Rotate a coordinate around a chosen centre — the maths behind a rotated work offset or a tilted fixture. Enter the point, the rotation angle and the centre to get the new X and Y.
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Request a Proposal →Rotating a coordinate system is a fundamental operation in CNC programming -- from G68 coordinate rotation to transformed work offsets and 5-axis part positioning. This calculator applies the standard 2D rotation matrix.
G68 is the Fanuc/Mazak G-code for rotating the work coordinate system. G68 X0 Y0 R45 rotates the XY plane 45 deg around the origin. Subsequent G01/G02/G03 moves are executed in the rotated frame. Cancel with G69. Haas, Okuma, and Siemens use similar commands.
First translate the point to the origin (subtract rotation centre coordinates), apply the rotation, then translate back (add rotation centre). This is equivalent to G68 X(xc) Y(yc) R(angle).
Coordinate rotation (G68) rotates the reference frame -- the tool stays perpendicular to the XY plane. Tool rotation (5-axis) tilts the tool relative to the part. They are fundamentally different operations with different G-code commands.
Enter the original X, Y coordinates and the rotation angle in degrees. The calculator gives the rotated coordinates. Use this to verify transformed toolpaths, check G68 rotations, or compute coordinates for parts mounted at an angle.
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ROTATING A COORDINATE SYSTEM? Coordinate conventions are a common source of misread drawings. See how to make a drawing unambiguous for a supplier.
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