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Woodworking Math

Mortise and tenon calculator

How thick to make a tenon for your stock, and how wide the mortise is. Enter the thickness of the piece being mortised and the calculator applies the one-third rule, rounds it to a hollow-mortise chisel you can buy, and gives the shoulder on each cheek.

Units

Usually the leg or stile, not the rail.

Tenon thickness and mortise width

1/4 in

Traditional rule, stated by Popular Woodworking, Fine Woodworking (Taunton Press) and Woodcraft

One third of the stock
0.25 in
Each cheek shoulder
1/4 in

Why: A 1/4 in tenon (a third of 3/4 in is 0.25 in), with 1/4 in shoulders.

Why these numbers?
  1. The situation

    Stock 3/4 in thick.

    From your input: stock thickness

  2. What that means

    A tenon is traditionally about one third the thickness of the stock being mortised.

    Traditional rule: Popular Woodworking, Fine Woodworking (Taunton Press) and Woodcraft , sources [1, 2, 3]

  3. So

    Hollow-mortise chisels come in 1/4, 5/16, 3/8, 1/2 in, so 3/4 in ÷ 3 = 0.25 in rounds to the 1/4 in chisel.

    3 sources agree , sources [4, 5, 6]

  4. The number

    Each shoulder: (3/4 in − 1/4 in) ÷ 2 = 1/4 in.

    Arithmetic: exact by definition

How we source these numbers

Where the one-third rule comes from

A tenon about a third as thick as the stock it goes into leaves a third of the wood on each side of the mortise. It is a traditional rule, not a measured optimum, so the tag under the answer says so and names the references that state it. To try another size, pick a chisel in the list and the shoulders follow.

The mortise is cut with a chisel of a fixed width, so the tenon is fitted to the mortise rather than the other way round. The calculator rounds a third of the stock to the nearest of the 1/4, 5/16, 3/8 and 1/2 in hollow-mortise chisels that the three makers it cites all sell, and says when the stock is too thick or too thin for that set.

Tenon length and mortise depth are left to you: the references disagree on a rule for them, so the calculator gives none.