Spherical to Rectangular Coordinates Calculator

Convert spherical coordinates (r, θ, φ) to rectangular coordinates (x, y, z)

m
Distance from origin (must be non-negative)
degrees
Angle in xy-plane from x-axis (0° to 360°)
degrees
Angle from z-axis (0° to 180°)

Understanding Spherical Coordinates

Key Components

1. Coordinate Parameters

  • Radius (r): Distance from origin
  • Azimuthal angle (θ): Angle in xy-plane
  • Polar angle (φ): Angle from z-axis

2. Applications

  • Physics simulations
  • 3D modeling
  • Navigation systems
  • Astronomy

Conversion Formulas

The conversion from spherical (r, θ, φ) to rectangular (x, y, z) coordinates:

  • x=rsin⁡(ϕ)cos⁡(θ)
  • y=rsin⁡(ϕ)sin⁡(θ)
  • z=rcos⁡(ϕ)

Usage Tips

For accurate coordinate conversion:

  • Ensure correct angle units (degrees/radians)
  • Verify angle ranges (θ: 0-360°, φ: 0-180°)
  • Keep radius non-negative
  • Consider significant figures
  • Check for proper quadrant