Rotate Graph Calculator

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 Rotation Inputs

Enter one point per line. Use formats like 2,3 or 2 3.

Example Data Table

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)

Formula Used

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.

How to Use This Calculator

  1. Enter each graph point on a separate line.
  2. Choose the rotation angle and unit.
  3. Set the rotation direction and pivot coordinates.
  4. Pick precision, graph style, and optional closed shape mode.
  5. Press Rotate Graph to view transformed coordinates, graph, and export options.

FAQs

1. What does this calculator rotate?

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.

2. Can I rotate around a point other than the origin?

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.

3. Does it support degrees and radians?

Yes. You can choose either degrees or radians. The script converts the input internally and applies the same rotation formula for accurate transformed coordinates.

4. Why do distances from the pivot stay the same?

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.

5. What is closed shape mode for?

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.

6. Can I use negative angles?

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.

7. What format should I use for points?

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.

8. What do the CSV and PDF downloads include?

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.

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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.