1. What is the Spherical Equation?

The spherical equation \( r^2 = x^2 + y^2 + z^2 \) defines the relationship between Cartesian coordinates (x, y, z) and the radial distance (r) from the origin in three-dimensional space. It's fundamental in physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the spherical equation:

Where:

• \( r \) — Radial distance from origin (radius)
• \( x \) — X-coordinate in Cartesian system
• \( y \) — Y-coordinate in Cartesian system
• \( z \) — Z-coordinate in Cartesian system

Explanation: The equation calculates the squared distance from the origin to a point in 3D space, following the Pythagorean theorem extended to three dimensions.

3. Importance of Spherical Coordinates

Details: Spherical coordinates are essential in fields like physics (for describing atomic orbitals), astronomy (for celestial coordinates), and computer graphics (for 3D rendering and lighting calculations).

4. Using the Calculator

Tips: Enter the x, y, and z coordinates of your point. The calculator will compute both the radius (r) and radius squared (r²). All values can be positive or negative.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between spherical and polar coordinates?
A: Polar coordinates are the 2D equivalent (r, θ), while spherical coordinates extend this to 3D (r, θ, φ).

Q2: Can I use this for geographic coordinates?
A: Not directly - geographic systems use latitude/longitude which are angular measurements, though the concept is related.

Q3: What if my point is at the origin?
A: Then r = 0 since x, y, and z are all 0.

Q4: How is this related to the distance formula?
A: This is essentially the 3D distance formula between the origin (0,0,0) and point (x,y,z).

Q5: What units should I use?
A: Any consistent units - the result will be in the same units as your inputs squared for r².