Rotate The Figure 180 Degrees Calculator

Rotating a figure 180 degrees means turning it completely around its center point. This transformation is fundamental in geometry, computer graphics, and engineering. Our calculator makes it easy to visualize and perform this operation on any 2D shape.

How to Use This Calculator

To rotate a figure 180 degrees:

Enter the coordinates of the figure's vertices in the input fields.
Click the "Calculate" button to perform the rotation.
View the rotated coordinates in the results section.
Use the visualization to see the transformation.

The calculator handles both clockwise and counter-clockwise rotations, though 180-degree rotation is the same in both directions.

How 180-Degree Rotation Works

Rotating a point (x, y) 180 degrees around the origin (0, 0) transforms it to (-x, -y). This is because:

Rotation matrix for 180°:

| -1 0 |

| 0 -1 |

When applied to (x, y):

x' = -x

y' = -y

For figures with multiple points, each vertex is transformed independently using this formula. The center of rotation can be changed by translating the figure before and after rotation.

Note: In computer graphics, this is often implemented using a scale transformation with (-1, -1) factors.

Worked Examples

Example 1: Simple Triangle

Original vertices: (1, 1), (2, 3), (3, 1)

Rotated vertices: (-1, -1), (-2, -3), (-3, -1)

The triangle has been flipped both horizontally and vertically.

Example 2: Square

Original vertices: (0, 0), (2, 0), (2, 2), (0, 2)

Rotated vertices: (0, 0), (-2, 0), (-2, -2), (0, -2)

The square is now in the opposite quadrant.

Comparison of Original and Rotated Points
Point	Original Coordinates	Rotated Coordinates
P1	(1, 2)	(-1, -2)
P2	(3, 4)	(-3, -4)
P3	(5, 1)	(-5, -1)

Frequently Asked Questions

What happens to a figure rotated 180 degrees twice?

Rotating a figure 180 degrees twice returns it to its original position and orientation. This is because 180° × 2 = 360°, which is a full rotation.

Can I rotate a figure around a different point?

Yes, to rotate around a different point, first translate the figure so that point becomes the origin, perform the rotation, then translate back. Our calculator handles this automatically if you specify a different center of rotation.

What's the difference between 180° and 360° rotation?

A 180° rotation flips the figure over its center point, while a 360° rotation returns it to its original position. The 180° rotation changes the figure's orientation while the 360° does not.