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Rotate Point 90 Degrees Calculator

Reviewed by Calculator Editorial Team

Use this calculator to rotate a point 90 degrees around another point in a 2D plane. Whether you're working with coordinates in geometry, game development, or CAD design, this tool provides an accurate and visual representation of the rotation.

How to Use This Calculator

To rotate a point 90 degrees around another point:

  1. Enter the coordinates of the point you want to rotate (X₁, Y₁).
  2. Enter the coordinates of the center point (X₂, Y₂).
  3. Select the direction of rotation (clockwise or counter-clockwise).
  4. 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

The formula for rotating a point (X₁, Y₁) 90 degrees around another point (X₂, Y₂) is:

For clockwise rotation:

X' = X₂ + (Y₁ - Y₂)

Y' = Y₂ - (X₁ - X₂)

For counter-clockwise rotation:

X' = X₂ - (Y₁ - Y₂)

Y' = Y₂ + (X₁ - X₂)

Where (X', Y') are the new coordinates after rotation.

Worked Examples

Example 1: Clockwise Rotation

Rotate point (3, 5) 90 degrees clockwise around point (1, 2).

  1. Calculate differences: (3-1) = 2, (5-2) = 3
  2. Apply clockwise formula: X' = 1 + 3 = 4, Y' = 2 - 2 = 0
  3. Result: (4, 0)

Example 2: Counter-clockwise Rotation

Rotate point (4, 6) 90 degrees counter-clockwise around point (2, 3).

  1. Calculate differences: (4-2) = 2, (6-3) = 3
  2. Apply counter-clockwise formula: X' = 2 - 3 = -1, Y' = 3 + 2 = 5
  3. Result: (-1, 5)

Frequently Asked Questions

What does rotating a point 90 degrees mean?
Rotating a point 90 degrees around another point means moving it in a circular path while maintaining the same distance from the center point.
Can I rotate a point in 3D space with this calculator?
No, this calculator works only with 2D coordinates. For 3D rotations, you would need a different tool.
What if I want to rotate by a different angle than 90 degrees?
This calculator specifically handles 90-degree rotations. For other angles, you would need a general rotation calculator.
Is there a difference between clockwise and counter-clockwise rotation?
Yes, the direction of rotation affects the sign of the differences in the formula. Clockwise rotation uses positive differences, while counter-clockwise uses negative differences.