Center of Rotation Calculator Online

The Center of Rotation Calculator is a tool designed to determine the precise point around which a set of points rotates. This pivot point is crucial in tasks ranging from architectural design to robotics, where precise angular adjustments are necessary.

Formula of Center of Rotation Calculator

To find the center of rotation, you need two sets of points: the original position (x1, y1) and the rotated position (x2, y2). The formula to calculate the center of rotation (h, k) is:

• Calculate the differences in the coordinates:
  • Delta x = x2 – x1
  • Delta y = y2 – y1
• Use the following calculations:
  • h = (x1 + x2) / 2 + (y2 – y1) / 2 * tan(theta / 2)
  • k = (y1 + y2) / 2 – (x2 – x1) / 2 * tan(theta / 2)

Here, theta represents the angle of rotation in radians, providing a crucial parameter for these calculations.

How to Use the Calculator

To use the Center of Rotation Calculator, input the coordinates of the original point (x1, y1) and the rotated point (x2, y2), along with the rotation angle in radians. The calculator then computes the coordinates (h, k) of the center of rotation, allowing you to visualize or adjust your designs accordingly.

which can then be verified or used in further design adjustments.

Table of Common Rotation Points

Example of Center of Rotation Calculator

Consider a point at (2,3) that rotates around a pivot to reach (4,6) with an angle of 30 degrees (converted to radians). By applying the formula:

• Delta x = 4 – 2 = 2
• Delta y = 6 – 3 = 3
• h = 3 + 3 * tan(15 degrees in radians)
• k = 4.5 – 2 * tan(15 degrees in radians)

This calculation yields the center of rotation,

Most Common FAQs