Polar to Cartesian Converter

A four-mode coordinate system converter for mathematics, physics, and engineering. Mode 1 - 2D Polar ↔ Cartesian: converts between (r, θ) and (x, y) with quadrant detection. Mode 2 - 3D Cylindrical ↔ Cartesian: converts (r, θ, z) to/from (x, y, z). Mode 3 - 3D Spherical ↔ Cartesian: converts (ρ, θ, φ) to/from (x, y, z) using physics convention where φ is the polar angle from the +z axis and θ is the azimuthal angle in the xy-plane. Mode 4 - Complex Numbers: converts between rectangular form (a + bi) and polar form (r·e^iθ), showing magnitude, phase angle, and formatted display. All modes support Degrees, Radians, and Gradians with one-click angle unit switching. Bidirectional - a Swap button reverses input and output for any mode. Adjustable precision (4–12 digits). Formulas reference panel shows the exact equations used. Results copy to clipboard. Correct atan2(y, x) implementation gives the full quadrant-aware angle in [−π, π]. 100% browser-based.