Coordinate Systems

Choose source coordinates and enter one number per field. Decimal point/comma and scientific notation are supported. Other systems update immediately. Click a result to copy its full available precision, without display rounding or unit text. Source changes preserve the valid point; selecting Polar XY projects onto xy and discards z. Angle-unit changes convert the actual entered angles, retaining full azimuth turns and the chosen direction at a pole. Other fields keep their raw text.

All lengths share a freely chosen unit. φ is azimuth from +x toward +y, returned in −π…π; θ is inclination from +z, in 0…π. Radii must be nonnegative. φ is undefined on the z-axis; both angles are undefined at the origin. Changing source uses zero for undefined input angles, but changing angle units preserves an already entered pole azimuth. A polar result is an xy projection, not an equivalent 3D point if z≠0.

The diagram auto-fits and normalizes coordinates before projecting, so huge or subnormal values remain drawable. Its scale is printed below. r is the point vector length, ρ its xy projection, φ the angle in xy, θ the angle from +z. Drag rotates; Ctrl/Meta-wheel or two-finger pinch zooms; ordinary wheel scrolls the page. Fit resets only the view. PNG exports the current diagram with source coordinates. No WebGL is needed.

Float64 and ten significant display digits limit precision; copies use the stored numeric value. Very large angles can lose precision, and an overflowing norm clears results. A unit change that would overflow or significantly change the direction through rounding is rejected without changing the source. Raw inputs, mode and units persist, including invalid strings; camera, diagram and results are not saved. OpenStax: cylindrical and spherical coordinates uses different angle symbols.