Cylindrical Coordinates Calculator
Convert Cartesian (x,y,z) and cylindrical (r,θ,z) coordinates in either direction; angles are in degrees.
Formula
x=r cosθ; y=r sinθ; r=√(x²+y²); θ is the quadrant-correct angle; z stays unchanged.
r or x ≈ (4)×(1.25) · θ (°) or y ≈ ((4)÷abs((4)))×2×atan(abs((1))÷((1.25)+abs((0.75))))×180÷pi · z ≈ (2)
How to use
- Choose the input coordinate system.
- Enter x,y,z or r,θ,z; other fields are ignored.
- Read the three target coordinates in the stated order.
Examples
- Cartesian (−1,1,−2) becomes (√2,135°,−2).
Frequently asked questions
What are the output positions?
Cartesian input gives (r,θ in degrees,z); cylindrical input gives (x,y,z). Use one length unit throughout.
What angle is returned?
The principal angle in (−180°,180°]. A point on the z-axis has no unique angle and is rejected in the Cartesian direction.
Can radius be negative?
No. Radius is nonnegative; z may have either sign.
Sources
Updated: