This calculator is designed to help students and professionals convert spherical coordinates to Cartesian coordinates, simplifying problems in trigonometry and physics.
Coordinate Converter
Results
Data Source and Methodology
All calculations are based on standard mathematical transformations from spherical to Cartesian coordinates. For detailed information, refer to the Wikipedia article on spherical coordinates. All calculations are rigorously based on these formulas and data provided by this source.
The Formula Explained
To convert spherical coordinates (r, θ, φ) to Cartesian coordinates (x, y, z), use the following formulas:
x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)
Glossary of Variables
- r: The radial distance from the origin to the point.
- θ: The polar angle measured from the positive z-axis.
- φ: The azimuthal angle measured from the positive x-axis.
- x, y, z: Cartesian coordinates representing the point in 3D space.
Practical Example
Example: Convert spherical coordinates (r = 5, θ = 45°, φ = 30°) to Cartesian coordinates.
Using the formulas:
- x = 5 * sin(45°) * cos(30°)
- y = 5 * sin(45°) * sin(30°)
- z = 5 * cos(45°)
This results in Cartesian coordinates approximately (x = 3.54, y = 1.77, z = 3.54).
FAQ
What are spherical coordinates?
Spherical coordinates represent points in three-dimensional space using three numbers: radial distance, polar angle, and azimuthal angle.
How do you convert spherical coordinates to Cartesian?
Use the formulas: x = r * sin(θ) * cos(φ), y = r * sin(θ) * sin(φ), z = r * cos(θ).
What is the use of converting these coordinates?
Converting coordinates is essential in various fields such as physics, engineering, and computer graphics for simplifying calculations and visualizations.
What units should the angles be in?
Angles should be in degrees for this calculator, but conversions to radians can be done if needed for different applications.