Convert (x,y,z) points to spherical (r, θ, φ) with radian/degree support. Upload thousands of points via CSV/TXT.
| # | Cartesian (x,y,z) | r (radius) | θ (polar) | φ (azimuth) | Unit |
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Perfect for electromagnetism, quantum mechanics, and orbital mechanics where spherical symmetry simplifies equations.
Upload thousands of points from CSV and get instant spherical coordinates — ideal for point cloud data and simulations.
Switch between radian and degree output for θ (inclination) and φ (azimuth) based on your application.
Provide Cartesian coordinates (x, y, z). Use integers or decimals.
Select angle unit (radians/degrees) and decimal precision.
Instantly receive r = √(x²+y²+z²), θ = arccos(z/r), φ = atan2(y,x).
Spherical coordinates (r, θ, φ) represent a point in three-dimensional space using radial distance from origin, polar angle measured from positive z-axis (inclination), and azimuthal angle from positive x-axis. This system is indispensable in fields like astrophysics (describing star positions), antenna radiation patterns, and fluid dynamics. For any point (x,y,z), the conversion formulas are: r = √(x² + y² + z²), θ = arccos(z / r) (0 ≤ θ ≤ π), φ = atan2(y, x) (−π < φ ≤ π). Example: Cartesian point (3,4,5) yields r ≈ 7.07, θ ≈ 0.785 rad (45°), φ ≈ 0.927 rad (53.13°). Bulk conversion helps LiDAR processing, 3D modeling, and robotic kinematics. Our tool validates negative inputs, zero divisions, and edge cases (z = ±r). Whether you're a student learning multivariable calculus or an engineer working on radar systems, this free online converter saves time and reduces error.
Spherical coordinates simplify problems with spherical symmetry: gravitational fields, electromagnetic waves, atomic orbitals, and navigation.
θ (polar angle) is measured from +z axis down; φ (azimuth) is measured from +x axis toward +y axis, standard physics convention.
Yes, reverse formulas: x = r sinθ cosφ, y = r sinθ sinφ, z = r cosθ. This tool focuses on forward conversion.
All calculations happen locally in your browser. Files never leave your device.
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