Transform Cartesian coordinates (x, y, z) into their spherical system (r, θ, φ) effortlessly. This online Spherical Coordinates Calculator is a vital tool for physicists, engineers, and mathematicians working with 3D space, simplifying complex geometric transformations and data analysis. Calculate radius, polar angle, and azimuthal angle with ease.
Formula:
To convert Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), use the following formulas:
- Radius (r): The distance from the origin to the point.
r = √(x² + y² + z²)- Polar Angle (θ): The angle between the positive z-axis and the line segment from the origin to the point (0 ≤ θ ≤ π).
θ = arccos(z/r)- Azimuthal Angle (φ): The angle between the positive x-axis and the projection of the line segment from the origin to the point onto the xy-plane (0 ≤ φ < 2π).
φ = atan2(y, x)
Where:
- x, y, z are the Cartesian coordinates.
- r is the radial distance (rho).
- θ is the polar angle (theta).
- φ is the azimuthal angle (phi).