Rotation Calculator
Rotate a point by a given angle in degrees about an arbitrary centre of rotation.
About Rotation Calculator
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
Worked example
With the default values below, Rotation Calculator returns Image X of 0.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Point x
- 4
- Point y
- 0
- Angle (degrees)
- 90
- Center x
- 0
- Center y
- 0
Results
- Image X
- 0.0000
- Image Y
- 4.0000
Step by step
- 1Translate to origin
- 2Apply rotation matrix
- 3Translate back
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.