Input variables
| Variable | Meaning | Unit |
|---|---|---|
| w | Usable roll width | mm |
| a | Decal width | mm |
| b | Decal height | mm |
| gap | Gap | mm |
| n | Decals needed | pieces |
| leader | Total leader and trailer | mm |
Equations
Decals across roll · pieces
cols = floor((w+gap)/(a+gap))
Rows required · rows
rows = ceil(n/max(cols,1))
Roll length if width fits · m
length = (rows*b+max(0,rows-1)*gap+leader)/1000
Notation
PI means π. ** means a power, sqrt means square root, and abs gives the absolute value. Trigonometric functions use radians. min and max select the smallest or largest argument.
ceil rounds upward, floor rounds downward, and round rounds to the nearest integer with halves toward positive infinity. roundup(value, step) rounds upward to the next multiple of the step; a zero step leaves the value unchanged.
Assumptions
- If the across-roll result is zero, the chosen orientation does not fit; the length result is not a feasible cutting plan.
- Use the cutter’s usable width after pinch-roller exclusions.
- Weeding borders and registration marks need their own allowance in decal size or gap.
- Grain, pattern direction or adhesive orientation can prevent rotation.
Precision and verification
The tool uses ordinary double-precision numeric arithmetic. Output is displayed to at most four decimal places; measurement precision is usually much lower. Check the worked examples, your project’s specifications, and a real sample before committing material.