ClarityHow to use this tool
- Enter x, y, z.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
Radius r = hypot(x,y,z), azimuth = atan2(y,x), and polar angle = acos(z/r). Azimuth is normalized to [0,360); polar angle is measured down from +z.
Using x = 1, y = 1, z = 1, the result is 1.73205081. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
No. Elevation is measured upward from the xy plane; the polar angle here is measured downward from +z. Away from singular cases, elevation equals 90° minus polar angle.
What to keep in mind
Uses physics-style polar angle from +z, not elevation above the xy plane. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.
Common questions
Is polar angle the same as elevation?
No. Elevation is measured upward from the xy plane; the polar angle here is measured downward from +z. Away from singular cases, elevation equals 90° minus polar angle.
How can I check the result?
Radius r = hypot(x,y,z), azimuth = atan2(y,x), and polar angle = acos(z/r). Azimuth is normalized to [0,360); polar angle is measured down from +z. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.