Cylindrical Coordinates Calculator
Cartesian Coordinates
Cylindrical Coordinates
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About Cylindrical Coordinates
Cylindrical coordinates are a three-dimensional coordinate system that extends polar coordinates by adding a third coordinate (z) that measures the height above the xy-plane.
Key Concepts:
- r: Radial distance from the z-axis
- θ: Angle from the positive x-axis in the xy-plane
- z: Height above the xy-plane
Conversion Formulas:
- Cartesian to Cylindrical:
- r = √(x² + y²)
- θ = arctan(y/x)
- z = z
- Cylindrical to Cartesian:
- x = r cos(θ)
- y = r sin(θ)
- z = z
Applications:
- Physics and engineering problems with cylindrical symmetry
- Fluid dynamics and heat transfer
- Electromagnetic field calculations
- 3D modeling and computer graphics
Tips:
- r is always non-negative
- θ is typically measured in radians
- z can be positive or negative
- Be careful with the quadrant when calculating θ
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