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Cabinets & furniture · Chair Leg Angle Calculator

Sightline and resultant for 12° rake and 14° splay

This is the worked example in The Black Dog's Woodshop derivation, which does not say which leg it is. Draw the sightline 40.4° from the baseline and set the bevel gauge 18.1° off square, so that its blade stands 18.1° from upright. The drawing opens on a front leg; change the numbers below for your own.

Short answer
Sightline, from the baseline
40.4°
Resultant, bevel gauge off square
18.1°

The sightline is measured at the mortise from the baseline through the left and right leg of the pair, parallel to the front of the seat, opening toward the middle of the seat. The resultant is measured off square: a bevel gauge set to it has its blade that far from upright. Drawn as a front leg; the two figures are the same for a front or a back leg. Assumes a flat, level seat. A plan that measures from the centreline shows 90° minus this sightline.

Your leg
Which pair of angles do you have?
Which leg is it?

A front leg rakes toward the front of the seat and a back leg toward the back. The two numbers are the same either way; the drawing flips to match your leg.

°
Lean off plumb, looking from the side. 0 to 60°, decimals allowed.
°
Lean off plumb, looking from the front. 0 to 60°, decimals allowed.

Convention used here: the seat is flat and level, and every lean is measured off plumb. The baseline is the line through the left and right leg of a pair, parallel to the front of the seat. The sightline angle is measured from that baseline, opening toward the middle of the seat, and the foot kicks the opposite way: out to the side by the splay, and toward the front or the back by the rake. The resultant is measured off square, so a bevel gauge set to it has its blade that far from upright. A plan that measures its sightline from the centreline instead will print 90° minus the figure shown here.

Result
Only the view that is the same for both legs is drawn. Pick front or back leg above to see the plan and the side view.

Based on: The Black Dog's Woodshop · Tested against 18 worked examples, 9 printed in a published source · How this is worked out →

Questions people ask

How do I convert rake and splay to a sightline and resultant angle?
Take the tangent of each angle. The sightline is the arctangent of tan(rake) divided by tan(splay), measured from the line joining the left and right leg of a pair. The resultant is the arctangent of the square root of tan²(rake) plus tan²(splay), measured off plumb. For 12° rake and 14° splay that gives a sightline of 40.4° and a resultant of 18.1°.
What are rake, splay, sightline and resultant?
Rake is how far a leg leans when you look at the chair from the side, and splay is how far it leans when you look from the front. Front legs rake forward and back legs rake back. The sightline is the line on the seat along which the leg appears to stand straight up. The resultant is the single angle the leg leans off plumb when you look square to that line. You set a bevel gauge to it off square, so that the blade stands that far from upright.
Which line is the sightline angle measured from?
On this page it is measured at the mortise from the baseline through the left and right leg of a pair, which runs parallel to the front of the seat. Zero means the sightline lies on that baseline and 90° means it runs front to back. A plan that measures from the centreline instead will show 90° minus this figure: Christopher Schwarz’s sawbench layout marks the same line as 64° from the line across the end of the bench and 26° from the line along it, where this calculator gives 63.8° and 26.2°.
What is the sightline when rake and splay are equal?
It is 45.0°, whatever the angle. The resultant is larger than either: 10° of rake with 10° of splay gives a resultant of 14.0°.
Is the resultant angle just rake plus splay?
No. 12° of rake and 14° of splay give a resultant of 18.1°, not 26°. The resultant is never smaller than the larger of the two angles, and it equals that angle only when the other one is zero.