Online Coordinate System Converter

Convert coordinates between 2D Cartesian and polar, or 3D Cartesian, cylindrical, and spherical spaces with step-by-step mathematical trigonometric transformations.

Coordinate System Converter

Convert between Cartesian, Polar, Cylindrical, and Spherical coordinate systems in 2D and 3D

X (Абсциса)

Y (Ордината)

Conversion Formulas:

r = √(x² + y²) = √(3.00² + 4.00²) = 5.0000

θ = arctan(y / x) = 53.13° (0.9273 rad)

x = r · cos(θ) | y = r · sin(θ)

2D Coordinate Plane

Conversion Results

Cartesian Coordinates

X = 3.0000

Y = 4.0000

Polar Coordinates

r (радіус) = 5.0000

θ (кут) =

53.13°

0.9273 rad

How to use

Select origin coordinate system (Cartesian 2D/3D, Polar, Cylindrical, Spherical).
Enter coordinate inputs (e.g., x, y or r, θ).
Choose angle units (degrees or radians).
View converted coordinates and mathematical conversion equations.

Coordinate Transformation Examples

Cartesian (x = 3, y = 4) → Polar: radius r = 5, angle θ ≈ 53.13° (0.927 rad).

Polar (r = 2, θ = 0°) → Cartesian: (x = 2, y = 0).

Cartesian 3D (1, 1, 1) → Spherical: r = √3 ≈ 1.732, θ ≈ 45°, φ ≈ 54.74°.

Calculation Methodology

Conversions use trigonometry: Cartesian to Polar follows r = √(x² + y²), θ = atan2(y, x); Polar to Cartesian follows x = r * cos(θ), y = r * sin(θ). Standard generalizations apply in 3D.

Frequently Asked Questions

Which coordinate frameworks are supported?

2D/3D Cartesian (rectangular), polar coordinates, cylindrical coordinates, and spherical coordinates.

How do Cartesian and polar coordinates differ?

Cartesian specifies position along perpendicular axes (x, y), whereas polar specifies distance from pole r and rotation angle θ.

Can 3D space coordinates be converted?

Yes, full 3D conversions between Cartesian (x, y, z), cylindrical (r, θ, z), and spherical (r, θ, φ) coordinates are supported.

Are angles computed in degrees or radians?

Both degrees and radians can be toggled according to user preference.

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