Spherical Coordinates Calculator

Convert between 3D Cartesian (x, y, z) and spherical (rho, theta, phi) coordinates using the ISO/physics convention where phi is the polar angle from the z-axis.

Frequently Asked Questions

What are spherical coordinates?

A 3D system (rho, theta, phi) where rho is the distance from the origin, theta is the azimuth in the xy-plane, and phi is the polar angle from the positive z-axis (ISO/physics convention).

Physics versus math convention?

Physics (used here) calls the azimuth theta and the polar angle phi. Many math textbooks swap them. Be explicit about which convention applies.

When do I integrate in spherical?

When the region or integrand has spherical symmetry. Volume of a ball, gravitational potential, atomic orbitals, and Earth-coordinate problems become much simpler in spherical.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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