Worked example
A 4,000 × 3,000 px rectangle rotated 30° needs at least a 4,965 × 4,599 px axis-aligned canvas. At 300 PPI, that canvas is 16.55 × 15.33 in.
The new corners are empty space
The result is the outer axis-aligned bounding rectangle, not a crop that is completely filled with image content. Unless the image is turned by a multiple of 90°, triangular empty regions remain at the corners of the new canvas.
Rotation does not create detail
Raster rotation can resample pixels. The required canvas size keeps the original rectangle from being clipped in ideal geometry; it does not guarantee sharpness or a particular interpolation method. Some editors may add an extra pixel because of their sampling and edge conventions.
Choose the print PPI separately
The physical dimensions describe the whole new canvas at your entered pixels per inch. For the visible photo alone or a trimmed region, use actual post-rotation pixel dimensions. W3C’s rotation matrix supplies the sine and cosine geometry behind the bounds.
Explore the related calculation
For a different starting point, try the photo mat opening calculator or return to the main calculator. Browse the complete tool directory for this site.
Reference and corrections
The definitions and assumptions above follow these sources; the examples and calculator arithmetic are original to this page.
Found a problem? Email contact@pixelstoinches.org.