The geometry of a tanto blade is simpler to describe than the tang, though it has more subtleties and nuances. The three main characteristics I want to focus on are tip shape, spine thickness, and bevel geometry. While kata document the profile of a blade, they leave much to be desired in terms of creating a three-dimensional form.
This discussion will not cover all variations of the tanto, but will provide a general starting point based on the work of a 13th century master. As illustrated in the post on the Aizu Shintogo Kunimitsu Tanto Kata, classical tanto form is informed by both functional requirements and traditional aesthetics. Viewed from the spine, the thickest point of the blade is at the machi (notches) and there is a distal taper towards the tip of the blade and towards the tip of the tang. This provides the highest strength at the most critical juncture of the blade (the stress at the blade-handle junction is also mediated and distributed by the habaki, but that is more physics for another post). The hirazukuri (one piece) bevels are mainly flat from the mune to the ha, but should have some degree of convex or haniku (“meat” behind the edge), to provide strength for the task.
While not an entirely rigid rule of thumb, my research indicates that the majority of tanto nagasa (blade length) will range between 20cm-30cm, kasane (thickness at the munemachi) will be 6mm-7mm, and motohaba (width at the machi) will be about 1/9 or 1/10 of the nagasa.
Very rarely is the motohaba to nagasa ratio of 1:10 exceeded, and then usually in an older piece that has been polished many times and worn down, in the slender form of yoroidoshi, or in the longer blade of sunnobi tanto. Shorter blades with nagasa closer to 20cm are often found approaching a 1:8 ratio.
Tanto Tip & Blade Form
Contrary to popular perception and terminology in the west, a classical tanto tip does not abruptly change angle in relation to the rest of the edge but simply flows seamlessly from it. The other misconception is that the angle where the tip meets the spine is not snub-nosed at all but is far more acute than most renditions that are placed in the modern tanto genre. The closest example of the abrupt chisel point blade in Japan is the continental pre-nihonto form known as chokuto, which were made in the 6th-8th century. Even the curved but slightly interrupted angle found on tachi and katana kissaki is only found on tanto when they have been made from the forward portion of a broken longsword. Studying examples from masters of the tanto, like Shintogo Kunimitsu, we see that the tanto has always had a very graceful and linear form, transitioning elegantly from edge to tip, and terminating in an elongated but strong point.
Similar to the interconnectedness of the edge and bevels of the tang with the width and height of the tang and the angle of the blade bevels, there is a strong connection between the distal taper and the width of the blade as it approaches the tip. Because the edge must terminate at a constant width of zero, in order to preserve a relatively consistent blade bevel angle as the distal taper narrows, the blade width must lessen proportionally. All of these nuances should be considered as the blade is designed and shaped. This connection between distal taper (kasane) and width (haba) is the reason that all classical tanto forms should taper at least slightly towards the tip along both axis.
When studying kata or oshigata, it is very useful to have a measurement for the thickness of the spine (motokasane or kasane). Historical examples range from between 3mm and 4mm for very “tired” blades that have been sharpened for centuries to slightly over 10mm for the burliest yoroi-doshi. The vast majority seem to fall in the 6mm-7mm range. The Aizu Shintogo is considered to be fairly worn but still checks in at a hefty 7.3mm.
Both the distal taper of the spine and the profile of the blade happen at approximately a 7:10 ratio, the saki kasane is approximately 70% of the moto kasane and the saki haba is about 70% of the moto haba. For example, the Aizu Shintogo is currently 7.3mm thick and 23.6mm wide at the machi and should, therefore be approximately 5.1mm thick and 16.52mm wide near where the tip begins to narrow. Though the location of the tip measurements (saki-) is more difficult to pinpoint on a tanto, they should be taken at the place where the edge clearly begins to narrow into the tip, around 3-5cm back from the tip. Often this is easier to locate by looking down on the spine rather than at the profile.
Fumbari & Ubuha
Though they are much more subtle for tanto as opposed to a larger blade like tachi, two more items of mention that are part of the classical style are fumbari and ubuha. Fumbari is the slight widening of the blade as it approaches the machi. Similar to a wide stance, this gives the blade a much more powerful and balanced look and is an important nuance. For most tanto, fumbari is almost immeasurable (though the reverse is absolutely to be avoided) and should be continued by the lines of the habaki. Ubuha (unaltered edge) is the remaining 3-5cm section of the original unsharpened edge next to the hamachi. This traditional practice provides extra strength as well as an indication of how many times a blade has been sharpened and polished. On well worn blades the ubuha will be completely gone and the edge sharpened right to the hamachi.
The example below was forged from shear steel and is at the coarsest stone of the kaji-togi stage, (rough polish) following yaki-ire (hardening). The edge was thicker at the time of yaki-ire to prevent warping and decarburization of the edge steel. At this stage the geometry is fairly close to its final form but there is still plenty of refining needed. Waterstones will be used to adjust and true all of the lines and surfaces as polishing progresses.
Read about the nakago (tang) and machi here: Classical Tanto Geometry: Nakago & Machi