What n-up actually means on an estimate
N-up is the number of finished pieces that fit on one press sheet. It is the hinge of a print estimate, because every other paper figure derives from it: press sheets equals quantity divided by n-up, parent sheets equals press sheets divided by sheets-out-of-parent, and the paper line on the quote is parent sheets times the M weight price. Get n-up wrong by one and a 100,000-piece run is out by thousands of sheets.
The calculation is not simply sheet area divided by piece area. Three things eat the sheet before any piece lands on it. The gripper margin is the strip along the lead edge that the press grippers physically hold; nothing can print there, and it is set by the press, not by you. The trim margin covers colour bars, register marks and the guillotine's final cut on the other edges. And the bleed makes every piece bigger than its finished size in every direction where the image runs off the edge.
Then there is rotation. A rectangular piece in a rectangular sheet has two grid orientations, and they rarely give the same yield. In the default example — a 3.5 × 2 in business card with 0.125 in bleed on a 12 × 18 sheet — one orientation gives 20 up and the other gives 21. That is a 5% paper saving for free, and it is why this calculator always reports both.
The formula, step by step
Start with the usable area. Take the gripper off one end of the press sheet length and the trim allowance off the other end, then take the trim off both sides of the width: Lu = press length − gripper − trim, and Wu = press width − 2 × trim. On an 18 × 12 sheet with a 0.5 in gripper and 0.25 in trim, that is 17.25 × 11.5 in — 198.4 in² of the sheet's 216 in², or 91.8% of it, gone before the first piece is placed.
Then build the cell. Each piece occupies a rectangle of finished size plus twice the bleed plus any extra gutter. Twice, because the bleed extends on both sides of every trim line. Adjacent cells therefore leave 2 × bleed + gutter between one piece's trim edge and its neighbour's, which is exactly the strip the guillotine takes out in two cuts. A 3.5 × 2 in card with 0.125 in bleed occupies a 3.75 × 2.25 in cell.
Then count both grids. Divide and take the floor in each direction, because a partial piece is worth nothing, and do it twice — once with the cell as oriented, once rotated 90°. Take the larger. Floor rather than round is the whole point: 17.25 / 3.75 = 4.6 means four columns, not five.
Then convert to sheets. Press sheets of good work is the quantity divided by n-up, rounded up. Sheets to order adds two different kinds of waste that behave differently: running spoilage scales with the run, while makeready is a flat charge that is consumed getting to colour regardless of how long the run is. That is why they are applied as ⌈sheets × (1 + spoilage)⌉ + makeready and not as one combined percentage — on a 48-sheet card run, a 25-sheet makeready is more than half the paper.
Finally, parent sheets. If you buy mill parent sheets and cut them down, the number of press sheets out of one parent is the same floor-division problem one level up, tested in both cutting orientations. A 12 × 18 press sheet out of a 25 × 38 parent gives 4 out: two across the 25 and two along the 38, using 24 × 36 in of the parent's 25 × 38 in.
Worked example: 1,000 business cards on a 12 × 18 sheet
Standard US business cards, 3.5 × 2 in finished, full bleed at 0.125 in, run 1,000 up on 12 × 18 in press sheets cut from 25 × 38 in parents. The press takes a 0.5 in gripper and the shop allows 0.25 in of trim, 5% running spoilage and 25 sheets of makeready.
- Usable area. Length 18 − 0.5 − 0.25 = 17.25 in; width 12 − 2 × 0.25 = 17.25 × 11.5 in.
- Cell size. 3.5 + 2 × 0.125 = 3.75 in by 2 + 2 × 0.125 = 3.75 × 2.25 in.
- Orientation one. ⌊17.25 / 3.75⌋ = 4 columns, ⌊11.5 / 2.25⌋ = 5 rows, so 4 × 5 = 20 up.
