Spherical Coordinates Calculator

Your details

Choose the direction of coordinate conversion.
Unit for all angular inputs and outputs.
x coordinate (positive right).
y coordinate (positive forward/into page).
z coordinate (positive up).
r (radial distance)
1.732051

Distance from the origin to the point.

theta (polar angle)54.73561deg
phi (azimuthal angle)45deg
theta (radians)0.955317rad
phi (radians)0.785398rad
rho (cylindrical radius)1.414214
z (cylindrical)1
Result(r=1.732051, theta=54.735610 deg, phi=45.000000 deg)
r1.732051
rho1.414214
theta (deg)54.73561
phi (deg)45

Cartesian to Spherical conversion complete. r = 1.7321.

  • The point is 1.7321 units from the origin.
  • theta = 54.7356 deg places the point above the xy-plane.
  • phi = 45.0000 deg gives the orientation in the xy-plane.
  • Cylindrical rho = 1.4142: distance from the z-axis measured in the xy-plane.
  • This calculator uses the physics (ISO 80000-2) convention: theta is the polar angle from +z, phi is the azimuthal angle in the xy-plane from +x.

Next stepNote: mathematicians sometimes swap theta and phi (math convention). Always confirm which convention your course or textbook uses before applying these results.

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