Spherical Coordinates Calculator

Spherical Coordinates Calculator

Convert between Cartesian and spherical coordinates in 3D space.

Last updated: June 2026 | By Patchworkr Team

Result

Enter x, y, and z as real numbers.

What are Spherical Coordinates?

Spherical coordinates describe a point by radius r, azimuth theta, and inclination phi.

r = sqrt(x^2 + y^2 + z^2)
theta = atan2(y, x)
phi = acos(z / r)

The standard range is theta in [0, 2pi) and phi in [0, pi].

How to Use

1. Choose the direction of conversion.

2. Enter the three coordinates or spherical parameters.

3. Read the live result and angle normalization.

Worked Example

For Cartesian point (1, 1, sqrt(2)):

r = 2

theta = pi/4

phi = acos(sqrt(2)/2)

FAQ

Can r be negative?

No. Radius is a distance.

What happens at the origin?

The angles are convention-dependent, so the tool shows 0 with a note.

Can phi be outside 0 to pi?

The tool rejects that because phi is the inclination angle.

Is theta periodic?

Yes. Theta wraps around the z-axis.

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