- Orientation two. Turn the card: ⌊17.25 / 2.25⌋ = 7 columns, ⌊11.5 / 3.75⌋ = 3 rows, so 7 × 3 = 21 up. The turned layout wins.
- Press sheets. ⌈1,000 / 21⌉ = ⌈47.62⌉ = 48 sheets of good work.
- Spoilage. 48 × 1.05 = 50.4, rounded up to 51.
- Sheets to order. 51 + 25 makeready = 76 press sheets.
- Parent sheets. A 25 × 38 parent yields ⌊25/18⌋ × ⌊38/12⌋ = 1 × 3 = 3 one way, or ⌊25/12⌋ × ⌊38/18⌋ = 2 × 2 = 4 the other. Best is 4 out, so ⌈76 / 4⌉ = 19 parent sheets.
- Yield check. Product area is 1,000 × 3.5 × 2 = 7,000 in². Paper bought is 76 × 18 × 12 = 16,416 in². So 7,000 / 16,416 = 42.6% of the paper becomes card, and 57.4% is waste — most of it makeready, on a run this short.
Now run the same job at 10,000 cards. Press sheets become ⌈10,000/21⌉ = 477, spoilage takes it to ⌈500.85⌉ = 501, plus the same 25 makeready gives 526 sheets. Product area is 70,000 in² against 526 × 216 = 113,616 in², so 61.6% becomes card and waste drops to 38.4%. The makeready has not changed; it has simply been spread over ten times the run, which is the entire economics of short-run printing in two numbers.
How to read the result
Look at the two orientations before you look at anything else. When they differ, you have a free decision to make, and the only reason to take the lower one is grain direction. On sheetfed stock the grain normally runs parallel to the long dimension of the sheet, and a fold made across the grain cracks the coating on heavier papers and gives a ragged hinge on covers. For a flat piece like a business card, grain is nearly irrelevant and you should take the higher yield. For a folded piece, grain wins the argument and you accept the lower n-up.
Read the waste percentage in the context of the run length. It is a genuine measure of how much of the paper you buy becomes product, and it counts makeready, which is fixed. On short runs it will look alarming and there is nothing wrong; on long runs it converges to the geometric waste — trim, gripper and the gaps between cells — which is the part you can actually design away.
If the waste is high on a long run, change the sheet, not the layout. Try the next press size up and re-run — but do the comparison properly. A 13 × 19 sheet instead of 12 × 18 raises the same business-card job from 21 up to 24 up, so you buy 21/24 = 87.5% as many sheets. Each sheet, though, is 247/216 = 114.4% of the area, and 0.875 × 1.144 = 1.001, so on stock priced purely by area the bigger sheet is a wash. It wins only when the price per sheet, the press time saved or a use for the offcut tips it, which is why yield alone never settles the question.
Watch what parent sheets do to the arithmetic. Press sheets are rounded up, then parent sheets are rounded up again, so on short runs the parent figure can be materially more paper than the press figure suggests. It is also where the second layer of trim waste hides: the 4-out cut above uses 24 × 36 in of a 25 × 38 in parent, leaving a 1 in and a 2 in offcut that nothing recovers.
The paper weight that follows from this sheet count comes from the paper basis weight and gsm calculator, which converts a sheet count and size into M weight and total run weight for pricing and freight.
Pieces up per sheet for common sizes, at 0.125 in bleed
| Finished size | 12 × 18 in | 12.5 × 19 in | 19 × 25 in | 23 × 35 in |
|---|---|---|---|---|
| 3.5 × 2 in (business card) | 21 | 24 | 48 | 90 |
| 6 × 4 in (postcard) | 4 | 8 | 12 | 25 |
| 7 × 5 in (photo card) | 4 | 4 | 9 | 18 |
| 8.5 × 5.5 in (half letter) | 3 | 4 | 8 | 10 |
| 11 × 8.5 in (letter) | 1 | 2 | 4 | 6 |
Usable areas behind these figures are 17.25 × 11.5, 18.25 × 12, 24.25 × 18.5 and 34.25 × 22.5 in respectively. Drop the bleed to zero and several cells improve: business cards on 12 × 18 go from 21 up to 24 up, because the cell shrinks from 3.75 × 2.25 in to 3.5 × 2.0 in and eight now fit across the 17.25 in length instead of seven.
