Rotate Coordinates 90 Degrees Calculator

Rotating coordinates 90 degrees is a common operation in geometry and computer graphics. This calculator helps you quickly rotate any (x, y) coordinate 90 degrees clockwise or counterclockwise around the origin (0,0).

How to Use This Calculator

Using the rotate coordinates 90 degrees calculator is simple:

Enter the original x-coordinate in the first input field
Enter the original y-coordinate in the second input field
Select whether to rotate 90 degrees clockwise or counterclockwise
Click the "Calculate" button to see the rotated coordinates

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

Formula Explained

Rotating coordinates 90 degrees around the origin (0,0) follows these simple formulas:

90° Clockwise Rotation

For a point (x, y), the rotated coordinates (x', y') are calculated as:

x' = y

y' = -x

90° Counterclockwise Rotation

For a point (x, y), the rotated coordinates (x', y') are calculated as:

x' = -y

y' = x

These formulas are derived from the standard rotation matrix for 90 degrees. The clockwise rotation formula swaps the coordinates and negates the new x-coordinate, while the counterclockwise rotation swaps the coordinates and negates the new y-coordinate.

Worked Examples

Example 1: Clockwise Rotation

Original coordinates: (3, 5)

Rotation: 90° clockwise

Calculation:

x' = y = 5
y' = -x = -3

Rotated coordinates: (5, -3)

Example 2: Counterclockwise Rotation

Original coordinates: (4, -2)

Rotation: 90° counterclockwise

Calculation:

x' = -y = 2
y' = x = 4

Rotated coordinates: (2, 4)

Note: These examples show the basic rotation formulas. In computer graphics and some applications, the y-axis may be inverted, which would affect the results. Always verify the coordinate system orientation when working with specific applications.

Frequently Asked Questions

What is the difference between clockwise and counterclockwise rotation?

Clockwise rotation moves points in the direction of a clock's hands, while counterclockwise rotation moves points in the opposite direction. The formulas for each are different as shown in the formula section.

Can I rotate coordinates around a point other than the origin?

Yes, but this requires translating the coordinates to the origin first, performing the rotation, and then translating back. This calculator only handles rotation around the origin.

How does this calculator handle negative coordinates?

The calculator works with any real number coordinates, including negative values. The rotation formulas will correctly transform negative coordinates as shown in the examples.

Is there a way to rotate coordinates by other angles besides 90 degrees?

Yes, but that would require a different calculator that uses trigonometric functions (sine and cosine) for the rotation formulas. This calculator is specifically for 90-degree rotations.