# Angle of Rotation Calculator - Calculate the Angle of Rotation of an Object in a Plane

 Order of Rotation
 Angle of Rotation = °

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The Angle of Rotation Calculator is a useful tool for finding the angle of rotation of an object in a plane. In this tutorial, we'll show you how to use the calculator and provide you with some examples to help you understand how it works.

## Step 1: Enter the Coordinates of Two Points

The first step is to enter the coordinates of two points in the plane that you want to find the angle of rotation for. Make sure to enter the values in the correct format and with the appropriate units.

## Step 2: Calculate the Distance Between the Two Points

Once you've entered the coordinates of the two points, click the "Calculate Distance" button on the calculator. Our Angle of Rotation Calculator will then display the distance between the two points.

d = √[(x2 - x1)² + (y2 - y1)²]

As you can see from the formula above, the distance between the two points is calculated using their x and y coordinates.

## Step 3: Enter the Coordinates of Two Rotated Points

Next, enter the coordinates of the same two points after they have been rotated. Again, make sure to enter the values in the correct format and with the appropriate units.

## Step 4: Calculate the Angle of Rotation

Once you've entered the coordinates of both sets of points, click the "Calculate Angle of Rotation" button on the calculator. Our Angle of Rotation Calculator will then display the angle of rotation of the object in the plane.

θ = arctan[(y2 - y1)/(x2 - x1)]

As you can see from the formula above, the angle of rotation is calculated using the x and y coordinates of the two points before and after the rotation.

## Examples

Let's look at some examples to see how the Angle of Rotation Calculator works:

• Two points with coordinates (1, 1) and (3, 3) have been rotated to points with coordinates (2, -2) and (4, 0). The angle of rotation is 45 degrees.
• Two points with coordinates (-3, 1) and (2, -2) have been rotated to points with coordinates (0, -3) and (5, -6). The angle of rotation is -45 degrees.
• Two points with coordinates (-2, 2) and (2, 2) have been rotated to points with coordinates (-1, -1) and (3, -1). The angle of rotation is 180 degrees.

As you can see from these examples, our Angle of Rotation Calculator can calculate the angle of rotation of an object in a plane quickly and accurately.

## Conclusion

The Angle of Rotation Calculator is a valuable tool for finding the angle of rotation of an object in a plane. By following the simple steps outlined in this tutorial, you can quickly and accurately calculate the angle of rotation

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