Lap Joint Calculator

Lap Joint Calculator settings for woodworking half-laps in real lumber sizes, from a 2x4 cross-lap to plywood corners, with the cut depth, shoulder marks and passes for each board.

Half-Lap Layouts From the Lap Joint Calculator

The Lap Joint Calculator works out woodworking half-laps, where each board is cut away so the two overlap in the thickness of one. It gives the cut depth, the shoulder marks on each board, the passes for your cutter, the glue face and the longest screw that will not break through.

"Lap joint" also names rebar lap splices and welded or bolted metal joints, which use different math. This tool is only for wood, and it covers four layouts. A cross-lap has both boards running past the joint, a T-lap ends one board mid-span on the other, an end-lap forms a corner and a splice joins two boards end to end.

Enter actual sizes, not nominal. Under the American Softwood Lumber Standard, PS 20, a dry 2x4 is 1-1/2 by 3-1/2 in and a 1x board is 3/4 in thick. A sheet sold as 3/4 in plywood usually measures 23/32 in, so its half-lap depth is 0.359 in, not 3/8 in.

Cut Depth When Boards Match or Differ

With two boards of the same thickness, each one loses half its thickness at the joint. The two then overlap in the space of one board, and both faces finish flush.

$$c=\frac{t}{2}$$

Two 1-1/2 in boards take a 0.750 in cut each. Woodsmith points out that the faces can only finish flush on both sides when the boards are exactly the same thickness, which is why it suggests running all the stock through the planer together first.

Boards that differ still work, and the joint then finishes as thick as the thicker board. The Uneven Thickness Split setting chooses how the cuts are shared between them.

Equal Cut Depths or Same Share of Each

Equal Cut Depths takes half the thinner board from both pieces. A 1-1/2 in board crossing a 3/4 in board gets two 0.375 in cuts, leaving 1.125 in and 0.375 in of wood at the joint.

$$c_1=c_2=\frac{t_{thin}}{2}$$

Same Share of Each removes the same fraction from both boards, so the thinner one is not cut down to a sliver. The fraction is the thinner board divided by the two thicknesses added together.

$$c_i=t_i\times \frac{t_{thin}}{t_1+t_2}$$

For the same pair that is one-third of each, a 0.500 in cut in the thick board and a 0.250 in cut in the thin one. Each keeps two-thirds of its thickness. Either way, the thinner board sits flush on one face and 0.750 in back from the thicker board's other face, which the Back Face Step row reports.

Setting the Blade Height on Scrap

Norm Abram told This Old House that tuning the depth and width so the pieces lap perfectly is the fussiest part of the joint, and that it pays to test on scrap first. The calculator's depth is the target, and the scrap cut confirms it.

Woodsmith sets the blade just under halfway, cuts the end of a test piece from one face, flips it and cuts again. It raises the blade in small steps until the center sliver disappears, which leaves the blade at exactly half the thickness without measuring.

Woodworker's Journal reads the test joint the same way. If the faces are offset, the tongues are too thick and the blade goes up. If there is a gap in the middle, the tongues are too thin and the blade comes down.

Shoulder Marks and Notch Width

A mid-span notch is as wide as the board crossing it, centered on the lap position you enter. The first card gives both shoulders measured from the board's own reference end.

$$x=p\pm \frac{w_{other}+f}{2}$$

Here p is the lap center, w is the width of the crossing board and f is any extra notch width. On the default cross-lap, board 1 centered at 12 in gets shoulders at 10.250 in and 13.750 in, and board 2 centered at 8 in gets 6.250 in and 9.750 in.

The extra width setting opens the notch by 1/64 or 1/32 in when you want an easier fit than a snug one. For a T-lap end, an end-lap or a splice, the shoulder sits one mating-board width or one overlap length from the end, and the cheek runs out to the end of the board.

A lap center must sit at least half a notch from the board end, or the notch would run off the board. The tool flags that before any results appear.

Passes for a Dado Stack, Saw Blade or Router

The Lap Joint Calculator counts one pass for every cutter width across the notch. The fence moves after each pass, and the last pass overlaps the one before it.

$$N=\lceil \frac{w_{notch}}{w_{cutter}}\rceil$$

A 3-1/2 in notch takes 5 passes with a 3/4 in dado stack, so the default joint needs 10 passes and four joints need 40. The same notch takes 28 passes with a 1/8 in full-kerf blade, so a dado stack cuts the same notch in far fewer passes.

With a router, the count multiplies by the depth steps. A 0.750 in cut at 1/4 in per pass is three levels for every width step, and the tool suggests taking it in stages rather than one full-depth pass.

Glue Face, Grain and Fasteners

The glue face on a cross, T or end lap is the width of one board times the width of the other, 12.25 sq in for two 3-1/2 in boards. Each board also gives up 9.19 cu in of waste, which the Waste Removed row reports.

That glue face is cross-grain, because the two boards run at right angles. The USDA Forest Products Laboratory Wood Handbook explains that bonding pieces whose grain runs in different directions builds stress as the moisture content changes. It advises gluing compatible grain directions wherever the design allows.

Framing lumber shows this quickly. One Garage Journal member warns that 2x4s used in a half-lapped workbench keep shrinking across their width and can open glued joints over time. A splice is the exception, since its two boards run the same way and meet long grain to long grain.

This Old House advises that frames built from 2-by lumber or thicker usually need mechanical fasteners, and the tool says so from 1-1/2 in stock up. The fourth card picks the longest common screw that stops 1/8 in short of the far face.

$$L_{screw}\le J-0.125$$

For a 1-1/2 in joint that is a 1-1/4 in screw, since the next common size, 1-1/2 in, would reach the far face. On uneven stock the joint is as thick as the thicker board, so J uses that thickness.

Half-Laps Outdoors and in Frames

Is a half-lap as strong as a bridle joint?

For a corner or T in square stock, one Fine Woodworking forum member rates a bridle as structurally far better than a half-lap. He adds that pinning a bridle adds real strength, while pinning a half-lap adds little.

A half-lap still wins on speed and on flat, flush frames where both faces show. When the corner carries load, the Bridle Joint Calculator sizes the slot and tenon for the same stock.

Do half-laps hold up in outdoor furniture?

Asked about white oak outdoor furniture moving between a dry and a humid climate, a Fine Woodworking forum reply favored bolts or screws over glue alone. If the joints are glued, it said the glue must be exterior grade.

That matches the cross-grain problem above, since outdoor wood swings through bigger moisture changes than indoor furniture. Screws driven from the back face keep the joint closed as the boards move.