Calculate rotated coordinates from angles, centers, and directions. Review steps, formulas, and rounded outputs instantly. Built for students, teachers, designers, and coordinate practice needs.
| Point | Center | Angle | Direction | Rotated Point |
|---|---|---|---|---|
| (2, 3) | (0, 0) | 90° | Counterclockwise | (-3, 2) |
| (4, 1) | (0, 0) | 180° | Counterclockwise | (-4, -1) |
| (5, 2) | (1, 1) | 90° | Clockwise | (2, -3) |
| (3, 4) | (1, 1) | 45° | Counterclockwise | (0.2929, 4.5355) |
| (-2, 6) | (0, 0) | 270° | Counterclockwise | (6, 2) |
For a point (x, y) rotated around center (h, k), first translate the point:
xt = x - h
yt = y - k
Then apply the rotation matrix:
xr = xt cos(θ) - yt sin(θ)
yr = xt sin(θ) + yt cos(θ)
Finally translate back:
x' = h + xr
y' = k + yr
Clockwise rotation uses a negative angle. Counterclockwise rotation uses a positive angle.
A rotation of a point calculator helps you move coordinates on the Cartesian plane. It shows how one point changes after a chosen angle. You can rotate around the origin or any custom center. That makes the tool useful for geometry class, graph work, and transformation practice. It also helps students verify manual answers quickly. Teachers can use it for examples. Designers can use it for coordinate checks in simple layouts and sketches.
The center of rotation controls the path of the point. If the center is the origin, the math is shorter. If the center is elsewhere, the calculator first translates the point. Then it rotates the translated values. After that, it shifts the result back. This process keeps the distance from the center unchanged. That is why rotation is called a rigid transformation. Shape and size stay the same during the move.
Many learners work in degrees first. Advanced courses often switch to radians. This calculator handles both. It also supports clockwise and counterclockwise rotation. That reduces sign mistakes. Common classroom tasks include 90 degree, 180 degree, and 270 degree turns. However, any angle can be used here. Decimal results are helpful when the angle is not standard. Rounded output makes the final coordinates easier to read and compare.
The page does more than show an answer. It displays steps, translated coordinates, and the rotation matrix. That improves understanding. The example data table gives quick practice cases. The export options help you save results for homework files or worksheets. Because the page uses a simple layout, the calculator remains easy to scan on large and small screens. It is a practical tool for algebra, trigonometry, coordinate geometry, and transformation review.
It finds the new coordinates of a point after rotation. You can rotate around the origin or another center. It also shows steps and supporting values.
Yes. Enter any center X and center Y values. The calculator translates the point, applies the rotation, and then shifts the point back.
Counterclockwise uses a positive angle in standard coordinate geometry. Clockwise uses the negative version of that angle. The final point changes because the direction changes.
Use whichever unit your problem gives you. School geometry often uses degrees. Higher math and trigonometry often use radians. This calculator supports both choices.
No. Rotation preserves the distance from the center. That is why it is called a rigid transformation. Only the direction of the point changes.
Many angles are not special angles. Their sine and cosine values are decimal numbers. The calculator rounds the final output using your selected decimal places.
Yes. A 360 degree rotation returns the point to its starting position. The same idea applies to 2π radians in radian mode.
You can save the calculated values for records, homework, or sharing. CSV is useful for spreadsheets. PDF is useful for a quick printable result sheet.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.