Sheet Nesting Calculator
Find how many rectangular parts fit on a sheet, the material utilization and how many sheets a job needs.
Inputs
Result
Parts per sheet
67pcs
- Material utilization
- 89.3%
- Best layout
- Mixed orientations
- Sheets needed
- 3for 200 parts
- Parts on the last sheet
- 66
Formula
Parts per row = ⌊(Usable length + Gap) ÷ (Part length + Gap)⌋
Results are estimates and should be verified for critical engineering or manufacturing applications.
How it works
The calculator lays rectangular parts on the sheet in a grid and counts how many fit. It tries the part in both orientations, then tries mixed layouts where a block of parts in one direction is combined with the leftover strip filled by rotated parts. It keeps the layout that fits the most parts.
- Gap is the space between parts: the cutting kerf plus any spacing your process needs.
- Edge margin is the unusable border around the sheet, for clamping or edge quality.
- Add a quantity to see how many sheets the job needs.
It's a quick estimate for quoting and material ordering. Nesting software can place irregular parts more tightly, so real yields are often equal or better.
Formula
- Usable size = Sheet size − 2 × Edge margin
- Parts per row = ⌊(Usable length + Gap) ÷ (Part length + Gap)⌋
- Parts per sheet = best of all layouts tried
- Utilization = Parts × Part area ÷ Sheet area
- Sheets needed = ⌈Quantity ÷ Parts per sheet⌉
Example
300 × 200 mm parts on a 3,000 × 1,500 mm sheet, 5 mm gap, 10 mm margin
- 1Usable area: 2,980 × 1,480 mm
- 2Straight: 9 × 7 = 63 parts · Rotated: 14 × 4 = 56 parts
- 3Mixed: 63 straight parts plus 4 rotated parts in the leftover strip = 67 parts
- 4Utilization: 67 × 0.06 m² ÷ 4.5 m² = 89.3%
- 5For 200 parts: ⌈200 ÷ 67⌉ = 3 sheets
67 parts per sheet, 3 sheets for 200 parts.
Frequently asked questions
What gap should I use for laser cutting?
Laser kerf is usually 0.1–0.4 mm, but most shops leave 3–10 mm between parts to avoid heat distortion and keep the skeleton rigid. Use the spacing your nesting software is set to.
Can I use it for plywood, glass or fabric?
Yes. The math works for any rectangular parts on a rectangular sheet. Set the gap to the saw kerf or cutting allowance.
Why is my nesting software getting more parts?
Software can mix many orientations, use common-line cutting and fit parts into holes. This calculator uses rectangular grids, which is a reliable lower bound.