Support guide · laser kerf bending
Kerf Bending Calculator - Laser Cut
How long the slotted zone of a living hinge has to be, why it is measured at the middle of the sheet, and how small the radius can go. Type three numbers below, or open the full living hinge generator for the cut path, 3D bend and files.
Calculator
Bend zone length W
Updates as you type.
Bend zone W =
Neutral radius R + t/2 = 31.5 mm. Enter t 1.5–12 mm, R 2–1000 mm and θ 30–180°.
Derivation
Why W is measured at the neutral axis
When a slotted sheet bends, the inside face gets shorter and the outside face gets longer. Halfway through the thickness one surface keeps its flat length: the neutral axis. Its radius is R + t/2, and an arc of θ degrees at that radius is π(R + t/2)θ/180 long. That is exactly the flat length the slits must cover.
Using the inner radius instead would make the hinge zone short by π × t/2 × θ/180, which is 2.36 mm for a 90° bend in 3 mm stock: enough to put the first solid leg into the curve and crack it.
How tight
The R_min torsion estimate in plain words
Each link between two rows of slits behaves like a short bar that twists as the sheet curves. A row spacing s bent to radius R + t/2 asks each bar to twist by roughly s / (R + t/2).
The bar can take a twist of φmax = η × γ × Lb / c. Lb = (cut length − bridge)/2 is the free length of each bar, c is the smaller of the net link and the thickness, γ is the allowed shear strain of the material and η the pattern factor.
Setting both equal gives R_min = max(t, s / φmax − t/2). For the 3 mm birch honeycomb preset that is 17.4 mm, so R 30 is Safe (at least 1.25 × R_min). Between R_min and 1.25 × R_min the studio says Marginal; below R_min, Too tight.
| Material | t (mm) | Starting kerf (mm) | Row spacing / cut length / bridge (mm) | Net link (mm) | Min link (mm) | R_min estimate (mm) |
|---|---|---|---|---|---|---|
| Baltic birch plywood | 3.0 | 0.15 | 1.8 / 20 / 2.4 | 1.65 | 0.90 | 15.4 |
| Baltic birch plywood | 4.0 | 0.18 | 2.4 / 25 / 3.2 | 2.22 | 1.20 | 22.4 |
| Baltic birch plywood | 6.0 | 0.22 | 3.6 / 35 / 4.8 | 3.38 | 1.80 | 37.3 |
| Basswood plywood | 3.0 | 0.15 | 1.8 / 20 / 2.4 | 1.65 | 0.90 | 12.6 |
| MDF | 3.0 | 0.15 | 1.8 / 20 / 2.4 | 1.65 | 0.90 | 26.6 |
| MDF | 6.0 | 0.20 | 3.6 / 35 / 4.8 | 3.40 | 1.80 | 64.5 |
| Cast acrylic | 3.0 | 0.15 | 1.8 / 20 / 2.4 | 1.65 | 0.90 | 40.7 |
Model estimate for Straight Slit with the suggested lattice and a typical CO2 starting kerf; empirical, confirm with the 5-step swatch.
Worked examples
90° and 180° bends
| Sheet | Radius | Angle | Formula | W | Rows (0.6t spacing) |
|---|---|---|---|---|---|
| 3 mm | R 30 mm | 90° | π × 31.5 × 90/180 | 49.48 mm | 28 rows at 1.8 mm |
| 3 mm | R 30 mm | 180° | π × 31.5 × 180/180 | 98.96 mm | 55 rows at 1.8 mm |
| 4 mm | R 18 mm | 180° | π × 20.0 × 180/180 | 62.83 mm | 27 rows at 2.4 mm |
| 6 mm | R 40 mm | 90° | π × 43.0 × 90/180 | 67.54 mm | 19 rows at 3.6 mm |
| 6 mm | R 50 mm | 120° | π × 53.0 × 120/180 | 111.00 mm | 31 rows at 3.6 mm |
- 01Measure the sheetEnter the real thickness t from calipers, not the nominal size; 3 mm plywood is often 2.9 to 3.2 mm.
- 02Choose the curveEnter the inner bend radius R and the bend angle θ in degrees.
- 03Read WW = π × (R + t/2) × θ / 180 is the length of sheet that must carry slits.
- 04Check R_minCompare R with the R_min estimate for your lattice, then confirm with a test strip.
Doubling the angle doubles W: the 3 mm corner goes from 49.48 mm at 90° to 98.96 mm at 180°, and the rows go from 28 to 55 at 1.8 mm spacing. R_min does not change with the angle, because each link twists the same amount per millimetre of curve.
FAQ
Questions makers ask
Does the bend angle change the minimum radius?
No. R_min depends on the lattice, the kerf, the pattern and the material, because each link twists by the same amount per millimetre of curve. The angle only changes how long the hinge zone is: 90° at R 30 in 3 mm stock needs 49.48 mm, 180° needs 98.96 mm.
What kerf value should I enter?
Cut a 20 mm square, measure it with calipers and take the difference: a 19.85 mm square means a 0.15 mm kerf. CO2 tubes on 3 mm plywood usually land between 0.10 and 0.25 mm; diode lasers are often narrower but char more.
My hinge cracked even though it showed Safe. Why?
The estimate assumes the slits run across the face grain of the outer veneer and the sheet is dry and flat. Bending with the grain, very dry stock or a bridge that lands on a knot can all fail early. That is why the swatch strips exist; bend them first.
How many slit rows fit in the bend zone?
N = floor(W / row spacing) + 1, centred in the zone so the first and last rows sit just inside the bend start and end lines. For W = 49.48 mm at 1.8 mm spacing that is 28 rows; at 180° it becomes 55 rows.