What is Rectangular to Spherical Coordinates Conversion?

Rectangular to spherical coordinates conversion is a mathematical process that transforms a point’s location from a three-dimensional Cartesian coordinate system (x, y, z) to a spherical coordinate system (r, θ, φ). This conversion is useful in various fields, including physics, engineering, and computer graphics, where representing points in 3D space using spherical coordinates can simplify certain calculations or provide a more intuitive understanding of spatial relationships.

How to Use the Rectangular to Spherical Coordinates Calculator

Step 1: Enter the X coordinate

Begin by inputting the X coordinate of your point in the first input field. This value represents the distance along the x-axis in the Cartesian coordinate system.

Step 2: Enter the Y coordinate

Next, enter the Y coordinate in the second input field. This value represents the distance along the y-axis in the Cartesian coordinate system.

Step 3: Enter the Z coordinate

Input the Z coordinate in the third field. This value represents the distance along the z-axis in the Cartesian coordinate system.

Step 4: Click the “Calculate” button

After entering all three coordinates, click the “Calculate” button. The calculator will process your input and convert the rectangular coordinates to spherical coordinates.

Step 5: Interpret the results

The calculator will display the results in the following format:

• r: The radial distance from the origin to the point.
• θ (theta): The polar angle from the positive z-axis, given in both radians and degrees.
• φ (phi): The azimuthal angle in the x-y plane from the x-axis, given in both radians and degrees.

Step 6: Review the explanations

Each result is accompanied by a brief explanation to help you understand what each value represents in the spherical coordinate system.