Point Rotation Calculator

Rotate a coordinate point around any center by a given angle and find the new coordinates. Uses the rotation matrix and shows the point before and after on a coordinate diagram.

Input

Enter the point coordinates, the rotation angle, and the center of rotation to compute the rotated coordinates. The center defaults to the origin if left blank.

Point x

Point y

Rotation angle

Angle unit

Center of rotation (defaults to the origin)

Center x

Center y

Result

Rotated coordinates

(-2, 4)

Distance from center (radius)

4.472136

Base angle of point

26.565051 deg

Center of rotation

(0, 0)

The rotated coordinates use the rotation matrix. For the relative point (dx, dy) from the center, the x part is dx cosθ minus dy sinθ and the y part is dx sinθ plus dy cosθ, then the center is added back. The angle is positive counterclockwise.

How it works

The rotated coordinates come from the rotation matrix. With the center moved to the origin, the relative point (dx, dy) maps to dx cosθ minus dy sinθ for x and dx sinθ plus dy cosθ for y, then the center is added back.
The angle θ is positive counterclockwise. Degree input is converted to radians by multiplying by pi divided by 180 before computing.
The distance (radius) from the center to the point is unchanged by rotation. It equals the square root of the sum of the squares of dx and dy.
The base angle is the direction of the original point measured from the center, found with the arctangent function and shown in degrees, roughly between minus 180 and 180 degrees.

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