# 3D Rotation Calculator

## The 3D Rotation Calculator

The 3D rotation calculator is a unique tool designed for calculating the new coordinates of a point after it has been rotated around the origin in three-dimensional space. The tool is primarily useful for individuals studying geometry or working in fields such as computer graphics, robotics, or any other discipline that requires manipulation of 3D shapes.

## How it works

The 3D rotation calculator utilizes the principles of 3D geometric transformations, more specifically, the rotation transformation. When a point is rotated around the origin in 3D space, the x, y, and z coordinates of the point change in accordance with the rotation angle and the axis of rotation.

The formulae used for the calculation are dependent on the axis of rotation:

- For rotation around the X-axis:
- Ynew = Y * cos(angle) - Z * sin(angle)
- Znew = Y * sin(angle) + Z * cos(angle)
- For rotation around the Y-axis:
- Xnew = X * cos(angle) + Z * sin(angle)
- Znew = -X * sin(angle) + Z * cos(angle)
- For rotation around the Z-axis:
- Xnew = X * cos(angle) - Y * sin(angle)
- Ynew = X * sin(angle) + Y * cos(angle)

where Xnew, Ynew, and Znew are the new coordinates, X, Y, and Z are the original coordinates, and angle is the angle of rotation. The angle must be provided in radians for the calculations, so if you're supplying it in degrees, make sure to convert it to radians first.

## How to use the calculator

To use the calculator, simply enter the original X, Y, and Z coordinates, the rotation angle (in degrees), and select the axis of rotation from the dropdown menu. Once all the fields are completed, click the "Calculate" button. If the inputs are valid, the calculator will display the new coordinates after rotation.

The calculator ensures that all fields are completed and the angle is within the acceptable range of 0-360 degrees. If the inputs are not valid, an error message is displayed and the calculation is not performed.

## Frequently Asked Questions

##### What is the 3D Rotation Calculator?

The 3D Rotation Calculator is a tool that helps you calculate the new coordinates of a point after it has been rotated around the origin in 3D space.

##### How does the 3D Rotation Calculator work?

The calculator uses the principles of 3D geometric transformations and applies rotation transformation formulas to the original coordinates using the rotation angle you provide.

##### How do I use the 3D Rotation Calculator?

Input the original X, Y, and Z coordinates, the rotation angle, and select the axis of rotation. Click "Calculate" to see the new coordinates after rotation.

##### What is the range of rotation angles that can be entered?

You can enter rotation angles within the range of 0-360 degrees. If the angle is outside this range, an error message will be displayed and the calculation will not be performed.

##### Do I need to convert the rotation angle to radians?

No, you can enter the rotation angle in degrees. The calculator will automatically convert it to radians before performing the calculations.