Rotate A Point 90 Degrees Calculator

Rotating a point 90 degrees is a common operation in geometry and computer graphics. This calculator helps you quickly find the new coordinates of a point after a 90-degree rotation, either clockwise or counterclockwise.

How to Use This Calculator

Using the calculator is simple:

Enter the original X and Y coordinates of your point in the input fields.
Select whether you want to rotate the point 90 degrees clockwise or counterclockwise.
Click the "Calculate" button to see the new coordinates.
The result will show the new X and Y coordinates after rotation.

The calculator will also display a visualization of the rotation using Chart.js, showing the original and rotated points on a coordinate plane.

How Point Rotation Works

Rotating a point 90 degrees around the origin (0,0) can be done using simple matrix multiplication. The formulas for rotating a point (x, y) 90 degrees are:

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

These formulas work because a 90-degree rotation is equivalent to swapping the coordinates and changing their signs based on the direction of rotation.

Note: This calculator assumes rotation around the origin (0,0). For rotation around other points, you would need to translate the point to the origin, perform the rotation, and then translate back.

Worked Examples

Example 1: Clockwise Rotation

Original point: (3, 4)

Rotate 90 degrees clockwise:

New X = 4

New Y = -3

Result: (4, -3)

Example 2: Counterclockwise Rotation

Original point: (5, -2)

Rotate 90 degrees counterclockwise:

New X = 2

New Y = 5

Result: (2, 5)

Frequently Asked Questions

Can I rotate a point around any other point besides the origin?

No, this calculator only rotates points around the origin (0,0). For rotation around other points, you would need to translate the point to the origin first, perform the rotation, and then translate back to the original coordinate system.

What happens if I rotate a point 90 degrees twice?

Rotating a point 90 degrees twice (either in the same direction or opposite directions) will result in a 180-degree rotation, which is equivalent to multiplying both coordinates by -1. For example, rotating (3,4) 90 degrees clockwise twice would result in (-3, -4).

Is there a difference between rotating clockwise and counterclockwise?

Yes, the direction of rotation affects the sign of the coordinates. Clockwise rotation swaps the coordinates and negates the new X, while counterclockwise rotation swaps the coordinates and negates the new Y.