The bit that is not Pythagoras
Run and rise give the hypotenuse and everybody knows how. The part that trips a first brace up is what happens at the ends. The brace does not stop at the two theoretical points on the post face and the beam soffit; it carries on into a housing cut into each, and the two housings do not add the same amount of length even when they are cut to the same depth.
The reason is that the two faces are perpendicular to each other and the brace is not perpendicular to either. A housing half an inch deep into the beam soffit is measured vertically, so the brace has to grow by half an inch divided by the sine of its angle to reach the bottom of it. The same half inch into the post face is measured horizontally, so it costs half an inch divided by the cosine. At exactly forty-five degrees the sine and the cosine are equal and both allowances come to the same figure, which is why braces at forty-five feel simpler than they are. Move the brace off forty-five and the two numbers separate immediately.
Which angle goes on which end
The cut at the beam end has to lie flat against the beam soffit, which is horizontal, so that cut face makes the brace angle itself with the axis of the brace. The cut at the post end lies against a vertical face, so it makes the complement. On a forty-five degree brace both are forty-five and the ends are interchangeable; on anything else they are not, and cutting both ends to the same bevel setting is the classic way to lose a brace. The check is that the two angles must add to ninety. If the numbers on your bevel do not, one of them is wrong.
| Run x rise | Angle to beam | At the post | Hypotenuse |
|---|---|---|---|
| 24 x 24 | 45 | 45 | 33-15/16" |
| 36 x 36 | 45 | 45 | 50-15/16" |
| 48 x 24 | 26.57 | 63.43 | 53-11/16" |
| 24 x 48 | 63.43 | 26.57 | 53-11/16" |
What the brace costs you in space
A knee brace eats the corner of a room, and how much it eats is not the same as its run or its rise. The figure that matters if something has to pass through the corner is the perpendicular distance from the inside corner to the brace, which is the run times the rise divided by the hypotenuse. For a thirty-six by thirty-six brace the page reports 25-7/16 inches, well short of either leg. The brace also takes a diagonal footprint across the post face, longer than the brace is wide, because it crosses a vertical face at an angle: a four inch brace at forty-five degrees needs a housing 5-11/16 inches long on that face.
What this page will not decide
Nothing here is structural. It does not know why the brace is there, what it resists, whether the frame needs eight of them or twenty, or whether a brace at twenty degrees is doing anything at all. Braces resist racking, the amount of bracing a frame needs is part of its engineering, and the answer changes with the frame, the sheathing, the loads and the jurisdiction. Enter the geometry your drawing gives and the page will cut it up honestly.
Questions people ask
Why are the two housing allowances different?
Because the housings are cut into faces at right angles to each other and the brace meets them at different angles. A given depth into the horizontal beam soffit costs the depth divided by the sine of the brace angle; the same depth into the vertical post face costs the depth divided by the cosine. Only at forty-five degrees are sine and cosine equal, so only there do the two allowances match.
What angle should a knee brace be?
That is a structural decision and this page does not make it. Bracing angle, length and count are part of the frame design, decided against the loads and the geometry of the building by whoever engineered it. Forty-five degrees is common, largely because it is convenient to cut and to lay out, but common is not the same as correct for your frame.
The angles on my bevel do not add up to ninety. What went wrong?
Something got measured from the wrong reference. The two end cuts on a straight brace are always complements, because one lies against a horizontal face and the other against a vertical one. If the pair does not sum to ninety, either an angle was taken off the wrong edge or the run and rise were swapped between the ends.
How do I find the theoretical corner point on real timber?
It is the intersection of the post face and the beam soffit extended, and on a real frame it is often not a mark on anything — the timbers may be housed into each other, the post may not be square, and the corner may be hidden by another member. Establish it as a layout point first, transfer it to both timbers, and measure the run and rise from it. Every number on this page is referenced to that point.
Can I use the same figures for a wind brace or a wall brace?
The geometry is the same triangle, and the housing arithmetic works wherever a brace lands on two faces at right angles. What is not transferable is anything structural: a brace in a different plane doing a different job is a different design question, and this page has no opinion on any of them.