Rotation Calculator
Rotate a point by a given angle in degrees about an arbitrary centre of rotation.
Inputs
Counter-clockwise is positive
Image X
0.0000
Image Y
4.0000
Step by step
Translate to origin
(4−0, 0−0) = (4, 0)
Apply rotation matrix
x' = cos(90°)×4 − sin(90°)×0
Translate back
(0.0000, 4.0000)
How it works
To rotate a point about center (cx, cy) by angle θ: translate the point so the center is at the origin, apply the 2D rotation matrix, then translate back.
Formula
Rotation Formula
x' = cos(θ)(x−cx) − sin(θ)(y−cy) + cx; y' = sin(θ)(x−cx) + cos(θ)(y−cy) + cy
- θ
- Rotation angle (CCW positive)
- cx,cy
- Center of rotation
- x,y
- Original point
Frequently Asked Questions
Is positive angle clockwise or counter-clockwise?
By mathematical convention, positive angles are counter-clockwise. Enter a negative angle for clockwise rotation.
What if the center is not the origin?
This calculator handles arbitrary centers by translating, rotating, and translating back.