How the Laser Cut Box Generator Works
A finger-jointed box is six (or five) flat panels whose edges are cut into alternating tabs and notches. Each tab on one panel drops into a notch on the next, so the box locks square and glues up with lots of long-grain contact.
The generator starts every panel as its full outside rectangle and cuts notches into it one material thickness deep. The front and back panels keep all eight corners. The bottom and lid meet the front and back along their full width, and meet the two sides only in the space between the front and back walls. Every edge gets an odd number of equal fingers, so the pattern is the same from either end and the two halves of a joint always match.
The Formulas
1. Inside and outside sizes
outer W = inner W + 2t
outer D = inner D + 2t
outer H = inner H + t (open) or + 2t (lid)
t is the material thickness. Use your measured thickness, not the label on the sheet.
2. Fingers on each edge
n = nearest odd number to L ÷ target
finger = L ÷ n
sides to bottom: L = D − 2t
Automatic picks a target of 3 × t. Fingers are kept at least one thickness wide.
3. Kerf compensation
cut line = part edge + kerf ÷ 2 (outwards)
tab drawn = finger + kerf
notch drawn = finger − kerf
The beam burns away half the kerf each side of the line, so after cutting both tab and notch are back to the finger width and the joint is snug.
4. Living hinge bend
hinge length = (R + t ÷ 2) × angle × π ÷ 180
lines = zone width ÷ spacing + 1
R is the inside bend radius. The length is measured at mid-thickness, which neither stretches nor squashes much as the panel bends.
Worked Example
Open tray, inside 100 × 60 × 40 mm, 3 mm birch ply, kerf 0.15 mm, automatic fingers
- Outside: 100 + 6 = 106 mm wide, 60 + 6 = 66 mm deep, 40 + 3 = 43 mm tall.
- Target finger 3 × 3 = 9 mm. Width edge: 106 ÷ 9 = 11.8, nearest odd is 11, so 11 fingers of 9.64 mm.
- Sides to bottom run between the front and back walls: 66 − 6 = 60 mm, 60 ÷ 9 = 6.7, so 7 fingers of 8.57 mm.
- Corners: 43 ÷ 9 = 4.8, so 5 fingers of 8.6 mm up each corner.
- Kerf: each width-edge tab is drawn 9.64 + 0.15 = 9.79 mm and each notch 9.64 − 0.15 = 9.49 mm. The front panel's cut outline measures 106.15 × 43.15 mm and comes out of the laser at 106 × 43 mm.
- Five parts laid out with 5 mm spacing fit on a sheet about 217 × 162 mm.
Practical Tips
- Measure your kerf. Cut a 20 mm square, measure it with calipers, and subtract from 20. A square that measures 19.84 mm means a kerf of 0.16 mm. Do it in the same material, power, speed and focus you will cut the box with.
- Test one joint first. Cut a small open tray before a big box. Too tight: lower the kerf figure a little. Too loose: raise it.
- Cut inner shapes first. Divider slots are in their own group in the SVG and on the HOLES layer in the DXF, so your laser software can cut them before the outlines.
- Glue and clamp. PVA wood glue works well on plywood and MDF. Check the box is square across the diagonals before the glue sets.
- Settings. Start with the diode laser settings page for speed, power and passes, and check scale on import: the SVG is 1 unit = 1 mm.
- Making a part from scratch rather than a box? The DXF part maker draws plates, flanges and gears, and the sheet cut optimizer nests rectangles on a sheet. The article how to make DXF files covers file prep in more depth.
- Safety. Never leave a laser running unattended, keep a fire extinguisher nearby, and extract the fumes. Do not cut PVC or vinyl: they give off chlorine compounds that harm you and the machine.
Frequently Asked Questions
Measure it rather than guess, because it changes with the lens, focus, power, speed and material. Cut a 20 mm square and subtract its measured size from 20 mm. On 3 mm ply it is often somewhere around 0.1 to 0.2 mm, but your figure is the one that counts.
Loose joints usually mean the kerf figure is too small (or zero), or the sheet is thinner than you entered. Tight joints mean the kerf figure is too big or the sheet is thicker. Measure the sheet with calipers, enter that thickness, and change the kerf in steps of about 0.02 mm until a test joint pushes together by hand.
Around two to four times the material thickness looks right and is strong; the automatic setting aims for three. Narrow fingers char and snap more easily, wide ones give fewer glue faces. The generator keeps an odd number of equal fingers on every edge, so the actual width is close to, not exactly, your target.
Thin plywood and MDF, around 3 mm, are the usual choice because the wood fibres flex. Acrylic is brittle and tends to crack, so most people avoid it for hinges. Results vary with the sheet, so cut a short test strip and bend it before cutting the real part.
The SVG sets its width and height in millimetres with one unit equal to one millimetre, so most laser software (LightBurn, xTool Creative Space, Inkscape) imports it at true size. If yours scales it, check its SVG import DPI setting, or use the DXF and choose millimetres as the import unit. Measure one panel on screen before cutting.
The generator draws the geometry; it cannot know your laser. Kerf, sheet thickness and fit vary, so cut a test joint before a whole box, and follow your laser maker's safety instructions.