90 Degrees Clockwise Calculator
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Reviewed by Calculator Editorial Team
Rotate points, shapes, and objects 90 degrees clockwise with our precise calculator tool. This guide explains the rotation formula, provides practical examples, and helps you interpret the results.
How to Use This Calculator
To rotate a point or shape 90 degrees clockwise:
- Enter the original coordinates (x, y) of the point or shape
- Select whether you're rotating a point or a shape
- Click "Calculate" to see the rotated coordinates
- Review the visualization to understand the rotation
The calculator will display the new coordinates after rotation and show a visual representation of the transformation.
Formula Explained
To rotate a point (x, y) 90 degrees clockwise around the origin (0,0), use this transformation:
New X = y
New Y = -x
For shapes, apply this transformation to each vertex of the shape. The rotation preserves distances and angles but changes the orientation.
Assumptions
- Rotation is performed around the origin (0,0)
- Coordinates are in Cartesian plane
- Positive x-axis points to the right, positive y-axis points up
Worked Examples
Example 1: Rotating a Point
Original point: (3, 4)
After 90° clockwise rotation:
New X = 4
New Y = -3
The point moves from the upper-right quadrant to the lower-right quadrant.
Example 2: Rotating a Square
Original square vertices: (1,1), (1,-1), (-1,-1), (-1,1)
After rotation:
| Original | Rotated |
|---|---|
| (1,1) | (1,-1) |
| (1,-1) | (-1,-1) |
| (-1,-1) | (-1,1) |
| (-1,1) | (1,1) |
The square is now rotated 90° clockwise, with vertices in the lower-right, lower-left, upper-left, and upper-right quadrants respectively.
Frequently Asked Questions
- Can I rotate around a different point?
- This calculator only rotates around the origin (0,0). For rotation around other points, you would need to translate the coordinates first.
- What happens to the shape's orientation?
- A 90° clockwise rotation changes the shape's orientation by 90° in the clockwise direction. The relative positions of points remain the same.
- Is this the same as a counter-clockwise rotation?
- No. A 90° counter-clockwise rotation would use the formula New X = -y and New Y = x. The direction of rotation is opposite.
- Can I rotate 3D objects with this calculator?
- No. This calculator only handles 2D rotations. For 3D rotations, you would need a different tool or formula.