Single, Wedged, Through Mortice & Tenon in Rebated Material Calculator

Provided

Material: x

Rebate: x

Available chisels or drills:

Rebate snap:

Wedge height:

Shoulder height:

End fraction:

End minimum:

Calculated

The Mortice Width

The mortice width starts out as 1/3 width of the material:

A third of the width:

This may not be an integer so we round up:

A third of the 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 greatly exceed 1/3 of the material

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:

And these are the final horizontal positions of the mortice:

Mortice x1:

Mortice x2:

The Mortice Height

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:

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:

Description

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.