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Rotation Calculator.

Rotate a 2D point about the origin by an angle in degrees.

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Use Cases

Rotating coordinates in geometry problems

Quickly find the new coordinates of a point after a rotation, which is useful for solving geometry exercises or verifying manual calculations.

Example: Rotate point (3, 4) by 90° to get (-4, 3).

Transforming graphics and design elements

In graphic design or game development, you often need to rotate objects. This calculator helps you compute the new position of a vertex or point after rotation.

Example: Rotate a design element's corner point (2, -1) by 45° to reposition it.

Frequently Asked Questions

How does the Rotation Calculator work?
You input the x and y coordinates of a point and the rotation angle in degrees. The calculator applies the standard rotation transformation (x' = x*cosθ - y*sinθ, y' = x*sinθ + y*cosθ) to output the new coordinates after rotating the point counterclockwise around the origin.
What is the unit of the angle in this calculator?
The angle is specified in degrees (°). You enter the rotation angle in degrees, and the calculator internally converts it to radians for the trigonometric calculations.
Does the calculator rotate around the origin or any other point?
The calculator rotates the point around the origin (0,0). It does not support rotating around an arbitrary pivot point. If you need to rotate around another point, you would first translate the point so that the pivot becomes the origin, rotate, and then translate back.

Tips & Common Mistakes

Tips

  • Remember that positive angles rotate counterclockwise, and negative angles rotate clockwise.
  • Double-check your angle: ensure it's in degrees, not radians, as the calculator expects degrees.
  • If you need to rotate around a point other than the origin, translate the point so that the pivot becomes the origin, rotate, then translate back.
  • Use the calculator to verify your manual rotation calculations, especially for non-standard angles like 30°, 45°, or 60°.

Common Mistakes to Avoid

  • Entering the angle in radians instead of degrees, leading to incorrect results.
  • Forgetting that the rotation is around the origin, not around the point itself or another pivot.
  • Mixing up the sign of the angle: positive is counterclockwise, negative is clockwise.

Last updated: August 13, 2026