# How to convert knife edge angle "ratios" into degrees?

European-style Japanese knives seem to be described (also here and here, and in my most recent post) in terms of "ratios" that always add up to 100. It's not exactly clear what this means in terms of angles off the center plane of the blade.

It appears that, even on knife forums, there is some confusion as to what these numbers mean. My first thought was that they were actually angles, since a 30 degree angle is common on European knives. Upon reflection, though, that can't be--when you're sharpening a 70/30 knife, dragging across a stone at a 70 degree would be a catastrophe. What, then, is that magic number, and how does it vary in relation to these "ratios"?

• Even worse, a ratio could be implemented purely via bevel depth (giving you an off center edge at equal angles), purely via angles (giving a centered edge with two differently deep bevels), and all combinations thereof. And cutting behaviour will actually be different in each case. Feb 2, 2018 at 10:02

I found this on chefknivestogo and I think it explains it quite well.

RAY <> A "50/50" usually references an edge. So on the cutting edge, it is an even 50/50 "V". It can be 50/50 at 12 degrees or 50/50 @20, but each sides angle is equivocal.

A double bevel is a knife design created by grinding. So from the spine to the cutting edge, there is a blade face that has been ground (most of the time). It can be a flat grind, a convex grind, a hollow grind, and any of these grinds can be symmetric (50/50) or asymmetric. So for instance, my Ginsanko Hiromoto Western Deba has an asymmetrical semi convex grind. It has a flat ground left blade face at around 30% of the total included angle and the right side blade face has a distinctly convex grind that is the other 70% of the total included angle, but the actual cutting edge has an asymmetry, as well. The actual cutting edge does not look like a "V" as it is, in fact, a 60/40 right-handed bias. It's a particularly unique blade, but exemplifies your point, quite well. :mrgreen:

In short, the numbers like 50/50 or 70/30 represent the percentage of the included angle on each side of the blade. So, for a 50/50 knife with an included angle of 50°, it would be ground to a 25° edge angle on each side of the blade. See diagram below: • Thank you! While that at least clears up the ambiguity about the meaning of the ratio, I'm still unsure of how to determine the angle at which I should be holding the knife to the sharpening stone. Jul 2, 2015 at 16:41
• I have searched extensively and can't find the included angle of the particular knife you have. However, I read in several places that Japanese knives often have an included angle of 20° - 30°. With a 30° included angle you would have an edge angle of 21° on one side and 9° on the other. Which side is which depends on if your knife is right or left handed. I think this may put you in the ballpark, but the only way to know for sure would be to find out what the original included angle was, if in fact you want to stay with the original angles. Jul 2, 2015 at 17:13
• Just wanted to note that the example in my other comment would be for a knife with a 70/30 bevel, such as the one you have. Jul 2, 2015 at 18:57

# You can't determine edge angle just from bevel ratio

You need to know what the height and width of the bevel is. Here's a simple diagram that explains why: Clearly, the edge angles for deep bevels are much smaller than the angles for shallow bevels, even at the same bevel ratios.

Once you have the bevel dimensions (w and h in the diagram below), you can calculate the edge angle using simple geometry: • Initially I thought that the formula was wrong because the drawing it is a little bit misleading since the x angle appears floating near the upper left corner of the triangle you had just drawn giving the impression that that is the angle that is intended to be found. Hence making the arctan be h divided by rw. Nov 27, 2018 at 5:54
• However after a closer inspection it looks that what it was intended is the other "portion" of the angle so that x+y makes the whole bottom corner of the triangle. What I would have done supposing that is the desired angle to know would had been using cosines law and the help of a caliper so with the three sides of the triangle you can easily compute the angle. Nov 27, 2018 at 5:54