Chair Angle Calculator

Chair Angle Calculator converts rake and splay into the sightline and resultant you bore along for front and back legs, then works out leg length, the footprint and all stretchers.

Chair Angle Calculator for Boring Leg Mortises

Chair legs lean in two directions at once, which makes them hard to bore by eye. The Chair Angle Calculator turns that lean into one line drawn on the seat and one bevel setting, for the front pair and the back pair separately.

It is built for Windsor chairs, staked chairs and stools, where round tenons go into bored mortises. Beyond the bore angles, it works out leg length, where the feet land and how long the stretchers run.

Rake is the lean you see from the side of the chair, and splay is the lean you see from the front. Both are measured from vertical in degrees, which matches the convention Lost Art Press prints on its Chairpanzee layout tool.

From Rake and Splay to One Bevel Setting

Look at a leg from the right direction and it appears dead vertical. That viewing line, drawn on the seat, is the sightline. The true lean along it is the resultant, and chairmakers bore along the sightline with a bevel set to the resultant.

$$\tan \alpha =\frac{\tan r}{\tan s}$$

$$R=\arctan \sqrt{{\tan }^{2}r+{\tan }^{2}s}$$

Here $r$ is rake, $s$ is splay, $\alpha$ is the sightline and $R$ is the resultant. This is the trigonometry behind the sightline method described in Drew Langsner's The Chairmaker's Workshop, and the same relationship Peter Galbert lays out with a graphical scale.

The default front legs have 5 degrees of rake and 10 of splay. That gives an 11.1 degree resultant along a 26.4 degree sightline. Galbert points out a handy check, since equal rake and splay always put the sightline at 45 degrees.

The sightline is measured from a baseline, the line joining the two front mortise centers on the seat underside. Lost Art Press sets 0 degrees on that line and repeats the layout for the back pair from its own baseline. The Chair Angle Calculator uses the same reference.

Watch which way your bevel reads. Published plans give the setting as the resultant measured from square, but a bevel laid against the flat seat reads the complement. The tool shows both, so 11.1 degrees from square is 78.9 degrees on the seat surface.

Why Seat Tilt Changes the Bore Angles

Rake and splay are design angles taken from the floor. Once the seat tilts back, the mortises have to be bored relative to the seat, not the floor. A reader note on Lost Art Press warns that skipping this correction shows up only when you level the finished chair and the rake looks wrong.

With the seat front raised by $p$ degrees, the rake measured from the seat changes by exactly the tilt angle. The splay shifts slightly too.

$$r_f^{\prime }=r_f-p$$

$$r_b^{\prime }=r_b+p$$

$$\tan s^{\prime }=\frac{\tan s}{\cos p\pm \tan r\sin p}$$

In the splay formula, use plus for the front legs and minus for the back legs. A 5 degree tilt cancels a 5 degree front rake completely. The front legs then bore at 10.0 degrees straight along the baseline, while the back legs grow from 17.8 to 22.1 degrees on a 63.5 degree sightline.

If the tilt is larger than the front rake, the leg leans backward relative to the seat. The tool flags this and tells you to lay the sightline out on the opposite side. Tilt is accepted from -15 to 20 degrees, and any setting that would point a leg up into the seat stops the calculation.

Leg Length, Foot Spread and Stretchers

Leg length runs along the centerline from the seat underside to the floor. On a level seat it depends on the seat height $h$, the seat thickness $t$ and both angles.

$$L=(h-t)\sqrt{1+{\tan }^{2}r+{\tan }^{2}s}$$

An 18 in seat that is 1-3/4 in thick leaves 16-1/4 in of drop. With the default angles, the front legs measure 16.562 in and the back legs 17.066 in. Blank length then adds the angled path through the seat and your through-tenon, so the front legs start at about 18-7/8 in.

Each foot moves out by the drop times the tangent of the splay. Front mortises 13 in apart put the front feet 18.731 in apart, and the full footprint runs 16.776 in from front feet to back feet. Check that spread against your floor space before you bore.

Stretcher lengths are figured center to center at the stretcher height, then one leg diameter comes off for the shoulders. Add both tenon lengths to get the blank. At a 6 in stretcher height, the defaults give a 14.677 in side stretcher between centers.

Treat those stretcher figures as planning numbers for stock and turning. Builders like the author of a Canadian Woodworking Windsor project measure between the dry-fit legs and add about 1/4 in. The extra length pushes the legs slightly apart so each stretcher stays tight in its sockets.

Seat heights from 6 to 40 in and rake or splay from 0 to 45 degrees are accepted. The tool warns above a 30 degree resultant because the feet reach well past the seat edge. How a chair holds up still varies with species, moisture content and how snug the tenons are, so dry-fit before glue-up.

If you turn your own legs and stretchers, the Lathe Speed Calculator sets the spindle speed for each blank diameter. For a seat height that suits a particular person, the Ergonomic Desk Calculator works it out from body height first.

Chair Leg Angles Builders Ask About

What angle should chair legs be?

There is no standard, and published builds vary widely. A Woodworkers Institute smoker's bow Windsor uses 10 degrees at the front and 15 at the back. A three-legged staked stool on Chairmaking.org bores the front legs at 13 degrees and the rear leg at 22.

The pattern across builds is that back legs lean more than front legs, which is why the tool keeps them separate. In a Northern Woodlands account, chairmaker Dave Sawyer drills his front legs half a degree under the 14 degree design angle. That small change puts inward pressure on the stretchers.

Can I use the chair angle calculator for a three-legged stool?

Yes, with one adjustment. Enter the two front legs as usual, then give the single rear leg rake and zero splay. Its sightline reads 90 degrees from the front baseline, which is the front-to-back centerline that other builders call 0 degrees.

Enter the rear leg with zero spacing between back mortises. The cut list still assumes a pair of back legs and a back stretcher, so build one rear leg and skip that stretcher.

How do I copy the angles from a chair I own?

Photograph the chair square from the side and square from the front. Rake and splay are easy to read off those two views with a protractor, and Lost Art Press sells its Chairpanzee partly for copying angles from photos of existing chairs.

Enter what you measured as floor angles. If the original chair has a tilted seat, measure the tilt too and enter it, so the tool gives you seat-relative bore angles rather than repeating the floor angles.

Is there a printable resultant and sightline chart?

The Resultant and Sightline Chart in the tool covers rake and splay from 4 to 16 degrees in 2 degree steps for a level seat. Each cell shows the resultant, then the sightline, such as 11.2 and 45 at 8 degrees each way.

Print Results opens the chart along with your cut list and all four result cards. That gives you a paper copy to keep at the drill press while you bore.