How this calculator works
Translate the pivot to the origin, multiply each point by the planar rotation matrix, then translate back. Every point is rotated by the same angle, preserving distances and orientation. The pivot itself stays fixed. Negative angles rotate clockwise. Small nonzero residues such as 6e-17 can occur at right angles because trigonometric values are stored with finite precision.
Formula
xNew = px + (x-px)cos(theta) - (y-py)sin(theta); yNew = py + (x-px)sin(theta) + (y-py)cos(theta).
Worked example
Rotating (1, 0) anticlockwise by 90 degrees about (0, 0) gives (0, 1). Rotating (2, 1) by 180 degrees about (1, 1) gives (0, 1).
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Frequently asked questions
Are the axes rotated too?
No. These are active rotations of points in a fixed coordinate system.
How do I undo a rotation?
Use the same pivot and the negative of the original angle.
Can I rotate a whole polygon?
Yes. Enter its vertices in order in the two matching lists. This tool returns coordinates rather than a drawing.