Rotate 90 Degrees Calculator

This calculator helps you determine the new position of an object after rotating it by 90 degrees clockwise or counterclockwise. Whether you're working with coordinates, vectors, or geometric shapes, this tool provides quick and accurate results.

How to Use This Calculator

Using the Rotate 90 Degrees Calculator is straightforward. Follow these steps:

Enter the original coordinates of the object in the "X-coordinate" and "Y-coordinate" fields.
Select the rotation direction: "Clockwise" or "Counterclockwise".
Click the "Calculate" button to see the new coordinates after rotation.
Review the result and use it in your calculations or drawings.

Note: This calculator assumes standard Cartesian coordinates where the positive X-axis points to the right and the positive Y-axis points upwards.

Formula Used

The rotation of a point (x, y) by 90 degrees can be calculated using the following formulas:

Clockwise Rotation:

x' = y

y' = -x

Counterclockwise Rotation:

x' = -y

y' = x

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

Worked Examples

Example 1: Clockwise Rotation

Original coordinates: (3, 5)

Rotation direction: Clockwise

Calculation:

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

Result: The new coordinates after clockwise rotation are (5, -3).

Example 2: Counterclockwise Rotation

Original coordinates: (4, -2)

Rotation direction: Counterclockwise

Calculation:

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

Result: The new coordinates after counterclockwise rotation are (2, 4).

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.

Can I rotate multiple points at once?

This calculator handles one point at a time. For multiple points, you would need to run the calculation for each point individually.

Is this calculator suitable for 3D rotations?

No, this calculator is specifically designed for 2D rotations. For 3D rotations, you would need a different tool.