🌐 Spherical Coordinates Calculator
Convert between Cartesian and spherical coordinates
Spherical Coordinates (ρ, θ, φ)
θ: azimuthal angle in xy-plane (0° to 360°), φ: polar angle from z-axis (0° to 180°)
How to Use This Calculator
Select Conversion Direction
Choose whether to convert from spherical to Cartesian or vice versa.
Enter Coordinates
Input the three coordinates based on your selection: (ρ, θ, φ) for spherical or (x, y, z) for Cartesian. Angles are in degrees.
Convert
Press "Convert" to get the equivalent coordinates in the other coordinate system.
Formula
Spherical → Cartesian:
x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)
Cartesian → Spherical:
ρ = √(x² + y² + z²)
θ = arctan2(y, x)
φ = arccos(z / ρ)
About Spherical Coordinates Calculator
The Spherical Coordinates Calculator converts between Cartesian (x, y, z) and spherical (ρ, θ, φ) coordinate systems. Spherical coordinates use distance from origin and two angles.
When to Use This Calculator
- Calculus: Convert coordinates for triple integrals and vector calculus
- Physics: Solve problems with spherical symmetry (spheres, atoms, etc.)
- Engineering: Analyze spherical structures and systems
- 3D Graphics: Convert between coordinate systems in rendering
- Electromagnetism: Solve Maxwell's equations in spherical coordinates
Understanding Spherical Coordinates
Spherical coordinates (ρ, θ, φ) represent a point in 3D space using: ρ (distance from origin), θ (azimuthal angle in xy-plane, 0° to 360°), and φ (polar angle from z-axis, 0° to 180°).
Frequently Asked Questions
What are spherical coordinates?
Spherical coordinates (ρ, θ, φ) represent a point in 3D space using distance ρ from origin, azimuthal angle θ in xy-plane, and polar angle φ from z-axis.
What's the difference from cylindrical coordinates?
Cylindrical uses (r, θ, z) where r is distance from z-axis. Spherical uses (ρ, θ, φ) where ρ is distance from origin. Spherical adds a polar angle φ.
What is the range of angles?
θ (azimuthal): 0° to 360° (angle in xy-plane). φ (polar): 0° to 180° (angle from z-axis). At φ = 0°, point is on +z-axis. At φ = 180°, point is on -z-axis.