Clear convention
Positive CCW means counter-clockwise rotation in the standard XY plane.
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Free CNC tool
XY coordinate rotation calculator
Transform a point into a rotated coordinate system without manually expanding the matrix or chasing sine signs.
Any X/Y centreCW and CCWMatrix and previewLocal calculations
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Rotate a point about a selected centre
The calculator translates the point into the centre's local system, applies a 2D rotation matrix and adds the centre offset back.
Result verification
Alongside X′ and Y′ you get radius, polar angle, displacement and matrix elements.
Before-and-after preview
The graphic shows centre, input point and rotated point at one scale.
FAQ
Frequently asked questions
Does distance from the centre change?
No. Pure rotation preserves radius and changes only the direction of the centre-to-point vector.
Does CW mean a negative angle?
Yes. In the mathematical convention used here CCW is positive and CW is negative.
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