THE NUMBERS, EXPLAINED
How to use this calculator.
Finds the fewest added blank pages within your limit, then the fewest signatures for that padded total. Signature sizes are positive multiples of four. At most 10,000 total pages; this count plan does not supply page imposition or folding instructions.
Start with your inputs
Enter interior pages, permitted signature sizes (pages), maximum blank pages allowed. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Interior pages | 100 |
| Permitted signature sizes (pages) | 16,8 |
| Maximum blank pages allowed | 4 |
A worked example
With the example inputs above, padded total pages is 104. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Padded total pages | 104 |
| Blank pages | 4 |
| Signature breakdown | 16 pages × 6, 8 pages × 1 |
| Signature count | 7 |
How this is calculated
Padded total pages
Search page totals from the requested count upward; use the first total that can be formed from allowed signatures.
Blank pages
Padded total minus requested pages.
Signature breakdown
For that total, dynamic programming minimizes signature count; report counts from largest size to smallest.
Signature count
Add the counts of all chosen signatures.
Symbols and units
- a
- Interior pages
- b
- Permitted signature sizes (pages)
- c
- Maximum blank pages allowed
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Finds the fewest added blank pages within your limit, then the fewest signatures for that padded total. Signature sizes are positive multiples of four. At most 10,000 total pages; this count plan does not supply page imposition or folding instructions.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Padded total pages; Blank pages; Signature breakdown; Signature count. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Finds the fewest added blank pages within your limit, then the fewest signatures for that padded total. Signature sizes are positive multiples of four. At most 10,000 total pages; this count plan does not supply page imposition or folding instructions.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
IngramSpark: use printer-specific cover templates ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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