Cylindrical Coordinates Calculator

Work out cylindrical coordinates instantly with clear inputs, formula shown and shareable results.

About Cylindrical Coordinates Calculator

Cylindrical coordinates keep the Cartesian z and use polar coordinates in the xy-plane, so x = ρ·cos φ and y = ρ·sin φ. They suit problems with an axis of symmetry, such as pipes and rotating bodies.

Formulas

Cylindrical to Cartesian

x = ρ·cos φ, y = ρ·sin φ, z = z

Spherical radius

r = √(ρ² + z²)

Worked example

With the default values below, Cylindrical Coordinates Calculator returns x of 3.000007. Change any input above and every figure here is recalculated in your browser.

Inputs used

Radial distance ρminimum 0: 5
Angle φ: 53.13 °
Height z: 7

Results

x: 3.000007
y: 3.999995
z (unchanged): 7.000000
Equivalent spherical radius: 8.60232527

Step by step

1Values used
2Cylindrical to Cartesian
3Spherical radius
4x= 3.000007
5y= 3.999995
6z (unchanged)= 7.000000
7Equivalent spherical radius= 8.60232527

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For ρ = 5, φ = 53.13°, z = 7?

x ≈ 3, y ≈ 4 and z = 7, giving a spherical radius of √74 ≈ 8.6023253.

When are cylindrical coordinates best?

Whenever a problem is symmetric about an axis — flow in a pipe, a solenoid's field, or a spinning disc.