Cartesian to Spherical Coordinate Converter
This calculator helps you convert Cartesian coordinates (x, y, z) into Spherical coordinates (r, θ, φ). It's designed for students, engineers, and math enthusiasts to simplify the process and reduce calculation errors.
Interactive Calculator
Results
Authoritative Content
Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da Wikipedia's Spherical Coordinate System.
The Formula Explained
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = atan2(y, x)
Glossary of Variables
- x, y, z: Cartesian coordinates
- r: Radius, the distance from the origin to the point
- θ: Theta, the angle from the positive z-axis
- φ: Phi, the angle from the positive x-axis in the xy-plane
Practical Example: A Step-by-Step Guide
For example, given Cartesian coordinates (x=3, y=4, z=5), the Spherical coordinates are calculated as follows:
- r = √(3² + 4² + 5²) = √50 ≈ 7.07
- θ = arccos(5/7.07) ≈ 0.785 radians
- φ = atan2(4, 3) ≈ 0.93 radians
Frequently Asked Questions (FAQ)
What are Cartesian coordinates?
Cartesian coordinates are a set of values that specify a point in space using three numbers, representing distances along mutually perpendicular axes (x, y, and z).
What are Spherical coordinates?
Spherical coordinates specify points in space using three values: the radius (r), the angle theta (θ), and the angle phi (φ).
Why convert between these systems?
Conversion is useful in fields like physics and engineering where different types of problems are easier to solve using different coordinate systems.
Can this calculator be used for negative coordinates?
Yes, the calculator supports negative inputs, which represent points in different quadrants.
How accurate are the calculations?
The calculations are accurate to several decimal places, depending on the precision of your inputs.