Tea and gift boxes
A 160 × 100 × 80 mm box with R 25 corners needs a 486.50 mm strip; R 25 is Safe for 3 mm birch.
Living hinge generator →Laser Cut Box with Living Hinge Generator
Give the inside length, width, height and corner radius. The studio lays out one wrap strip with four 90° hinge zones, sized at the neutral axis, plus the top and bottom plates, and checks every corner against R_min.
Lattice cut length · bridge · row spacing
Fills row spacing 0.6t, cut length 5t + 5 (12–60 mm) and bridge 0.8t from the thickness.
Panel size · legs · margin
- Bend zone W
- Corner zone W90
- 25.92 mm
- Wrap strip
- 383.67 mm
- Pattern open area
- Web
- R_min estimate
- 10.0 mm
- Bend check
- Safe
Inner cuts · 1stBend guides · no cutOutline · last
Too tight.
Links too thin.
Web too thin.
Cast acrylic is brittle. Acrylic living hinges crack after a few bends; use it for flat vent panels, or cut a swatch before any hinge.
Very dense. The preview draws the first 120,000 cut-outs; the numbers count every one.
Proof preview · not a cut file
Free proof
Pro · cut-ready files of this design
Early Launch Price · 50% Off
7-Day Maker & CNC Pass · every Pro export
Proof saved. The cut-ready version of this design is in the Pro pack below.
Readout
- Panel open area
- Flat panel
- 383.67 × 60.00 mm
- Slit rows
- 72 rows
- Hinge zones
- 4
- Top + bottom plates
- 120.00 × 80.00 mm · R15.00
- Net link
- 1.35 mm
- Min link
- 0.90 mm
- Cut-outs
- Hole range
- Total cut length
- 5.18 m
R_min, laser time and open area are estimates from the torsion and area models. Confirm the bend with the 5-strip swatch before a full cut.
Pro pack · built for the design above
Production Laser DXF/SVG & 3D STEP CAD Pack
Layered, de-duplicated, cut-ordered DXF R12 and LightBurn SVG with correct kerf handling, a STEP + STL solid of this hinge, and a 5-step swatch that follows your own design.
| You get | Free | Pro |
|---|---|---|
| Every pattern, live 2D/3D, W, R_min, open area | Yes | Yes |
| Proof PNG (≤ 1000 px) + formula TXT | Yes | Yes |
| Kerf-compensated DXF R12 + LightBurn SVG | — | Yes |
| STEP AP214 + binary STL solid | — | Yes |
| 1:1 swatch + datasheet PDF | — | Yes |
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7 days of every Pro export
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Ready-made designs
Three boxes, ready to cut
Click one to load it into the studio above; every value stays editable.
How to use it
Four steps from sheet to cut file
No Generate button: every step redraws the 2D path, the 3D bend and the numbers at once.
- 01Enter the inside of the boxInner length, width and height are the space you need inside, before the wrap thickness.
- 02Choose the corner radiusR is the inner radius at each corner. It must stay at or below half the shorter side.
- 03Read the wrap stripEach corner needs W90 = π(R + t/2)/2; four of them plus the flats give the strip length.
- 04Cut strip and platesExport the strip with four hinge zones and two rounded plates, then glue the seam on a long side.
Geometry
How the wrap length is derived
Flats plus four quarter arcs, measured mid-thickness.
The inside of the strip follows a rounded rectangle of L × W with corner radius R. Each corner is a quarter arc, and a sheet only keeps its flat length at the neutral axis, half a thickness out from the inner face. So each corner uses W90 = π(R + t/2)/2 of strip.
| Corner radius | W90 per corner | Long / short flat | Wrap length |
|---|---|---|---|
| R 8 mm | 14.92 mm | 104.00 / 64.00 mm | 395.69 mm |
| R 12 mm | 21.21 mm | 96.00 / 56.00 mm | 388.82 mm |
| R 15 mm | 25.92 mm | 90.00 / 50.00 mm | 383.67 mm |
| R 20 mm | 33.77 mm | 80.00 / 40.00 mm | 375.09 mm |
| R 25 mm | 41.63 mm | 70.00 / 30.00 mm | 366.50 mm |
| R 30 mm | 49.48 mm | 60.00 / 20.00 mm | 357.92 mm |
Assembly
Seam, plates and fit
The strip starts and ends in the middle of a long side, so the glue seam lands on a flat face you can clamp against a block. The hinge zones are centred on each corner and every slit row stays one bridge away from the top and bottom edges, so the rim does not tear when you close the loop.
The two plates are L × W with corner R and sit inside the wrap. Cut them from the same sheet as the strip; because the outline is kerf-compensated outward by half the kerf, a 0.15 mm kerf gives a light press fit that glues well. Sand the plate edge, not the strip.
| Box | Corner | W90 | Wrap | R_min est. | Status |
|---|---|---|---|---|---|
| 120 × 80 × 60 mm | R 15 | 25.92 mm | 383.67 mm | 10.0 mm | Safe |
| 160 × 100 × 80 mm | R 25 | 41.63 mm | 486.50 mm | 10.0 mm | Safe |
| 90 × 60 × 40 mm | R 18 | 30.63 mm | 278.52 mm | 10.0 mm | Safe |
Where it fits
Use cases and related tools
Real jobs makers cut with these numbers, and the tool page that fits each one.
Jewelry and trinket boxes
Small boxes with large corners spend most of the strip in hinge zones; check R_min before you go tighter.
Auxetic options →Vented electronics boxes
Add a hex or slot vent to a plate with the perforated panel tool after you size the box.
Perforated panel DXF →Check a radius before cutting
Work out W and the minimum radius for any sheet with the formula explained step by step.
Kerf bending calculator →Send the file to the laser
Layer colours, cut order and import settings for LightBurn, Glowforge, xTool, RDWorks and VCarve.
DXF & SVG guide →Compare every pattern
See all 12 hinge and vent patterns with their flexibility or open-area formula before you choose.
Pattern library →Questions
Frequently asked questions
R_min values are estimates from the torsion model; confirm with a test cut.
How long is the wrap strip for a rounded box?
Wrap = 2(L − 2R) + 2(W − 2R) + 4 × W90, with W90 = π(R + t/2)/2 at the neutral axis. A 120 × 80 mm box with R 15 corners in 3 mm stock gives 180 + 100 + 4 × 25.92 = 383.67 mm.
Why is the strip measured at the neutral axis?
The inside face of a bent sheet is compressed and the outside face is stretched; only the middle of the thickness keeps its flat length. Using R + t/2 keeps the inner box size exact once the strip is wrapped and glued.
Where should the glue seam go?
The generator starts and ends the strip in the middle of a long side, away from the hinge zones. A seam on a flat face is easy to clamp, stays out of sight when the long side faces the back, and never sits on a stressed link.
What is the largest corner radius I can use?
Half the shorter side. At R = W/2 the short sides become full semicircles and the flat length is zero. Larger values are refused because the strip would no longer close around the plates.
Do the plates include finger joints or a lid hinge?
No. The pack gives the wrap strip and two plates of L × W with corner R. The plates sit inside the wrap and are glued; lids, finger joints and hardware are not part of this generator.
Same engine
The rest of the toolkit
Every tool shares one geometry engine, so numbers match between pages and files.