Joinery Proportion Calculator
The one-third tenon rule is a derivation, not a tradition: x = (t-x)/2 solves to exactly t/3, where the tenon equals one mortise wall.
Box joints and dovetails
Where the one-third tenon rule comes from
It is repeated everywhere as a tradition and it is actually a derivation. A tenon of thickness x cut from stock of thickness t leaves two mortise walls, each (t − x)/2. Set the tenon equal to one wall — so neither is the obvious weak point — and:
x = (t − x)/2 ⟹ 2x = t − x ⟹ x = t/3
Exactly one third. Not approximately — the tenon and each mortise wall come out identical at every stock thickness. Deviate and you simply choose which part fails first:
| Fraction | Tenon | Each wall | Weaker part |
|---|---|---|---|
| 0.2 | 0.300″ | 0.600″ | tenon |
| 0.25 | 0.375″ | 0.563″ | tenon |
| one third | 0.500″ | 0.500″ | balanced |
| 0.4 | 0.600″ | 0.450″ | walls |
| 0.5 | 0.750″ | 0.375″ | walls |
On 1½″ stock a third is exactly ½″, which is why ½″ mortise chisels are so common — the tool exists because the arithmetic keeps landing there.
Odd fingers, or the joint looks accidental
A box joint with an odd number of fingers starts and ends with a finger on the same board, so both edges of the joint match and it reads as deliberate. An even count leaves one board starting with a finger and the other with a socket, which looks like it happened rather than like it was planned. The finger width is simply the board width divided by the count, so pick the count first and let the width fall out — the reverse gives you a part-finger at one end, which is the other way this joint goes wrong.
Dovetail slopes are closer together than the argument suggests
| Slope | Angle | |
|---|---|---|
| 1:4 | 14.04° | Steep — strong mechanically but leaves fragile short grain at the tail corners. |
| 1:5 | 11.31° | Steep — strong mechanically but leaves fragile short grain at the tail corners. |
| 1:6 | 9.46° | The conventional softwood angle. |
| 1:7 | 8.13° | The conventional hardwood angle. |
| 1:8 | 7.13° | The conventional hardwood angle. |
| 1:10 | 5.71° | Shallow — very little short grain, but approaching a finger joint in behaviour. |
The conventional advice is 1:6 for softwood and 1:8 for hardwood, and those are 2.34 degrees apart. Two and a third degrees is less than most people's sawing accuracy, which is worth knowing before spending an evening arguing about it. The reason to prefer a shallower slope in hardwood is not mechanical grip — it is that a steeper tail leaves more short grain at its corners, and hardwood short grain breaks off when you knock the joint together.
Notes
- Cut the mortise first. It is far easier to trim a tenon to fit a mortise than the reverse, so the mortise sets the size and the tenon chases it.
- Round to a chisel you own. The tool shows the nearest sixteenth, because a tenon sized to a chisel you have beats a tenon sized to three decimal places.
- Tenon length matters more than thickness for racking. A third of the stock thickness is about strength in shear; resistance to a frame racking comes mostly from the tenon's width and length, not how thick it is.
- These are proportions, not engineering. A joint carrying a real structural load needs more than a rule of thumb — this is furniture-scale guidance.
How to use
- Enter your stock thickness for the tenon and mortise sizes.
- Round to a chisel you actually own — the tool shows the nearest sixteenth.
- Use an odd finger count on box joints so both edges match.
- Cut the mortise first and trim the tenon to fit it.
Frequently asked questions
How thick should a tenon be?
One third of the stock, and that is a derivation rather than a tradition. A tenon of thickness x leaves two mortise walls of (t−x)/2 each. Set the tenon equal to one wall and x = (t−x)/2 solves to exactly x = t/3 — the thickness at which neither is the obvious weak point.
What happens if the tenon is thinner or thicker than a third?
You choose which part fails first. Thinner and the tenon is the weakest element; thicker and the mortise walls are. Neither is wrong if you know which you are doing — a through tenon in thin stock is often deliberately thinner than a third.
Why are half-inch mortise chisels so common?
Because a third of one-and-a-half-inch stock is exactly half an inch, and inch-and-a-half is the commonest thickness for furniture legs and frames. The tool exists because the arithmetic keeps landing on that number.
How many fingers should a box joint have?
An odd number. That way the joint starts and ends with a finger on the same board, so both edges match and it reads as deliberate. An even count leaves one board starting with a finger and the other with a socket, which looks accidental.
How do I work out box joint finger width?
Board width divided by the finger count. Pick the count first and let the width fall out — doing it the other way round leaves a part-finger at one end, which is the commonest way this joint goes wrong.
What dovetail angle should I use?
The convention is 1:6 for softwood and 1:8 for hardwood, which are 9.46 and 7.13 degrees. Worth knowing before spending an evening on it: those are only 2.34 degrees apart, which is less than most people’s sawing accuracy.
Why use a shallower dovetail angle in hardwood?
Not for mechanical grip — almost any slope resists pull-out adequately. It is that a steeper tail leaves more short grain at its corners, and hardwood short grain snaps off when you knock the joint together. The angle is chosen for the grain, not the mechanics.
Should I cut the mortise or the tenon first?
The mortise. It is far easier to pare a tenon down to fit a mortise than to enlarge a mortise accurately, so let the mortise set the size and have the tenon chase it.
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