90 Degrees Counterclockwise Calculator

This calculator helps you determine the new coordinates of a point when rotated 90 degrees counterclockwise around the origin. It's useful in geometry, computer graphics, and physics applications where coordinate transformations are needed.

How to Use This Calculator

To use the 90 degrees counterclockwise calculator:

Enter the original x-coordinate of your point in the first input field
Enter the original y-coordinate of your point in the second input field
Click the "Calculate" button to see the rotated coordinates
Review the result and use the "Reset" button to clear the form if needed

The calculator will display the new coordinates after rotation and show a visualization of the rotation.

Formula Explained

Rotating a point 90 degrees counterclockwise around the origin (0,0) can be calculated using the following transformation:

(x', y') = (-y, x)

Where:

(x, y) are the original coordinates
(x', y') are the new coordinates after rotation

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

Worked Examples

Example 1: Basic Rotation

If you have a point at (3, 4):

(x', y') = (-4, 3)

The rotated point is (-4, 3).

Example 2: Negative Coordinates

For a point at (-2, 5):

(x', y') = (-5, -2)

The rotated point is (-5, -2).

Example 3: Origin Point

For a point at (0, 0):

(x', y') = (0, 0)

The rotated point remains (0, 0).

Frequently Asked Questions

What does a 90-degree counterclockwise rotation do to a point?: A 90-degree counterclockwise rotation swaps the x and y coordinates and negates the new x-coordinate. This moves the point to the left side of the origin.
Can I rotate a point more than 90 degrees with this calculator?: No, this calculator specifically handles 90-degree counterclockwise rotations. For other rotation angles, you would need a different calculator.
What happens if I rotate a point that's already on the x-axis?: If the original point is on the x-axis (y=0), the rotated point will be on the y-axis with the same absolute value but opposite sign.
Is this rotation formula the same for clockwise rotations?: No, a 90-degree clockwise rotation uses the formula (x', y') = (y, -x). The counterclockwise rotation formula is different.
Can I use this calculator for 3D coordinates?: No, this calculator only works with 2D coordinates. For 3D rotations, you would need a different tool.