Rotate 90 Degrees Clockwise Calculator

This calculator helps you rotate a point, vector, or shape 90 degrees clockwise around the origin (0,0) in a 2D coordinate system. It's useful for geometry, computer graphics, and engineering applications.

How to Use This Calculator

To rotate a point or vector 90 degrees clockwise:

Enter the original x-coordinate in the first input field
Enter the original y-coordinate in the second input field
Click the "Calculate" button
View the rotated coordinates in the result panel
Optionally view the rotation visualization

The calculator uses standard 2D rotation matrix mathematics to perform the transformation. The rotation is performed around the origin (0,0) by default.

Rotation Formula

To rotate a point (x, y) 90 degrees clockwise around the origin, use this formula:

Rotated X = y

Rotated Y = -x

This formula works because a 90-degree clockwise rotation swaps the x and y coordinates and negates the new x coordinate.

For example, rotating (3, 5) 90 degrees clockwise gives (5, -3).

Worked Examples

Example 1: Rotating a Point

Original point: (4, 7)

Rotated 90° clockwise:

Rotated X = 7

Rotated Y = -4

Result: (7, -4)

Example 2: Rotating a Vector

Original vector: (2, -3)

Rotated 90° clockwise:

Rotated X = -3

Rotated Y = -2

Result: (-3, -2)

FAQ

What is the difference between clockwise and counter-clockwise rotation?

Clockwise rotation moves points to the right, while counter-clockwise rotation moves them to the left. For 90° counter-clockwise, use the formula (y, -x).

Can I rotate around a point other than the origin?

This calculator only rotates around the origin (0,0). For rotation around other points, you would need to translate the coordinates first.

What happens if I rotate a point multiple times?

Rotating 90° clockwise four times returns the point to its original position. Each rotation is equivalent to multiplying by the rotation matrix.