Decode a Rotation Matrix
Find the angle from a matrix. Runs entirely in your browser, so your data never leaves your device.
0 chars · 0 lines
Output
The result appears here as you type.
How to use Decode a Rotation Matrix
- 1. Paste your rotation matrix. Enter a 2x2 or 3x3 rotation matrix in the input pane, one row per line. The matrix should represent a pure rotation, without scaling or shear.
- 2. Read the extracted angle. The tool works out the rotation angle that the matrix represents by comparing its entries against the standard sine and cosine layout, returning the angle in degrees.
- 3. Copy the angle. Copy the extracted angle from the output pane to use in a calculation, comparison, or documentation of the original transform.
When to use Decode a Rotation Matrix
Decode a Rotation Matrix extracts the angle a 2x2 or 3x3 rotation matrix represents, the reverse of building one from a known angle. Use it when you have a matrix but need to know what rotation it encodes.
- Reverse-engineering a graphics transform. A 3D scene file stores an object's orientation as a rotation matrix rather than an angle, and decoding it tells you the actual degrees of rotation applied to the object.
- Debugging a robotics joint reading. A robot arm reports its joint orientation as a rotation matrix from its encoder, and extracting the angle lets you confirm the joint moved to the commanded position.
- Checking a homework answer in reverse. You built a rotation matrix from an angle for a linear algebra exercise and want to confirm decoding it returns the same angle you started with.
- Auditing a computer vision pipeline. A pose estimation algorithm outputs a rotation matrix for an object in an image, and decoding it into a human-readable angle makes the result easier to sanity-check.
Examples
A 2×2 rotation by 90°
Input
0 -1 1 0
Output
90°
A 3×3 rotation about the x axis
Input
1 0 0 0 0.707107 -0.707107 0 0.707107 0.707107
Output
45°
About the Decode a Rotation Matrix tool
Decode a Rotation Matrix is a free online tool that works entirely inside your web browser. Find the angle from a matrix. 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.
There is nothing to configure. Provide the input and the result appears on its own. 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 Decode 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.
Is it safe to paste sensitive or confidential data?
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 much text can I process at once?
There is no fixed limit. Because the work happens on your own device rather than on a shared server, the practical ceiling is your machine's memory, which comfortably handles inputs far larger than typical online tools allow.
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.