Polar Coordinate Calculator

The formulas

Polar to Cartesian: x = r × cos(θ), y = r × sin(θ). Cartesian to polar: r = √(x² + y²), θ = atan2(y, x) — the two-argument arctangent, which correctly figures out the angle's quadrant instead of the plain arctangent, which can't tell a point in the upper-right from one in the lower-left.

Angle convention matters

This calculator measures angle counterclockwise from the positive X axis, which is the standard math and most CNC control convention (G16 polar coordinate programming on most Fanuc-style controls uses the same convention) — but always confirm your specific control's angle direction and zero reference before trusting a polar move in an actual program.

Where this is useful beyond CNC programming

Manual layout of a hole on a bolt circle, checking an angled feature's coordinates against a print given in polar dimensions, or converting a CMM report between coordinate systems are all the same conversion — this just saves re-deriving it by hand.