FromSphericalCoordinates[{r,θ,ϕ}]
gives the {x,y,z} Cartesian coordinates corresponding to the spherical coordinates {r,θ,ϕ}.


FromSphericalCoordinates
FromSphericalCoordinates[{r,θ,ϕ}]
gives the {x,y,z} Cartesian coordinates corresponding to the spherical coordinates {r,θ,ϕ}.
Details

- FromSphericalCoordinates converts points in the standard range
,
,
.
- FromSphericalCoordinates automatically threads over arrays of {r,θ,ϕ} triples.
Examples
open all close allProperties & Relations (5)
FromSphericalCoordinates checks that inputs obey the restrictions of spherical coordinates:

This point violates the condition on the polar angle :
Extract the symbolic transform from CoordinateTransformData to apply it to singular points:
The conversion back to spherical coordinates is not well defined:

FromSphericalCoordinates[pt] is a special case of CoordinateTransform:
FromSphericalCoordinates inverts ToSphericalCoordinates:
FromSphericalCoordinates[{x,y,z}] uses spherical coordinates about the axis:
FromPolarCoordinates[{x,y,z}] uses spherical coordinates about the axis:
The spherical coordinates used by FromPolarCoordinates generalize to higher dimensions:
FromSphericalCoordinates changes the coordinate values of points:
TransformedField changes the coordinate expressions for fields:
Related Guides
History
Text
Wolfram Research (2015), FromSphericalCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/FromSphericalCoordinates.html.
CMS
Wolfram Language. 2015. "FromSphericalCoordinates." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FromSphericalCoordinates.html.
APA
Wolfram Language. (2015). FromSphericalCoordinates. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FromSphericalCoordinates.html
BibTeX
@misc{reference.wolfram_2025_fromsphericalcoordinates, author="Wolfram Research", title="{FromSphericalCoordinates}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FromSphericalCoordinates.html}", note=[Accessed: 18-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_fromsphericalcoordinates, organization={Wolfram Research}, title={FromSphericalCoordinates}, year={2015}, url={https://reference.wolfram.com/language/ref/FromSphericalCoordinates.html}, note=[Accessed: 18-August-2025]}