Rotate Point 90 Degrees Counter Clockwise Calculator

Rotating a point 90 degrees counter clockwise is a common geometric transformation used in computer graphics, engineering, and mathematics. This calculator provides an easy way to perform this operation and visualize the result.

How to Use This Calculator

To rotate a point 90 degrees counter clockwise:

Enter the original coordinates of the point in the input fields.
Click the "Calculate" button to perform the rotation.
View the rotated coordinates in the result section.
Use the chart to visualize the original and rotated points.

The calculator uses standard Cartesian coordinates where positive x values point to the right and positive y values point upwards.

The Rotation Formula

To rotate a point (x, y) 90 degrees counter clockwise around the origin (0, 0), use the following transformation:

New X = -y

New Y = x

This formula works because a 90-degree counter clockwise rotation swaps the x and y coordinates and changes the sign of the new x coordinate.

Note: This formula assumes the point is being rotated around the origin. For rotation around other points, you would need to translate the point to the origin first, perform the rotation, and then translate back.

Worked Examples

Let's look at a couple of examples to understand how the rotation works.

Example 1: Simple Point

Original point: (3, 5)

After 90° counter clockwise rotation:

New X = -5

New Y = 3

Result: (-5, 3)

Example 2: Negative Coordinates

Original point: (-2, 4)

After 90° counter clockwise rotation:

New X = -4

New Y = -2

Result: (-4, -2)

Comparison Table

Original Point	Rotated Point
(1, 2)	(-2, 1)
(-3, 0)	(0, -3)
(0, -5)	(5, 0)

Frequently Asked Questions

What happens if I rotate a point 90 degrees clockwise?: The formula would be New X = y and New Y = -x. This is the inverse of the counter clockwise rotation.
Can I rotate a point around a different center point?: Yes, you would need to translate the point to the origin first, perform the rotation, and then translate back to the original center point.
Is this the same as rotating a vector?: Yes, rotating a point is equivalent to rotating a vector from the origin to that point.
What's the difference between degrees and radians?: Degrees and radians are different units for measuring angles. 90 degrees is equal to π/2 radians. This calculator uses degrees.