MathLiveSpherical coordinates to Cartesian coordinates
These equations convert a point given by radial distance, polar angle and azimuthal angle into Cartesian x, y, z coordinates. They are used in physics and mathematics whenever a problem has spherical symmetry or uses a coordinate system centred on the origin.
\begin{aligned} x &= r \sin\theta \cos\phi \\ y &= r \sin\theta \sin\phi \\ z &= r \cos\theta \end{aligned}What the symbols mean
| Cartesian coordinate x | |
| Cartesian coordinate y | |
| Cartesian coordinate z | |
| radial distance from the origin | |
| polar angle measured from the positive z-axis (radians) | |
| azimuthal angle measured in the xy-plane from the positive x-axis (radians) |
About this formula
- FieldMathematics
- TopicCoordinate systems
- LevelUniversity
- Also calledspherical to cartesian conversion, spherical coordinates formula, spherical coordinate transformation, convert spherical to rectangular coordinates, spherical coordinate system equations, polar angle azimuthal angle to xyz
- SourceWikidata Q203218
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