Rotation 90 Degrees Calculator

This rotation 90 degrees calculator helps you rotate points, shapes, and objects 90° clockwise or counterclockwise. The calculator uses standard rotation formulas and provides visual results. The guide explains how to perform rotations manually and when to use different rotation types.

How to Use This Calculator

To rotate a point or shape 90 degrees:

Enter the original coordinates (x, y) of the point or shape.
Select the rotation direction (clockwise or counterclockwise).
Click "Calculate" to see the new coordinates.
View the visualization to understand the rotation.

The calculator handles both 2D and 3D rotations, though 3D rotations require additional parameters. For complex shapes, you may need to rotate each vertex individually.

Rotation Formula

The standard formula for rotating a point (x, y) 90° around the origin is:

Clockwise rotation: x' = y y' = -x Counterclockwise rotation: x' = -y y' = x

For rotations around other points, you must first translate the point to the origin, perform the rotation, then translate back.

Note

These formulas assume standard Cartesian coordinates where positive x is right and positive y is up. The origin (0,0) is the center of rotation.

Worked Examples

Example 1: Rotating a Point Clockwise

Original point: (3, 4)

Rotation: 90° clockwise

Calculation:

x' = y = 4 y' = -x = -3

New coordinates: (4, -3)

Example 2: Rotating a Point Counterclockwise

Original point: (5, -2)

Rotation: 90° counterclockwise

Calculation:

x' = -y = 2 y' = x = 5

New coordinates: (2, 5)

Frequently Asked Questions

What is the difference between clockwise and counterclockwise rotation?: Clockwise rotation moves points to the right (positive x direction), while counterclockwise moves them to the left (negative x direction). The formulas use opposite signs for the y-coordinate.
Can I rotate a shape around a point other than the origin?: Yes, you can rotate around any point by first translating the shape so that point becomes the origin, performing the rotation, then translating back.
How do I rotate a 3D object 90 degrees?: 3D rotations require additional parameters (axis of rotation) and more complex formulas. This calculator handles 2D rotations only.
What are some practical applications of 90° rotations?: 90° rotations are used in computer graphics, game development, robotics, and engineering to change the orientation of objects without scaling.