Rotate custom points around any chosen pivot. Check new coordinates, distances, and visual movement instantly. Great for transformations, graph practice, classroom tasks, and revision.
Enter one point per line. Use formats like 2,3 or 2 3.
| Point | Original Coordinate | Angle | Pivot | Rotated Coordinate |
|---|---|---|---|---|
| P1 | (4, 0) | 90° CCW | (0, 0) | (0, 4) |
| P2 | (4, 3) | 90° CCW | (0, 0) | (-3, 4) |
| P3 | (0, 3) | 90° CCW | (0, 0) | (-3, 0) |
The calculator rotates each point around a selected pivot. It first shifts the point so the pivot becomes the temporary origin. Then it applies the rotation matrix and shifts the point back.
x' = px + (x - px)cos(θ) - (y - py)sin(θ)
y' = py + (x - px)sin(θ) + (y - py)cos(θ)
Where:
x, y = original point
px, py = pivot coordinates
θ = rotation angle
Clockwise rotation uses a negative angle. Counterclockwise rotation uses a positive angle. Distances from the pivot remain unchanged after rotation.
It rotates any list of coordinate points around a pivot you choose. The result includes transformed coordinates, a comparison graph, lengths, centroids, and optional closed-shape area values.
Yes. Enter any pivot X and pivot Y values. The calculator shifts points relative to that pivot, performs the rotation, and returns the final coordinates in the original graph space.
Yes. You can choose either degrees or radians. The script converts the input internally and applies the same rotation formula for accurate transformed coordinates.
Rotation is a rigid transformation. It changes orientation and position relative to the pivot, but it does not stretch or shrink the graph. That is why pivot distances remain equal before and after.
Closed shape mode connects the last point back to the first. This lets the calculator estimate closed path length and polygon area, which is useful for rectangles, triangles, and other enclosed figures.
Yes. You can enter a negative angle directly, or you can keep the angle positive and switch the direction. Both approaches are mathematically valid when interpreted consistently.
Enter one point per line using either comma-separated or space-separated values. Examples include 2,3 or 2 3. Empty lines are ignored automatically.
They include the full point table with original coordinates, rotated coordinates, and pivot distances. The PDF also adds a compact summary so you can save or share the rotation results easily.
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.