Mortise and Tenon Calculator

Mortise and Tenon Calculator for sizing a tenon from the leg or stile it enters. It sets the mortise depth, checks wall thickness and miters the ends when two aprons meet in a leg.

Mortise and Tenon Calculator for Legs, Rails and Stiles

The Mortise and Tenon Calculator sizes a glued joint from the rail's thickness and width and the leg or stile's thickness and width. Enter actual milled sizes, not nominal ones, since a 2x4 apron is really 1 1/2 by 3 1/2 inches.

It returns the tenon thickness, which is also the mortise width, plus the tenon width, length and mortise depth. It also reports the thinnest mortise wall and the long-grain glue area, with a to-scale drawing and gauge settings below.

Furniture makers use it for table legs and aprons, chair rails, workbench stretchers and frame-and-panel doors. Inches are the default, with a millimeter switch that converts every entry.

Which Board Sets the Tenon Thickness

The one-third rule is a trade convention, not a code value. In Christopher Schwarz's tenon rules for Popular Woodworking, traditional texts apply it to the stock being mortised, and he calls that an important distinction.

His example joins a 7/8 inch apron to a 1 1/2 inch leg with a 1/2 inch tenon. The calculator's default settings reproduce that joint exactly, leaving a 3/16 inch cheek cut on each face of the apron.

Many online sizing formulas divide the rail thickness instead. On the same apron that gives 0.292 inch, which rounds down to a 1/4 inch chisel, so the tenon comes out half as thick. The calculator divides the leg or stile by default.

$$t=\frac{T_m}{3}$$

Here $T_m$ is the thickness of the leg or stile being mortised. The result then rounds down to the nearest chisel size in the tool's list, from 1/8 to 1 inch, or 3 to 25 mm in metric.

A thick leg on a thin rail can push one-third past what the rail can hold. When that would leave less than 1/8 inch (3 mm) of cheek on each face, the tenon is capped before rounding.

Three Rules in the Mortise and Tenon Calculator

Fine Woodworking's guide to mortise-and-tenon variations takes a 1 inch apron into a 2 inch leg. Its author calls the one-third result too weak for a table and beefs the tenon up to 3/4 inch.

The table below runs that same apron and leg through each thickness rule the calculator offers. All three rows use a 1/8 inch rail setback from the face of the leg.

The half-of-leg rule lands on the same 3/4 inch tenon Fine Woodworking chose, because the cap stops at a 1/8 inch cheek. Schwarz links half-thickness mortises to hollow-chisel mortisers, which put less sideways strain on the work than chopping by hand.

Tenon Length and Mortise Depth in a Leg

Schwarz gives a minimum tenon length of five times its thickness for most cabinetwork. A table leg often can't hold that, since a 1/2 inch tenon would need 2 1/2 inches, more than the full width of a 1 1/2 inch leg.

So the calculator defaults to two-thirds of the leg or stile width. Builders on the Fine Woodworking forum quote a range of one-half to two-thirds of the leg width for this joint. The five-times option remains for door stiles and frames with room to spare.

$$D=L+g$$

The mortise depth $D$ is the tenon length $L$ plus a glue space $g$. Fine Woodworking's guide to fitting the joint cuts the tenon about 1/32 inch short, and Woodcraft's joint guide uses about 1/16 inch.

A common slip is swapping leg thickness and leg width. Thickness runs across the mortise and sets the tenon thickness, while width is the direction the tenon travels. On a square leg the two match, but on a rectangular stile the swap changes every result.

If the depth reaches the full leg width, the calculator stops and suggests a through tenon. That option sets the length to the full width plus a proud allowance, so the end can be trimmed flush after glue-up.

When One Wide Tenon Becomes Two or More

The tenon width is the rail width less the top and bottom shoulders. Those shoulders keep the mortise below the end of the leg and above the lower edge of the apron.

$$W_t=W_r-S_{top}-S_{bot}$$

Schwarz reports George Ellis's rule that a tenon wider than six times its thickness should be split. The calculator counts how many tenons that takes and makes each tenon and each gap the same width.

Take a 3/4 inch door rail 6 inches wide into a 3/4 inch stile, with 3/4 and 1/4 inch shoulders. The 1/4 inch tenon would be 5 inches wide, twenty times its thickness, so the tool splits it into three 1 inch tenons with 1 inch gaps.

