Units, precision and validation
Physical inputs are normalized to millimetres. Intermediate calculations retain JavaScript double precision; only displayed values are rounded for readability. Dimensions and quantities must be positive, gaps cannot be negative, countable items must be whole numbers, and waste must be at least 0% and less than 100%.
Whole-label capacity
Capacity is rounded down to complete labels before waste. Waste is then applied to that whole-label capacity and rounded down again. Required rolls and ribbons are rounded up because partial consumable units cannot satisfy a production requirement.
Roll geometry
Web length uses the ideal annular-area model L = π(D² − d²)/(4t), where D is outer diameter, d is core outside diameter and t is combined wound-layer caliper. Label count divides web length by feed pitch. This calculation is exact for the idealized geometry but actual roll yield remains an estimate because compression, adhesive, winding tension and construction vary.
Actual printhead resolution
Raster calculations use dots = millimetres × actual dots/mm, equivalently millimetres ÷ 25.4 × actual DPI. Presets use 8, 12 and 24 dots/mm, exactly equal to 203.2, 304.8 and 609.6 DPI. The familiar 203, 300 and 600 DPI descriptions are nominal labels. A custom actual DPI option is available for other hardware. Zebra documents these standard dots/mm values in its ZPL printhead resolution reference.
Raster rounding
Nearest rounding minimizes absolute geometric error. Floor keeps the raster from exceeding a physical boundary; ceiling keeps it from falling below one. A result below one dot is rejected, and ZPL print width is rejected below the documented two-dot minimum.
ZPL dimensions
^PW sets print width in dots. Zebra documents ^LL as necessary for continuous media; by default it applies only to continuous media, while the optional Y parameter applies the value to all media. Gap and mark media can derive length through calibration. Review the official ^PW reference and ^LL reference for the target printer.
Barcode dimensions
The optimizer selects the closest candidate among user-allowed whole-dot module widths. It intentionally provides no compliance threshold or universal quiet zone: use the current symbology and application specification. GS1 documents application-specific X-dimensions, quiet zones, height and verification requirements in its General Specifications.
Check digits
GTIN and SSCC checks use the GS1 modulo-10 method: body digits are weighted 3 and 1 from right to left and the final digit completes the next multiple of ten. A valid checksum detects errors but does not establish allocation, ownership or authorization. Batch validation applies the same deterministic function independently to each complete identifier.
Cost accounting boundaries
Proportional consumed cost values material at its waste-adjusted usable yield. Whole-unit purchase cost rounds rolls and ribbons up before applying unit prices. Direct-thermal mode excludes ribbon quantities and cost. Purchase cost assumes every required unit is bought specifically for the job and does not credit existing inventory or leftover stock. Setup is included in both views; unentered freight, tax, wear, downtime and finishing remain excluded.
A label-failure estimate is a separate incremental worksheet. It combines documented replacement production, rework labor, measured downtime and attributable charges; it does not assume a universal failure rate or speculative penalty.
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