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Pieces per sheet calculator

To find how many pieces fit on a sheet, take each side of the sheet, subtract the edge margin twice, add one spacing gap, divide by the piece size plus the spacing and round down. Multiply the two directions, repeat with the piece turned 90°, and keep the larger count. A 12 × 20-inch sheet holds 30 pieces of 2 × 3 inches with 1/8-inch spacing and a 1/4-inch edge margin, 5 across and 6 down. Rotated, only 27 fit. Either way, 25% of the sheet becomes offcut. Use inches, millimetres or any unit, as long as every size is in the same one.

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Calculator

How many fit on your sheet

Result · Sheet yieldFig. 1

Pieces per sheet

The normal orientation fits more.

Offcut: 25.0%
Sheet used: 75.0%
Material / piece: $0.355

Normal Best

5 × 6 = 30

Rotated 90°

3 × 9 = 27

Show the math

The calculator lays the pieces out in a single uniform grid, once as entered and once turned 90°, and reports the better of the two.

Pieces along a side: ⌊(sheet side − 2 × edge + spacing) ÷ (piece side + spacing)⌋
Normal layout: along(sheet width, piece width) × along(sheet height, piece height)
Rotated layout: along(sheet width, piece height) × along(sheet height, piece width)
Pieces per sheet: the larger of normal and rotated
Offcut: 1 − pieces × piece width × piece height ÷ (sheet width × sheet height)
Material per piece: sheet cost ÷ pieces per sheet ÷ (1 − extra waste)

Why add one spacing gap? Five pieces in a row need only four gaps between them. Adding a gap to the usable length and dividing by piece-plus-gap counts exactly that: n pieces and n − 1 gaps.

Worked examples

2 × 3-inch keychains on a 12 × 20-inch sheet

Spacing 0.125", edge margin 0.25". Across the 12" side: ⌊(12 − 0.5 + 0.125) ÷ 2.125⌋ = ⌊5.47⌋ = 5. Down the 20" side: ⌊(20 − 0.5 + 0.125) ÷ 3.125⌋ = ⌊6.28⌋ = 6. That's 30 pieces. Rotated, 3 across and 9 down make 27. The 30 pieces cover 30 × 6 = 180 of the sheet's 240 square inches, so the offcut is 25%. At $9.80 a sheet and 8% extra waste, material comes to $9.80 ÷ 30 ÷ 0.92 = $0.355 per piece.

3.5-inch square ornaments on the same sheet

A square piece gives the same count both ways: 3 across, 5 down, 15 pieces. They cover 15 × 12.25 = 183.75 square inches, an offcut of 23.4%. At $3.50 for a birch sheet and 10% waste, that's $0.259 per ornament.

Metric: 50 × 30 mm tags on a 600 × 400 mm sheet

Spacing 3 mm, edge 5 mm. Normal: ⌊593 ÷ 53⌋ = 11 across and ⌊393 ÷ 33⌋ = 11 down, 121 pieces. Rotated: ⌊593 ÷ 33⌋ = 17 across and ⌊393 ÷ 53⌋ = 7 down, 119. The normal layout wins by two, with a 24.4% offcut. Nothing about the formula changes with the unit.

Offcut is already in your material cost

Dividing the sheet cost by the number of pieces spreads the whole sheet, offcut included, over the pieces you sell. That's why the 25% offcut on the keychain sheet doesn't need its own line in a price. The extra-waste percentage is for losses on top: test cuts, a flawed sheet, a scratched piece. Count the offcut once, not twice. If you sell small items cut from the leftover strips, you can lower the waste figure to reflect that.

When you can beat the grid by hand

Mixed orientation. If the strip left along one side is wider than the piece's other dimension, an extra row of rotated pieces may fit. The calculator counts one uniform grid, which is the number you can repeat sheet after sheet.
Shared cut lines. Rectangles that touch can share a single cut. Set spacing to 0 to count that layout.
Irregular shapes. Enter the bounding box (the smallest rectangle around the shape). Nesting software can interlock irregular parts more tightly; treat the grid count as the safe figure to price on.

Questions about sheet yield

How many pieces can I cut from a 12 × 20-inch sheet?

It depends on the piece size, spacing and edge margin. With 1/8-inch spacing and a 1/4-inch margin, a 12 × 20-inch sheet fits 30 pieces of 2 × 3 inches or 15 pieces of 3.5 × 3.5 inches. Enter your own sizes above to get the exact count for your design.

Does the calculator work in millimetres?

Yes. It has no built-in unit, so it works in millimetres, centimetres or inches. Enter every size, spacing and margin in the same unit and the count comes out the same as if you had converted.

Does it account for laser kerf?

Kerf is the width of material the beam removes. If your pieces need a clear gap between them, include the kerf in the spacing you enter. If neighbouring pieces share one cut line, set spacing to 0.

Why does rotating the pieces change the count?

Because each direction rounds down separately. A 2 × 3 piece on a 12 × 20 sheet fits 5 × 6 = 30 one way but only 3 × 9 = 27 the other, since the leftover space on each side is different. The calculator checks both and uses the larger.

How do I work out the material cost per piece?

Divide the sheet cost by the pieces per sheet, then divide by one minus your extra waste percentage. A $9.80 sheet holding 30 pieces with 8% waste costs $0.355 per piece. Enter a sheet cost above and the calculator does this for you.

What about round or irregular shapes?

Enter the width and height of the smallest rectangle that contains the shape. Round pieces in a square grid waste the corners between them, so the count is conservative; staggered rows or nesting software may fit a few more.