Points Rotation 90 Degrees Calculator

Rotating points 90 degrees around an axis is a common operation in computer graphics, physics simulations, and engineering design. This calculator helps you perform 90-degree rotations quickly and accurately.

How to Use This Calculator

To rotate a point 90 degrees around an axis, follow these simple steps:

Enter the original coordinates of your point in the X and Y fields.
Select the axis of rotation (X, Y, or Z).
Choose the direction of rotation (clockwise or counter-clockwise).
Click "Calculate" to see the rotated coordinates.

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

Rotation Formula

90-Degree Rotation Matrix

For a point (x, y) rotated 90 degrees around the Z-axis:

Clockwise rotation:

x' = y

y' = -x

Counter-clockwise rotation:

x' = -y

y' = x

The calculator uses these simple formulas to compute the new coordinates after rotation. For other axes, the formulas are adjusted accordingly.

Worked Examples

Example 1: Clockwise Rotation

Original point: (3, 4)

Rotation: 90 degrees clockwise around Z-axis

Calculation:

x' = 4

y' = -3

Result: (4, -3)

Example 2: Counter-Clockwise Rotation

Original point: (5, -2)

Rotation: 90 degrees counter-clockwise around Z-axis

Calculation:

x' = 2

y' = 5

Result: (2, 5)

Note

These examples show how the coordinates change when rotating points 90 degrees around the Z-axis. The same principles apply to other axes with appropriate adjustments to the formulas.

FAQ

What is the difference between clockwise and counter-clockwise rotation?

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

Can I rotate points around the X or Y axis?

Yes, the calculator supports rotation around all three axes (X, Y, and Z). The formulas adjust accordingly for each axis, but the basic 90-degree rotation principles remain the same.

What if I need to rotate by a different angle?

This calculator specifically handles 90-degree rotations. For other angles, you would need a more general rotation calculator that accepts any angle of rotation.