You cut all six panels, you push them together, and one corner has a gap you can see daylight through. Nothing was wrong with the drawing. The numbers were wrong.
A finger joint is decided by four numbers: how wide each finger is, how many there are, how deep they go, and how much material the beam takes away. Get all four right and the box closes with hand pressure and stays closed. Get one wrong and you are sanding.
Finger width: two to three times the material thickness
Finger width, segment count and finger depth on a single edge.
In 3 mm plywood that means fingers roughly 6 to 9 mm wide. Narrower and the fingers start snapping off while you are lifting the sheet out of the machine, especially across the grain. Wider and there is barely any glue area left at the corner, so the joint looks fine and fails the first time the box is picked up by one side.
The ratio matters more than the absolute number. If you switch from 3 mm to 6 mm ply and keep the same finger width, the joint goes from correct to fragile-looking and glue-starved in one step.
Divide the edge into an odd number of segments
Take the edge length, divide by your target finger width, and round to the nearest odd number. With an odd count, one panel starts and ends with a finger and the mating panel starts and ends with a socket, so the corner reads the same from either side and both outside faces come out flush.
With an even count you get a finger at one end and a socket at the other on the same edge. It still assembles, but the two visible corners of that edge no longer match, which is obvious on a lid or a front panel.
Finger depth is the OTHER sheet thickness
This is the one that catches people who are drawing the joint by hand. The fingers on panel A have to be as deep as panel B is thick, because they pass through panel B and end flush with its outer face. If you make them as deep as panel A instead, and the two sheets are not identical, the joint sits proud or sinks below the surface.
On a box cut from one sheet the two are the same and the mistake hides. Mix a 3 mm side with a 6 mm base and it stops hiding.
Kerf: the joint is loose by twice the beam
The same 12 mm drawn twice, and what the machine hands back.
The beam has width. It removes material from both sides of every line it follows, so a finger comes out about one kerf narrower than drawn and a slot comes out about one kerf wider. Those errors add: a 0.2 mm kerf gives a joint that is roughly 0.4 mm loose.
The fix is to compensate on one side only. Grow the finger by one kerf, or shrink the slot by one kerf, not both. Doing both overcorrects and you end up hammering panels together and splitting them.
Your kerf is your own. Cut a 20 mm test square, measure it with calipers, and the shortfall is your beam width for that material at that power and speed. It moves when any of those move, so it is worth re-measuring when you change sheet stock.
Measure the sheet, every time
Sheet material is sold to a nominal thickness, not an actual one. Plywood sold as 3 mm regularly measures anywhere from 2.7 to 3.2 mm, and it can vary across a single sheet. Every number above depends on the real thickness, so measure the piece you are about to cut rather than trusting the label. This is the single most common reason a design that fitted last month does not fit today.
Doing it without redrawing the joint
All of this is arithmetic, which is exactly the kind of thing that should not be done by hand every time the material changes. In FlexCut3D you put sliders on length, width, height and material thickness, and the finger joints and slots recalculate as you drag. Set thickness to 4 mm and the joint fits. Set it to 6 mm and it still fits, with the finger count and depth following along.
Kerf has its own slider: outer edges offset outward so parts come out slightly smaller, inner cutouts offset inward so holes keep their intended size, and you watch the compensation update in the layout view while you drag. When it is right, export laser-ready SVG and send it to the machine.
It runs in the browser, so there is nothing to install: open the app and start.
What to try next
Cut one test corner before committing a whole sheet: two 60 mm squares with a single jointed edge between them. It costs a few centimetres of material and tells you in one minute whether your kerf number is right. Once that corner presses together with thumb pressure and does not fall apart, the same numbers will carry the whole box.