FromPolarCoordinates.html}, note=[Accessed: 15-July-2025 ]}