The mortise and tenon is the backbone of furniture and timber-frame joinery because it combines a large long-grain glue surface with a mechanical interlock. Sizing it well is mostly about one ratio and a couple of length rules, which this calculator applies to your actual stock dimensions.
How it works
The dominant rule is the rule of thirds: make the tenon roughly a third of the rail thickness so that the tenon and the two mortise walls share the load evenly.
tenon_thickness = rail_thickness / 3
mortise_wall = (rail_thickness - tenon_thickness) / 2 (each side)
tenon_length = 2.5 to 3 x tenon_thickness
glue_area = 2 x tenon_width x tenon_length (both cheeks)
shear_capacity = glue_area x allowable_shear(species)
The bonded width is the tenon width minus a small shoulder on each edge. Because the cheeks are long-grain to long-grain, they carry the glue strength, so the capacity estimate multiplies that cheek area by a conservative allowable shear stress for the chosen species group.
Tips, example, and notes
For a 20 mm thick, 60 mm wide oak rail, the tool suggests a tenon close to 6.7 mm thick with mortise walls about 6.7 mm each, a length around 17 to 20 mm, and a generous cheek glue area that yields a healthy shear estimate for dense hardwood.
Keep the fit snug but not forced; a tenon that needs hammering squeezes glue out of the joint and can split the mortise. Cut the mortise first and pare the tenon to it. The shear figure assumes a clean, fully clamped glue-up, so for chairs and other high-stress pieces consider adding a draw-bored peg or a haunch rather than relying on glue area alone.