Units and stored dimensions
One inch equals exactly 25.4 millimetres. ISO A-series presets are stored in millimetres; US paper and photo formats are converted from their native inch dimensions. This avoids repeatedly copying rounded inch equivalents back into later calculations.
Centimetres are converted to millimetres by multiplying by 10. Inches are converted by multiplying by 25.4. Orientation swaps the two stored edges but does not alter the physical format or aspect ratio.
Pixels and physical print size
Required pixels equal physical inches multiplied by the selected PPI. Available print inches equal source pixels divided by PPI. Width and height are calculated separately because a file and a print can have different proportions.
All displayed raster dimensions are rounded to the nearest whole pixel only after the full unit conversion and multiplication. Intermediate values remain unrounded. Pixel inputs are positive whole numbers; physical sizes and PPI must be positive finite values.
Effective PPI
Horizontal effective PPI equals usable pixel width divided by printed width in inches. Vertical effective PPI uses usable pixel height and printed height. The lower value is reported as the limiting density when the image fills the target.
Effective PPI is different from a resolution tag saved in file metadata. Changing a tag from 72 to 300 without resampling changes the suggested physical scale, not the number of image pixels or the captured detail.
Aspect ratio and crop retention
The fill-crop estimate compares the source width-to-height ratio with the target ratio. Retained area is the smaller ratio divided by the larger ratio after the orientations are aligned; cropped percentage is one minus that retained fraction.
For example, a portrait 2:3 image filling a portrait 4:5 print retains about 83.3% of its area and removes about 16.7%. Moving the crop changes which part is removed, but the ratio still determines the amount removed. A print laboratory may apply an additional production crop that this geometric estimate cannot predict.
Bleed, trim and safe area
The full artwork canvas equals trim size plus bleed on both opposing edges. A 210 × 297 mm trim with 3 mm bleed therefore becomes 216 × 303 mm. The safe area equals trim size minus the chosen safe margin on both edges.
Bleed and safe margin are deliberately editable because provider requirements differ. The calculator does not silently assume that 3 mm bleed or a 5 mm safe margin applies to every product.
Quality labels and tolerance
Meets target allows a 0.1% tolerance for unavoidable whole-pixel rounding. Close to target means at least 80% of the selected target; Limited means at least 50%. Below that level, the interface warns that more source pixels or a smaller print is needed.
These labels compare a calculated density with the visitor's selected target. They do not judge focus, motion blur, compression, sharpening, color, paper, printer screening or viewing distance and must not be treated as a production guarantee.
Verification and correction process
Automated tests cover known conversions, common paper presets, orientation changes, crop ratios, bleed boxes, readiness thresholds and invalid input. Rendered-page checks cover crawlable links, self-canonical URLs, structured metadata and public sitemap entries.
When a calculation report is received, the numerical inputs are reproduced in a deterministic test before the displayed explanation is changed. Material content revisions update the public review date and sitemap last-modified value.
Methodology you can inspect and reproduce
The formulas described above are implemented in one shared module and checked by deterministic tests. External references are used for fixed definitions; provider-specific production requirements are deliberately left editable.