Single, Wedged, Through Mortice & Tenon in Rebated Material Calculator
Material: x
Rebate: x
Round to:
Chisels:
Use chisels:
Straight fraction:
Rebate snap:
Wedge height:
Shoulder height:
End fraction:
End minimum:
Stile length:
Rail length:
Rebate x:
Rebate y:
The mortice width starts out as a fraction of the material width (typically 1/3):
Suggested width:
Round to the specified unit (Round to: ):
Rounded width:
We're going to create the mortice with a chisel or drill, so we'll adjust the width of the mortice to match the tool we use to create it.
First, we exclude any tools that would create a mortice that is too small or too large (less than 1/4 or greater than 1/2 of the material width):
Applicable chisels or drills:
Then we pick the best tool from the applicable tools:
Tool that best matches mm mortice:
Specifically, we use the largest chisel or drill that doesn't exceed the rounded width
With this information, the mortice width is defined:
Mortice width:
The mortice will be normally be centred horizontally so the position naturally follows from the mortice width and material width:
Mortice x1 centered:
Mortice x2 centered:
But if the edges of the mortice are within mm of the edge of the rebate (), we move the mortice to align the edge with the rebate without changing its width:
Mortice x1 snapped:
Mortice x2 snapped:
The advantage of snapping the mortice position based on the rebate is that the mortice will then either be wholly within the rebate (which reduces the amount of material to be removed, making hand tool construction easier) or wholly outside the rebate (making it possible to increase the mortice & tenon height, increasing the strength of the tenon). In both cases, it also reduces the number of layout lines.
And these are the final horizontal positions of the mortice:
Mortice x1:
Mortice x2:
The neck of the mortice (the point at which it transitions from flared to straight) is determined as a small fraction () of the overall width from the inner edge. But if the mortice overlaps the rebate, we make sure that the mortice doesn't start flaring within the rebate. These calculations give us this distance from the outer edge:
Neck x:
And now we know the final dimensions of our wedges:
x x
It's OK for the mortice to overlap its own rebate in the receiving piece, but it does affect the height of the mortice
Mortice overlaps rebate:
If the mortice doesn't overlap the rebate, the mortice can extend to the bottom of the available area.
If the mortice does overlap the rebate, the mortice cannot extend to the bottom of the available area, we must exclude the rebate height. If we were to allow the mortice to extend to the bottom, the tenon would not be able to fill it completely because of the rebate in the tenon piece.
Tenon bottom maximum:
With a shoulder defined on the tenon, the position of the mortice can't extend quite as far. The shoulder is mm:
Tenon bottom maximum:
If the tenon bottom is close to the rebate, we snap it to the rebate position:
Tenon bottom snapped:
The outer mortice needs space for the wedge so its bottom can be lower by the wedge height ( mm):
Mortice y2:
The position of the top of the outer mortice is determined as a small fraction of the material height (End fraction = ) but importantly limited by the need to preserve enough material strength at the top of the mortice so it cannot be less than the minimum (End minimum = mm) nor can it produce an inner mortice with less than the defined shoulder height ( mm)
Mortice y1:
The height of the outer mortice is determined by the positions of its top and bottom:
Mortice height:
The inner mortice can be calculated from the outer mortice by insetting by the wedge height at top and bottom
Inner Mortice y1:
Inner Mortice y2:
Inner Mortice height:
And gathering the outer mortice in one place:
Outer Mortice y1:
Outer Mortice y2:
Outer Mortice height:
On a stile that is mm, the inner mortice distance is:
Stile inner mortice distance:
On a rail that is mm, the outer shoulder distance is:
Rail outer shoulder distance:
This page describes the design criteria and calculations for deciding on the layout of a mortice and tenon joint when used to join the corners of frames where the material has rebates and a single, wedged, through tenon will be used.
Imagine looking at the side of the top-left corner of a window frame: the rebates meet in the bottom right corner of the rectangle where the stile and rail overlap. This view defines the meanings of x, y, width, height.
This calculator uses "smart rounding": if the granularity is 3 mm or less, it always rounds up; if it's more than 3 mm, it will round up or down to the closest value. You can round to non-integers like 0.5 if you want.
Weirdly, this calculator currently requires rails and stiles to be same width.