Convert polar coordinates to rectangular X,Y and back. Enter radius and angle, or an X,Y pair, to get the other form — used for bolt patterns, cams and rotary table work.
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Request a Proposal →Polar coordinates (radius r, angle θ) describe points by distance and direction from an origin. Rectangular coordinates (X, Y) describe points by perpendicular offsets. Converting between them is essential for bolt circles, rotary tables, and polar interpolation on CNC lathes.
Polar interpolation (G12.1 on Fanuc, G112 on some controls) lets you program face contouring on a lathe using X-C coordinates as if they were X-Y. The C-axis (rotary) becomes the Y-axis equivalent. This is used for hexagons, squares, and other prismatic features on turned parts.
Bolt circle coordinates are polar by nature: each hole is at a constant radius (D/2) at evenly spaced angles (360 deg /N). The bolt circle calculator uses polar-to-rectangular conversion to output X-Y coordinates.
Standard mathematics: angle measured counter-clockwise from the positive X-axis. In CNC, the zero-angle direction depends on the machine: on a VMC, 0 deg is typically the +X direction (to the right). Always verify your machine's convention.
Enter the radius and angle (from positive X-axis, CCW). The calculator gives the X and Y coordinates. For rectangular to polar, enter X and Y to get the radius and angle. Verify the quadrant -- arctan returns values between -90 deg and +90 deg .
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SWITCHING COORDINATE SYSTEMS? The same conversion on your side has to survive translation at the supplier. See how to brief a tool shop on complex geometry.
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