Ellis first halves the rail width and then applies the six-times test. The calculator keeps the full width between shoulders, which holds on to more cheek area for glue.

Mortise Walls, Setback and Shoulders

Most aprons sit slightly back from the face of the leg, which leaves a small reveal. That setback moves the mortise inward and adds to the wood outside it.

$$w_o=s+\frac{T_r-t}{2}$$

$$w_i=T_m-w_o-t$$

Here $s$ is the setback, $T_r$ the rail thickness and $w_i$ the wall on the inner side. With the default 1/8 inch setback, the example leg keeps 5/16 inch outside the mortise and 11/16 inch inside.

Fine Woodworking's article on strong tenons in skinny legs leaves at least 1/4 inch outside the mortise to resist splitting. It also sets tenons at least 3/8 inch below the top of the leg unless a haunch fills that space.

The default 3/4 inch top shoulder clears that limit with room to spare. If you are sizing the leg itself, the table leg calculator helps set a section with enough wood around both mortises.

Two Aprons Meeting in One Leg

With a second rail entering the adjacent face of the leg, the two mortises can run into each other. A square-ended tenon can only reach this far before it hits.

$$L_{max}=W_m-w_o-t$$

In the default joint that is 1.5 minus 0.3125 minus 0.5, or 0.6875 inch. The two-thirds rule wants 1 inch plus glue space, so the ends have to change shape.

Fine Woodworking's variations guide miters tenons that intersect so each can run longer. The Mortise and Tenon Calculator switches the Tenon Ends row to a 45-degree miter and adds its gauge line, starting 5/8 inch from the shoulder on the inner cheek.

A mitered tenon still can't pass the far cheek of the other mortise. Past that point the card turns red, and builders on Sawmill Creek suggest moving the aprons closer to the outer face to leave more wood where the tenons meet.

Two through tenons cannot cross at the same height in one leg. When both rails are set to Through Tenon, the calculator warns you to make the second joint blind.

Glue Area, Haunches and Loose Tenons

Only the tenon cheeks count as glue area, because they meet the mortise walls long grain to long grain, the surface a glued joint actually depends on.

$$A=2\times n\times w_e\times L$$

Here $n$ is the number of tenons and $w_e$ the width of each. Some formulas online add the tenon's edges too, but those meet the end grain at each end of the mortise. Woodcraft notes the joint relies far more on glue along the sides of the tenon than on its end.

The default joint gives 6.00 square inches per joint and 24.00 for a four-leg table. If you plan to glue all four at once, the clamp pressure calculator covers the clamping side of the glue-up.

A loose tenon is glued into a mortise in both parts, so each joint gets four cheeks instead of two. The calculator gives the loose tenon stock length, twice the embedded length, and how many pieces to mill.

A haunched tenon fills the top shoulder with a short stub. The calculator sizes it at one-third of the tenon length and adds its cheeks to the glue area.

Measurements to Double-Check

Measure a tapered or curved apron at the joint, not at its midpoint, since the shoulders and tenon width come from the rail width where it meets the leg.

Builders on Sawmill Creek cap a single tenon at about 4 inches wide, since wood movement becomes an issue beyond that. The wood movement gap calculator shows how far a board of that width moves in service.

Mortise and Tenon Fit and Glue-Up Questions

How tight should a mortise and tenon fit?

The joint should slide together by hand without a mallet. A long-standing answer on Sawmill Creek adds that it should still be tight enough that gravity will not pull it apart when turned on end.

Fine Woodworking warns that a fit that is too tight scrapes the glue to the bottom of the mortise, leaving a glue-starved joint. A fit that is too loose leaves too little surface contact for a good bond.

Do the tenon shoulders add strength?

Forum builders on Woodworking Talk treat the top and bottom shoulders as the structural ones on a table apron. The face shoulders mostly hide the edges of the mortise, so they add little strength.

A Fine Woodworking forum answer keeps at least 1/8 inch of shoulder at the bottom of an apron. The calculator's default bottom shoulder is 1/4 inch, twice that minimum.

Should you cut the mortise or the tenon first?

Cut the mortise first. Its width is fixed by the chisel or bit, while a tenon can be pared or sawn to fit the opening afterward. Fine Woodworking's fitting guide follows that order, then uses a spacer on the saw so every tenon matches the mortise. The chisel size in the hero result is the one to cut with.