# Image Rotation Matrix Apply rotation transformation using rotation matrix mathematics. See the 2x2 rotation matrix in action and understand the trigonometric principles behind image rotation. > Canonical page: https://elysiatools.com/en/tools/image-rotation-matrix - **Category:** Media - **Keywords:** image, rotation, matrix, rotate, angle, degrees, trigonometry, mathematics, transform, cosine, sine ## Overview The Image Rotation Matrix tool allows you to precisely rotate images using linear algebra and trigonometric principles. By applying a 2x2 rotation matrix, you can achieve exact angular adjustments for your digital assets while maintaining control over background transparency and output quality. ## Inputs - **Image File** (file): Upload any image file (JPEG, PNG, WebP, GIF, BMP, TIFF) for rotation matrix transformation - **Rotation Angle (degrees)** (range): Rotation angle in degrees (-180 to 180, 0 = no rotation). Positive = clockwise, negative = counter-clockwise - **Background Color** (text): Background color for transparent areas (hex #RRGGBB or #RRGGBBAA, or color name) - **Output Format** (select): Choose output format or keep original. PNG recommended for transparency - **Quality (1-100)** (number): Output quality for lossy formats (JPEG, WebP). Higher = better quality but larger file size ## When to use - Correcting the orientation of images captured at non-standard angles. - Applying precise geometric transformations for graphic design or technical documentation. - Standardizing image assets by rotating them to a specific degree while preserving transparency. ## How it works - Upload your image file in any supported format like PNG, JPEG, or WebP. - Set the desired rotation angle in degrees, where positive values rotate clockwise and negative values rotate counter-clockwise. - Configure optional settings such as background color for empty areas and output file format. - Process the image to apply the rotation matrix transformation and download your result. ## Use cases - Aligning scanned documents that were captured at a slight tilt. - Creating rotated UI elements for web design projects. - Batch-processing images to a specific orientation for consistent gallery layouts. ## Frequently asked questions ### How does the rotation matrix work? The tool uses a 2x2 rotation matrix based on sine and cosine functions to calculate the new coordinates for every pixel in your image relative to the center point. ### Can I keep the background transparent? Yes, by setting the background color option to 'transparent' and choosing PNG as your output format, you can preserve transparency in the areas created by the rotation. ### What is the maximum rotation angle? You can rotate images between -180 and 180 degrees. ### Does rotating an image affect its quality? Rotating an image involves pixel interpolation. Using a high quality setting (up to 100) for lossy formats like JPEG or WebP helps minimize visual artifacts. ### Which file formats are supported? You can upload JPEG, PNG, WebP, GIF, BMP, and TIFF files. ## Related tools - [Image Composite Matrix](https://elysiatools.com/en/tools/image-composite-matrix): Apply composite transformation by combining multiple basic transformations (scaling, rotation, shearing). See how transformation matrices multiply and create complex effects. - [Image Custom Matrix](https://elysiatools.com/en/tools/image-custom-matrix): Apply custom 2x2 transformation matrix to images. Input any four matrix values \[a, b; c, d\] to create unique transformations. Great for learning linear algebra and image processing. - [Image Scaling](https://elysiatools.com/en/tools/image-scaling): Apply scaling transformation to images with visual matrix representation. Supports uniform and non-uniform scaling with real-time preview. - [Image Shear](https://elysiatools.com/en/tools/image-shear): Apply shear transformation to create slanted or skewed images. Visualize shear matrices and see how they distort the image geometry. - [Image Translation](https://elysiatools.com/en/tools/image-translation): Apply translation transformation to move images horizontally and vertically. Visualize the translation matrix and see how pixel coordinates shift. - [Batch Image Convert](https://elysiatools.com/en/tools/batch-convert): Convert multiple images to different formats with quality settings and batch processing - [Image Affine Transformation](https://elysiatools.com/en/tools/image-affine): Apply affine transformation for scaling, rotation, shearing, and translation - [Image Linear Transformation](https://elysiatools.com/en/tools/image-linear): Apply linear transformation (a * input + b) to adjust image levels, brightness, and contrast ## Samples - [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion - [Web Image Processing TypeScript Samples](https://elysiatools.com/en/samples/web-image-processing-typescript): Web TypeScript image processing examples including image read/save, scaling, and format conversion - [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion - [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion ## Related content - [Image Geometry Transform Tools](https://elysiatools.com/en/hubs/image-geometry-transform-tools): Choose rotation, flip, crop, affine, perspective, scale, or padding transforms and verify framing, dimensions, orientation, and clean transparent or background edges.