Rotate Points 90 Degrees Calculator
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
Rotating points 90 degrees is a common operation in geometry, computer graphics, and engineering. This calculator helps you quickly rotate any point around the origin by 90 degrees clockwise or counterclockwise.
How to Use This Calculator
To rotate a point 90 degrees:
- Enter the original X and Y coordinates of your point in the input fields.
- Select whether you want to rotate clockwise or counterclockwise.
- Click the "Calculate" button to see the rotated coordinates.
- The result will show the new coordinates after rotation.
The calculator also provides a visual representation of the rotation using Chart.js.
Rotation Formula
To rotate a point (x, y) 90 degrees around the origin, you can use the following formulas:
Clockwise Rotation
New X = y
New Y = -x
Counterclockwise Rotation
New X = -y
New Y = x
These formulas are derived from the standard 2D rotation matrix, simplified for 90-degree rotations.
Worked Examples
Example 1: Clockwise Rotation
Original point: (3, 5)
Rotated point: (5, -3)
Explanation: For clockwise rotation, the new X becomes the original Y (5) and the new Y becomes the negative of the original X (-3).
Example 2: Counterclockwise Rotation
Original point: (4, -2)
Rotated point: (2, 4)
Explanation: For counterclockwise rotation, the new X becomes the negative of the original Y (-2 becomes 2) and the new Y becomes the original X (4).
Frequently Asked Questions
- Can I rotate points around a different center?
- This calculator only rotates points around the origin (0,0). For rotation around other points, you would need to translate the points first.
- What happens if I rotate a point 360 degrees?
- Rotating a point 360 degrees brings it back to its original position. The point remains unchanged.
- Is there a difference between clockwise and counterclockwise rotation?
- Yes, the direction of rotation affects the sign of the new coordinates. Clockwise rotation uses positive Y and negative X, while counterclockwise uses negative Y and positive X.
- 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.