Cylindrical to Cartesian Converter
Convert cylindrical coordinates (r, θ, z) to Cartesian coordinates (x, y, z). Select degrees or radians, see the exact formulas, and understand how cylindrical relates to polar and spherical systems.
Convert coordinates
Measured in x-y plane from +x axis, counterclockwise.
Result (Cartesian)
x: –
y: –
z: –
Note: Cartesian z equals cylindrical z. Only x and y are transformed.
Need the inverse? Try Cartesian to Cylindrical.
Formulas used
Cylindrical coordinates are basically polar coordinates in the x-y plane, extended with a vertical height z.
Definition
- r: radial distance from the z-axis (r ≥ 0)
- θ: angle in the x-y plane measured from +x axis
- z: same as Cartesian z (height)
Conversion to Cartesian
x = r · cos(θ)y = r · sin(θ)z = z
Degrees to radians
If your angle is in degrees, convert it first:
θrad = θdeg × π / 180
Relationship to other systems
Cylindrical: (r, θ, z) Polar: (r, θ) — just drop z Spherical: (ρ, θ, φ) — adds a polar angle from the z-axis and uses distance from origin instead of distance from z-axis.
FAQ
Why do we use cylindrical coordinates?
They are ideal for problems with rotational symmetry around the z-axis: fluid flow in pipes, electromagnetism around wires, or objects like cylinders.
What happens if r is 0?
The point is on the z-axis, so x = 0 and y = 0 regardless of θ. z stays as entered.
My angle is 450° — is that ok?
Yes. The converter reduces it via sine and cosine, so any real angle works.
Formula (LaTeX) + variables + units
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x = r · cos(θ) y = r · sin(θ) z = z
θrad = θdeg × π / 180
- No variables provided in audit spec.
- Cartesian to Cylindrical — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/cartesian-to-cylindrical
Last code update: 2026-01-19
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