2D Point Rotation Calculator

Rotate a point in a 2D plane around the origin. Enter the initial coordinates and the rotation angle to find the new coordinates.

Enter Point and Angle

Point X-coordinate:

Point Y-coordinate:

Rotation Angle:

Rotated Point

Rotated X-coordinate:

Rotated Y-coordinate:

Visualization

Understanding 2D Point Rotation

In mathematics, rotating a point in a 2D plane around the origin (0, 0) involves transforming its coordinates based on a given angle. If a point P has coordinates (x, y), and we rotate it by an angle θ (theta) counter-clockwise around the origin, the new coordinates (x', y') of the rotated point P' can be calculated using the rotation formulas:

x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)

Here, cos(θ) and sin(θ) are cosine and sine of the rotation angle θ, respectively. The angle θ is typically given in radians or degrees. This calculator allows you to input the original coordinates (x, y) and the rotation angle in either degrees or radians to find the new rotated coordinates (x', y'). The visualization helps to see how the point moves in the 2D plane after rotation.

Learn more about point rotation on resources like Wikipedia or Khan Academy's geometry section.