How do you convert cylindrical to Cartesian coordinates?

Use x = r · cos(θ), y = r · sin(θ), and z = z. The z-coordinate stays the same in both cylindrical and Cartesian systems.

Can I enter angles in degrees?

Yes. Choose degrees or radians in the converter. If you use degrees, the tool converts them to radians internally before applying the formulas.

What is the difference between cylindrical and polar coordinates?

Cylindrical coordinates extend polar coordinates with a vertical z component. So cylindrical is (r, θ, z), while polar is just (r, θ) in a plane.

Cylindrical to Cartesian Converter | Convert (r, θ, z) to (x, y, z)

Convert coordinates

r (radial distance) from z-axis

θ (azimuthal angle)

Measured in x-y plane from +x axis, counterclockwise.

z (height)

Angle unit

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:

θ_rad = θ_deg × 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.