Spherical Coordinates Calculator

Convert Cartesian (x, y, z) to spherical (ρ, θ, φ).

ρ (radius) 1.732

θ (azimuth) (°) 45

φ (polar/inclination) (°) 54.736

Formula: ρ = √(x²+y²+z²), θ = atan2(y,x), φ = acos(z/ρ)

Step-by-step with your numbers:

1. Values used:

2. x = 1

3. y = 1

4. z = 1

6. ρ (radius) = 1.732

7. θ (azimuth) = 45°

8. φ (polar/inclination) = 54.736°

Did we solve your problem today?

Spherical coordinates locate a point by its distance from the origin and two angles.

The math behind it

ρ is the distance from the origin, θ is the azimuth angle in the xy-plane, and φ is the inclination measured from the positive z-axis.

(1, 1, 1) → ρ ≈ 1.732, θ = 45°, φ ≈ 54.74°.

Which angle convention is this?

The physics/ISO convention: θ azimuth, φ inclination from the z-axis.