Imposition mistakes that cost paper
- Adding bleed once instead of twice. Bleed extends on both sides of every trim line, so a 0.125 in bleed adds 0.25 in to each dimension of the cell, not 0.125 in.
- Forgetting the gripper. Half an inch off an 18 in sheet is 2.8% of the length, and on a tight layout that is the difference between four columns and three.
- Rounding the division instead of flooring it. 4.6 pieces across is 4 pieces across. Rounding to 5 produces a layout that physically does not fit.
- Testing only one orientation. In the worked example the turned layout is 5% better; on other size combinations the gap is far larger.
- Combining spoilage and makeready into one percentage. Makeready is flat and dominates short runs; spoilage scales with the run. A single percentage is right at exactly one run length and wrong everywhere else.
- Ignoring grain on a folded piece. The higher n-up is worthless if the fold cracks. Decide grain first, then take the best yield available in that orientation.
- Forgetting the second rounding at the parent sheet. Press sheets round up, then parent sheets round up again, and on a small job that can be several sheets of real paper.
What a dutch cut does that this grid does not
This calculator lays out one uniform grid across the whole usable area. Estimators also use a dutch cut (also called a bastard cut), which divides the sheet into two blocks and runs a different rotation in each — for example a block of pieces running long-way at one end and a block running short-way in the strip that would otherwise be waste. On awkward size combinations a dutch cut can beat the single-grid answer, sometimes substantially. It costs an extra guillotine cut and makes the cutting instructions more error-prone, so it is worth the trouble mainly on long runs. Treat the figure here as the guaranteed-simple yield and check by hand whether a split layout does better before committing a large order.
Where this sits in the estimate
The imposition is the first of four calculations that price the paper on a job. First the yield, which is this page. Second the sheet count, which is quantity, spoilage and makeready applied to the yield. Third the paper weight, from grammage and sheet area — the basis weight and gsm calculator converts a sheet count into an M weight and a run weight in pounds and kilograms, which is what the mill prices against. Fourth the freight, which for a skid of paper depends on both weight and cube; the freight density and class calculator settles the LTL classification and the dimensional weight calculator covers parcel shipments of the finished job.
Bindery changes the geometry. A folded and bound product is imposed in signatures, not in flat pieces, and page count, creep and trim all enter. For a bound book the spine dimension follows from the page count and the caliper of the stock rather than from anything on this page — the book spine width calculator handles that side. For a folding carton the flat blank is the piece to enter here, and the structural performance of the finished box is a separate question answered by the box compression strength calculator.
Digital presses shift the trade-offs but not the arithmetic. A toner or inkjet cut-sheet device usually has a smaller gripper and no plate makeready, so the makeready allowance falls sharply and short runs stop looking so wasteful. The geometry is unchanged: enter the device's own unprintable margin as the gripper and set makeready to the few sheets your operator actually uses.
Key terms
- N-up
- The number of finished pieces imposed on one press sheet. Also written "up", as in "21 up".
- Gripper margin
- The strip along the lead edge held by the press grippers. Unprintable, fixed by the press, and taken off the sheet before layout.
- Bleed
- Image extended past the trim line so that a small cutting variation does not leave a white sliver. Adds twice its value to each cell dimension.
- Makeready
- Sheets consumed bringing the press to colour and register before the first saleable sheet. A flat quantity, not a percentage.
- Parent sheet
- The mill-size sheet that press sheets are cut from, such as 25 × 38 in for text stock.
- Dutch cut
- A layout that splits the sheet into blocks running at different rotations to recover area a single grid would waste.