MATH CALCULATOR
Spherical Coordinates Calculator
Convert between Cartesian and spherical coordinates effortlessly with our online calculator.
What is the Spherical Coordinates Calculator & How does it work?
Spherical coordinates are a three-dimensional coordinate system that uses a radius, an azimuthal angle, and a polar angle to specify the position of a point in space. This system is particularly useful in physics and engineering for problems involving symmetry about a point.
Conversely, to convert from Cartesian coordinates (x, y, z) to spherical coordinates (r, ΞΈ, Ο), use the following formulas:
begin{align*}x &= r sin(theta) cos(phi)\y &= r sin(theta) sin(phi)\z &= r cos(theta)end{align*}
r = radial distance, ΞΈ = polar angle, Ο = azimuthal angle
Conversely, to convert from Cartesian coordinates (x, y, z) to spherical coordinates (r, ΞΈ, Ο), use the following formulas:
Parameters
Resultβ
Frequently Asked Questions
How do I convert from Cartesian to spherical coordinates?
Use the formulas: r = sqrt(x^2 + y^2 + z^2), ΞΈ = arccos(z/r), Ο = atan2(y, x).
What are the advantages of using spherical coordinates?
Spherical coordinates simplify problems with symmetry about a point in physics and engineering.
Can you explain what each variable represents in spherical coordinates?
r is the radial distance, ΞΈ is the polar angle from the positive z-axis, and Ο is the azimuthal angle from the positive x-axis.
How do I convert from spherical to Cartesian coordinates?
Use the formulas: x = r sin(ΞΈ) cos(Ο), y = r sin(ΞΈ) sin(Ο), z = r cos(ΞΈ).
When should I use spherical coordinates instead of Cartesian?
Use spherical coordinates for problems involving radial symmetry or when dealing with spherical objects.
What is the range of values for each angle in spherical coordinates?
ΞΈ ranges from 0 to Ο, and Ο ranges from 0 to 2Ο.
Results are for informational purposes only and do not constitute professional advice.