Convert between Cartesian (x, y, z) and Spherical (r, θ, φ) coordinate systems.
Input Data
Conversion Results
(r: 1.73, θ: 45.0°, φ: 54.7°)
Coordinates
Transformation using trigonometric mappings in 3D space.
Radius (r)1.732
Azimuth (θ)45.0°
Polar (φ)54.7°
About this calculator
What are Spherical Coordinates?
Spherical coordinates represent points in 3D space using three values: distance from origin (r), an angle from the positive X-axis in the XY plane (θ), and an angle from the positive Z-axis (φ). This system is extremely useful for problems involving symmetry around a point.
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Pro Tips
θ (theta) is usually between 0° and 360°.
φ (phi) is usually between 0° and 180°.
Conversion depends on which convention you follow (some swap θ and φ).
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Fun Facts
"GPS systems use a form of spherical coordinates (Latitude, Longitude, Altitude)."
"In astronomy, Right Ascension and Declination are celestial spherical coordinates."
"Quantum mechanics uses spherical coordinates to describe the probability density of electrons in atoms."
Formula: r = √(x²+y²+z²), θ = atan2(y,x), φ = acos(z/r)
