The Rectangular to Cylindrical Equation Calculator is a tool used in mathematics to convert coordinates from the rectangular coordinate system (x, y, z) to the cylindrical coordinate system (r, θ, z). This conversion helps determine the radial distance (r) from the origin to a point in the xy-plane, the polar angle (θ) in radians between the positive x-axis and the line connecting the origin to the point, and the z-coordinate, which remains unchanged.
Formula of Rectangular to Cylindrical Equation Calculator
The conversion formulas are as follows:
- r = √(x² + y²)
- θ = atan2(y, x)
- z = z
Explanation:
- r represents the radial distance from the origin to the point in the xy-plane.
- θ is the polar angle measured in radians between the positive x-axis and the line connecting the origin to the point.
- z remains the same as the z-coordinate in rectangular coordinates.
General Terms Table:
| Term | Definition |
|---|---|
| Radial Distance (r) | Distance from the origin to a point in the xy-plane. |
| Polar Angle (θ) | Angle in radians from the positive x-axis to a point. |
| Cylindrical Coordinates | Representation of a point in the cylindrical coordinate system. |
The table above provides users with a quick reference to essential terms used in cylindrical coordinate conversions.
Example of Rectangular to Cylindrical Equation Calculator
Consider a point in the rectangular coordinate system with coordinates (3, 4, 5). Using the Rectangular to Cylindrical Equation Calculator, the conversion yields:
- r = √(3² + 4²) = 5 units
- θ = atan2(4, 3) ≈ 0.93 radians
- z = 5 units
Most Common FAQs
The calculator helps convert coordinates from rectangular to cylindrical systems, simplifying spatial calculations.
The polar angle represents the rotation from the positive x-axis to the point in the xy-plane, measured in radians.
The z-coordinate remains constant as it already represents the vertical position in both coordinate systems.