Create a Rotation Matrix
Generate from a given angle. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Create a Rotation Matrix
- 1. Set the rotation angle. Enter a value in Angle (degrees) for how far you want the rotation matrix to turn a point or object around the chosen center or axis.
- 2. Choose the dimension and axis. Pick 2D (2x2) or 3D (3x3) from the Dimension setting. For 3D rotations, also choose the Axis, X, Y or Z, that the rotation turns around.
- 3. Adjust precision and formatting. Set Decimal places to control rounding, and use Element separator to choose how numbers within each row are divided in the generated matrix.
- 4. Copy the generated matrix. Copy the resulting rotation matrix into your code, shader, or calculation, ready to multiply against vectors or other matrices.
When to use Create a Rotation Matrix
Create a Rotation Matrix generates the standard 2D or 3D rotation matrix for a given angle, sparing you from typing out the sine and cosine terms by hand. It suits graphics, robotics, and geometry work.
- Implementing a 2D game rotation. You need the rotation matrix for turning a sprite by a specific angle in a 2D game engine, and generating it directly avoids manually writing the sine and cosine terms.
- Setting up a 3D graphics transform. A 3D scene needs an object rotated a fixed number of degrees around the Y axis, and pasting the generated 3x3 matrix into your shader code saves deriving it by hand.
- Checking a robotics kinematics calculation. A robot arm's forward kinematics uses rotation matrices for each joint, and generating one at a known angle lets you verify your derivation matches the expected values.
- Teaching rotation matrices in a course. A linear algebra course covers how rotation matrices are built from sine and cosine, and generating examples at different angles gives students concrete matrices to study.
Examples
A 2D rotation by 45°
Output
0.707107 -0.707107 0.707107 0.707107
A 3D rotation of 90° about the x axis
Output
1 0 0 0 0 -1 0 1 0
About the Create a Rotation Matrix tool
Create a Rotation Matrix is a free online tool that works entirely inside your web browser. Generate from a given angle. Because the processing happens on your own device, nothing you enter is uploaded, logged or stored anywhere.
This page is one of 234 Math utilities on EditSafely. Each one does a single job well, and all of them follow the same rule: your input stays on your machine.
You can shape the output with 5 settings, including Angle (degrees), Dimension, Axis and Decimal places, and the result refreshes the moment you change one. 2 worked examples further down the page show exactly what the tool produces for real inputs.
Because nothing leaves your device, the tool is suitable for sensitive content such as internal documents, credentials or customer data. It also responds instantly, since every keystroke is handled on your own machine rather than by a remote API.
Frequently asked questions
Does Create a Rotation Matrix cost anything?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
No data leaves your device. The whole tool is JavaScript that runs inside your browser tab, so there is no upload, no server-side processing and no log of what you did. If you disconnect from the internet after the page loads, it keeps working.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
Nothing to install and no account needed. Open the page in any up-to-date browser, including on a phone or tablet, and the tool is ready.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.