How to use it
- Choose the conversion.
- Fill the boxes that apply; the hints say which. Other boxes are ignored.
- For angles you type, choose degrees or radians.
How it works
From Cartesian, r = √(x² + y²) with θ = atan2(y, x), lifted to the range 0 to 360° (0 to 2π). In 3D, the cylindrical radius is √(x² + y²), and the spherical radius is √(x² + y² + z²) with polar angle arccos(z / r). Conversions back use the sine and cosine formulas.
Worked example
The point (3, 4) has r = 5 and θ = atan2(4, 3) ≈ 53.13° (0.9273 rad). The point (−1, 1) has r = √2 ≈ 1.4142 and θ = 135°.
The 3D point (1, 1, 1) has spherical r = √3 ≈ 1.7321, polar angle ≈ 54.7356° and azimuth 45°.
Tips
- Angles come out in 0 to 360°, so a point below the x-axis gives an angle above 180° instead of a negative one.
- Round trips can differ in the last digit because of floating-point rounding.