Sheet Imposition Rotation Calculator
Which uniform card orientation yields more pieces after trim margins and gutters?
Method, formula and assumptions
Subtract two outer margins from each sheet dimension. Along each axis, fit count = floor((usable dimension + gutter)/(piece dimension + gutter)). Compare two uniform orientations; whole sheets = ceil(quantity/best yield).
Input definitions and supported units
- Parent sheet width (mm): Measured or assumed numerical value, from 1 to 10000; must be positive.
- Parent sheet height (mm): Measured or assumed numerical value, from 1 to 10000; must be positive.
- Piece width including bleed (mm): Measured or assumed numerical value, from 1 to 10000; must be positive.
- Piece height including bleed (mm): Measured or assumed numerical value, from 1 to 10000; must be positive.
- Outer margin on each edge (mm): Measured or assumed numerical value, from 0 to 1000; zero is supported where the stated method permits it.
- Gap between pieces (mm): Measured or assumed numerical value, from 0 to 1000; zero is supported where the stated method permits it.
- Required pieces: Whole-number count, from 0 to 1000000000; zero is supported where the stated method permits it.
Worked example with answer
A 320 x 450 mm sheet with 10 mm margins, 90 x 60 mm bleed-inclusive pieces and 5 mm gutters yields 18 unrotated or 16 rotated pieces. 1,000 pieces need 56 sheets at the 18-piece yield.
How to use the results
Compare uniform orientations before quoting a run. The output never assumes mixed orientations or guillotine cut feasibility.
Results retain full precision internally and display up to four decimal places. Very small nonzero results use scientific notation rather than appearing as zero. Check the labels before comparing values across units.
Limitations and references
Not a nesting optimizer or press specification. Gripper allowance, grain direction, marks, duplex alignment and spoilage can reduce real yield.
The method is a self-contained arithmetic, geometric or explicitly stated mathematical model. There are no imported tariffs, empirical presets or equipment specifications; measured values and allowances must come from your own process.
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