Input variables
| Variable | Meaning | Unit |
|---|---|---|
| w | Printable sheet width | mm |
| h | Printable sheet length | mm |
| a | Transfer width | mm |
| b | Transfer height | mm |
| g | Gap between transfers | mm |
| m | Outer margin | mm |
Equations
Transfers at 0 degrees · pieces
normal = max(0,floor((w-2*m+g)/(a+g)))*max(0,floor((h-2*m+g)/(b+g)))
Transfers at 90 degrees · pieces
rotated = max(0,floor((w-2*m+g)/(b+g)))*max(0,floor((h-2*m+g)/(a+g)))
Best of these two grids · pieces
best = max(normal,rotated)
Artwork area / whole sheet · %
use = 100*best*a*b/(w*h)
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
- This compares two uniform grids; it is not a mixed-size or globally optimal nesting algorithm.
- Use the printer’s printable area, and include required cutting space in the gap field.
- A rotated transfer must be acceptable for the artwork and printer workflow.
- Utilization excludes the white-ink underbase and is an area measure, not a cost or ink estimate.
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.